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data2<-read.csv("/Users/munira/Desktop/Education/Masters/Illinois Institute of Technology/Coursework/545-Stats/Completed/Lab Projects/Project2Data.csv", header=TRUE)

library(psych)

numvar<-data2[,sapply(data2,is.numeric)]

describe(numvar)
summary(numvar)
##      UNITID            CONTROL         ADM_RATE        SAT_AVG    
##  Min.   :  100654   Min.   :1.000   Min.   :0.000   Min.   : 720  
##  1st Qu.:  174242   1st Qu.:1.000   1st Qu.:0.563   1st Qu.: 973  
##  Median :  230472   Median :2.000   Median :0.713   Median :1040  
##  Mean   : 1663052   Mean   :2.215   Mean   :0.691   Mean   :1059  
##  3rd Qu.:  447652   3rd Qu.:3.000   3rd Qu.:0.845   3rd Qu.:1120  
##  Max.   :48414501   Max.   :3.000   Max.   :1.000   Max.   :1545  
##                                     NA's   :5505    NA's   :6399  
##       UGDS          UGDS_WHITE       UGDS_BLACK       UGDS_HISP     
##  Min.   :     0   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:   116   1st Qu.:0.2667   1st Qu.:0.0359   1st Qu.:0.0276  
##  Median :   406   Median :0.5560   Median :0.1000   Median :0.0717  
##  Mean   :  2332   Mean   :0.5099   Mean   :0.1899   Mean   :0.1621  
##  3rd Qu.:  1890   3rd Qu.:0.7474   3rd Qu.:0.2568   3rd Qu.:0.2000  
##  Max.   :151558   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##  NA's   :713      NA's   :713      NA's   :713      NA's   :713     
##    UGDS_ASIAN       UGDS_AIAN        UGDS_NHPI        UGDS_2MOR     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0024   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0127   Median :0.0026   Median :0.0000   Median :0.0175  
##  Mean   :0.0338   Mean   :0.0137   Mean   :0.0045   Mean   :0.0239  
##  3rd Qu.:0.0326   3rd Qu.:0.0074   3rd Qu.:0.0025   3rd Qu.:0.0338  
##  Max.   :0.9727   Max.   :1.0000   Max.   :0.9983   Max.   :0.5333  
##  NA's   :713      NA's   :713      NA's   :713      NA's   :713     
##     UGDS_NRA        UGDS_UNKN         PPTUG_EF         NPT4_PUB    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :-2434  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.: 6297  
##  Median :0.0000   Median :0.0142   Median :0.1489   Median : 8751  
##  Mean   :0.0160   Mean   :0.0451   Mean   :0.2259   Mean   : 9625  
##  3rd Qu.:0.0116   3rd Qu.:0.0455   3rd Qu.:0.3766   3rd Qu.:12704  
##  Max.   :0.9286   Max.   :0.9027   Max.   :1.0000   Max.   :28201  
##  NA's   :713      NA's   :713      NA's   :734      NA's   :5792   
##    NPT4_PRIV        COSTT4_A        TUITFTE           INEXPFTE     
##  Min.   : -581   Min.   : 4610   Min.   :      0   Min.   :     0  
##  1st Qu.:13314   1st Qu.:14188   1st Qu.:   4643   1st Qu.:  3443  
##  Median :18254   Median :22882   Median :   9015   Median :  5490  
##  Mean   :18230   Mean   :24853   Mean   :  10401   Mean   :  7360  
##  3rd Qu.:22720   3rd Qu.:31275   3rd Qu.:  13690   3rd Qu.:  8283  
##  Max.   :89406   Max.   :79212   Max.   :1292154   Max.   :735077  
##  NA's   :3015    NA's   :3673    NA's   :433       NA's   :433     
##      PFTFAC         PCTPELL           C150_4       PFTFTUG1_EF   
##  Min.   :0.000   Min.   :0.0000   Min.   :0.000   Min.   :0.001  
##  1st Qu.:0.296   1st Qu.:0.3588   1st Qu.:0.328   1st Qu.:0.321  
##  Median :0.540   Median :0.5233   Median :0.467   Median :0.530  
##  Mean   :0.567   Mean   :0.5321   Mean   :0.478   Mean   :0.528  
##  3rd Qu.:0.864   3rd Qu.:0.7143   3rd Qu.:0.625   3rd Qu.:0.739  
##  Max.   :1.000   Max.   :1.0000   Max.   :1.000   Max.   :1.000  
##  NA's   :3658    NA's   :737      NA's   :5222    NA's   :4039   
##     RET_FT4         PCTFLOAN     
##  Min.   :0.000   Min.   :0.0000  
##  1st Qu.:0.618   1st Qu.:0.3333  
##  Median :0.741   Median :0.5849  
##  Mean   :0.707   Mean   :0.5231  
##  3rd Qu.:0.833   3rd Qu.:0.7473  
##  Max.   :1.000   Max.   :1.0000  
##  NA's   :5410    NA's   :737
names(which(max(table(data2$ADM_RATE))==table(data2$ADM_RATE)))
## [1] "1"
names(which(max(table(data2$SAT_AVG))==table(data2$SAT_AVG)))
## [1] "1010" "1050"
names(which(max(table(data2$UGDS))==table(data2$UGDS)))
## [1] "39"
names(which(max(table(data2$UGDS_WHITE))==table(data2$UGDS_WHITE)))
## [1] "0"
names(which(max(table(data2$UGDS_BLACK))==table(data2$UGDS_BLACK)))
## [1] "0"
names(which(max(table(data2$UGDS_HISP))==table(data2$UGDS_HISP)))
## [1] "0"
names(which(max(table(data2$UGDS_ASIAN))==table(data2$UGDS_ASIAN)))
## [1] "0"
names(which(max(table(data2$UGDS_AIAN))==table(data2$UGDS_AIAN)))
## [1] "0"
names(which(max(table(data2$UGDS_NHPI))==table(data2$UGDS_NHPI)))
## [1] "0"
names(which(max(table(data2$UGDS_2MOR))==table(data2$UGDS_2MOR)))
## [1] "0"
names(which(max(table(data2$UGDS_NRA))==table(data2$UGDS_NRA)))
## [1] "0"
names(which(max(table(data2$UGDS_UNKN))==table(data2$UGDS_UNKN)))
## [1] "0"
names(which(max(table(data2$PPTUG_EF))==table(data2$PPTUG_EF)))
## [1] "0"
names(which(max(table(data2$NPT4_PUB))==table(data2$NPT4_PUB)))
## [1] "5686"  "6371"  "7240"  "7534"  "11603" "12106"
names(which(max(table(data2$NPT4_PRIV))==table(data2$NPT4_PRIV)))
## [1] "22150"
names(which(max(table(data2$COSTT4_A))==table(data2$COSTT4_A)))
## [1] "32064"
names(which(max(table(data2$TUITFTE))==table(data2$TUITFTE)))
## [1] "0"
names(which(max(table(data2$INEXPFTE))==table(data2$INEXPFTE)))
## [1] "4273"
names(which(max(table(data2$PFTFAC))==table(data2$PFTFAC)))
## [1] "1"
names(which(max(table(data2$PCTPELL))==table(data2$PCTPELL)))
## [1] "1"
names(which(max(table(data2$C150_4))==table(data2$C150_4)))
## [1] "0"
names(which(max(table(data2$PFTFTUG1_EF))==table(data2$PFTFTUG1_EF)))
## [1] "1"
names(which(max(table(data2$RET_FT4))==table(data2$RET_FT4)))
## [1] "1"
names(which(max(table(data2$PCTFLOAN))==table(data2$PCTFLOAN)))
## [1] "0"
cormatrix<-cor(numvar, use = "p")
## Warning in cor(numvar, use = "p"): the standard deviation is zero
round(cormatrix,2)
##             UNITID CONTROL ADM_RATE SAT_AVG  UGDS UGDS_WHITE UGDS_BLACK
## UNITID        1.00    0.12     0.20   -0.02 -0.27      -0.20       0.16
## CONTROL       0.12    1.00     0.18    0.12 -0.42      -0.24       0.20
## ADM_RATE      0.20    0.18     1.00   -0.35 -0.13       0.11      -0.03
## SAT_AVG      -0.02    0.12    -0.35    1.00  0.25       0.22      -0.47
## UGDS         -0.27   -0.42    -0.13    0.25  1.00       0.00      -0.10
## UGDS_WHITE   -0.20   -0.24     0.11    0.22  0.00       1.00      -0.51
## UGDS_BLACK    0.16    0.20    -0.03   -0.47 -0.10      -0.51       1.00
## UGDS_HISP     0.10    0.13     0.02   -0.02  0.03      -0.55      -0.21
## UGDS_ASIAN   -0.02   -0.02    -0.22    0.47  0.13      -0.21      -0.13
## UGDS_AIAN    -0.01   -0.10     0.05   -0.08 -0.04      -0.09      -0.09
## UGDS_NHPI     0.01   -0.01     0.03   -0.07 -0.01      -0.09      -0.05
## UGDS_2MOR    -0.03   -0.05    -0.07    0.24  0.10      -0.02      -0.10
## UGDS_NRA     -0.13   -0.11    -0.23    0.36  0.11      -0.07      -0.12
## UGDS_UNKN     0.07    0.13    -0.02   -0.10 -0.01      -0.20      -0.06
## PPTUG_EF     -0.07   -0.26     0.08   -0.35  0.16      -0.03       0.03
## NPT4_PUB      0.02      NA     0.03    0.34  0.15       0.22      -0.03
## NPT4_PRIV    -0.11   -0.19    -0.11    0.36  0.13       0.04      -0.03
## COSTT4_A     -0.04    0.42    -0.28    0.52 -0.16       0.09      -0.07
## TUITFTE       0.04    0.14    -0.14    0.53 -0.05      -0.01       0.01
## INEXPFTE     -0.10   -0.15    -0.41    0.64  0.04       0.07      -0.07
## PFTFAC       -0.25   -0.26    -0.17    0.17  0.05       0.18      -0.15
## PCTPELL       0.30    0.46     0.24   -0.71 -0.26      -0.35       0.35
## C150_4       -0.22   -0.12    -0.32    0.80  0.14       0.24      -0.32
## PFTFTUG1_EF  -0.02    0.17    -0.06    0.40 -0.07       0.08      -0.06
## RET_FT4      -0.27   -0.29    -0.21    0.74  0.17       0.22      -0.31
## PCTFLOAN      0.15    0.43     0.11   -0.51 -0.18       0.01       0.21
##             UGDS_HISP UGDS_ASIAN UGDS_AIAN UGDS_NHPI UGDS_2MOR UGDS_NRA
## UNITID           0.10      -0.02     -0.01      0.01     -0.03    -0.13
## CONTROL          0.13      -0.02     -0.10     -0.01     -0.05    -0.11
## ADM_RATE         0.02      -0.22      0.05      0.03     -0.07    -0.23
## SAT_AVG         -0.02       0.47     -0.08     -0.07      0.24     0.36
## UGDS             0.03       0.13     -0.04     -0.01      0.10     0.11
## UGDS_WHITE      -0.55      -0.21     -0.09     -0.09     -0.02    -0.07
## UGDS_BLACK      -0.21      -0.13     -0.09     -0.05     -0.10    -0.12
## UGDS_HISP        1.00       0.03     -0.06     -0.02     -0.09    -0.06
## UGDS_ASIAN       0.03       1.00     -0.05      0.10      0.11     0.16
## UGDS_AIAN       -0.06      -0.05      1.00     -0.01     -0.02    -0.03
## UGDS_NHPI       -0.02       0.10     -0.01      1.00      0.07    -0.01
## UGDS_2MOR       -0.09       0.11     -0.02      0.07      1.00     0.03
## UGDS_NRA        -0.06       0.16     -0.03     -0.01      0.03     1.00
## UGDS_UNKN       -0.09      -0.03     -0.03      0.00      0.08    -0.01
## PPTUG_EF        -0.01       0.04      0.04      0.01      0.03    -0.08
## NPT4_PUB        -0.24       0.03     -0.10     -0.08      0.04     0.19
## NPT4_PRIV       -0.18       0.08     -0.06      0.00      0.20     0.25
## COSTT4_A        -0.18       0.16     -0.11     -0.05      0.11     0.32
## TUITFTE         -0.05       0.03     -0.04      0.00      0.04     0.09
## INEXPFTE        -0.08       0.07      0.01      0.00      0.05     0.12
## PFTFAC          -0.10      -0.02      0.04      0.00      0.02     0.11
## PCTPELL          0.21      -0.15      0.01      0.04     -0.11    -0.29
## C150_4          -0.06       0.29     -0.11     -0.01      0.12     0.23
## PFTFTUG1_EF     -0.04      -0.02     -0.02      0.00     -0.01     0.16
## RET_FT4         -0.02       0.25     -0.06     -0.02      0.10     0.22
## PCTFLOAN        -0.18      -0.16     -0.14     -0.05      0.05    -0.10
##             UGDS_UNKN PPTUG_EF NPT4_PUB NPT4_PRIV COSTT4_A TUITFTE
## UNITID           0.07    -0.07     0.02     -0.11    -0.04    0.04
## CONTROL          0.13    -0.26       NA     -0.19     0.42    0.14
## ADM_RATE        -0.02     0.08     0.03     -0.11    -0.28   -0.14
## SAT_AVG         -0.10    -0.35     0.34      0.36     0.52    0.53
## UGDS            -0.01     0.16     0.15      0.13    -0.16   -0.05
## UGDS_WHITE      -0.20    -0.03     0.22      0.04     0.09   -0.01
## UGDS_BLACK      -0.06     0.03    -0.03     -0.03    -0.07    0.01
## UGDS_HISP       -0.09    -0.01    -0.24     -0.18    -0.18   -0.05
## UGDS_ASIAN      -0.03     0.04     0.03      0.08     0.16    0.03
## UGDS_AIAN       -0.03     0.04    -0.10     -0.06    -0.11   -0.04
## UGDS_NHPI        0.00     0.01    -0.08      0.00    -0.05    0.00
## UGDS_2MOR        0.08     0.03     0.04      0.20     0.11    0.04
## UGDS_NRA        -0.01    -0.08     0.19      0.25     0.32    0.09
## UGDS_UNKN        1.00     0.00     0.01      0.17     0.12    0.06
## PPTUG_EF         0.00     1.00    -0.46     -0.02    -0.49   -0.05
## NPT4_PUB         0.01    -0.46     1.00        NA     0.92    0.58
## NPT4_PRIV        0.17    -0.02       NA      1.00     0.71    0.55
## COSTT4_A         0.12    -0.49     0.92      0.71     1.00    0.76
## TUITFTE          0.06    -0.05     0.58      0.55     0.76    1.00
## INEXPFTE         0.00    -0.03     0.30      0.27     0.46    0.73
## PFTFAC          -0.08    -0.24     0.23     -0.03     0.12    0.03
## PCTPELL          0.02    -0.13    -0.11     -0.31    -0.25   -0.05
## C150_4          -0.14    -0.40     0.57      0.34     0.55    0.38
## PFTFTUG1_EF     -0.06    -0.72     0.40      0.12     0.45    0.36
## RET_FT4         -0.19    -0.36     0.32      0.19     0.32    0.20
## PCTFLOAN         0.16    -0.23     0.61      0.29     0.43    0.13
##             INEXPFTE PFTFAC PCTPELL C150_4 PFTFTUG1_EF RET_FT4 PCTFLOAN
## UNITID         -0.10  -0.25    0.30  -0.22       -0.02   -0.27     0.15
## CONTROL        -0.15  -0.26    0.46  -0.12        0.17   -0.29     0.43
## ADM_RATE       -0.41  -0.17    0.24  -0.32       -0.06   -0.21     0.11
## SAT_AVG         0.64   0.17   -0.71   0.80        0.40    0.74    -0.51
## UGDS            0.04   0.05   -0.26   0.14       -0.07    0.17    -0.18
## UGDS_WHITE      0.07   0.18   -0.35   0.24        0.08    0.22     0.01
## UGDS_BLACK     -0.07  -0.15    0.35  -0.32       -0.06   -0.31     0.21
## UGDS_HISP      -0.08  -0.10    0.21  -0.06       -0.04   -0.02    -0.18
## UGDS_ASIAN      0.07  -0.02   -0.15   0.29       -0.02    0.25    -0.16
## UGDS_AIAN       0.01   0.04    0.01  -0.11       -0.02   -0.06    -0.14
## UGDS_NHPI       0.00   0.00    0.04  -0.01        0.00   -0.02    -0.05
## UGDS_2MOR       0.05   0.02   -0.11   0.12       -0.01    0.10     0.05
## UGDS_NRA        0.12   0.11   -0.29   0.23        0.16    0.22    -0.10
## UGDS_UNKN       0.00  -0.08    0.02  -0.14       -0.06   -0.19     0.16
## PPTUG_EF       -0.03  -0.24   -0.13  -0.40       -0.72   -0.36    -0.23
## NPT4_PUB        0.30   0.23   -0.11   0.57        0.40    0.32     0.61
## NPT4_PRIV       0.27  -0.03   -0.31   0.34        0.12    0.19     0.29
## COSTT4_A        0.46   0.12   -0.25   0.55        0.45    0.32     0.43
## TUITFTE         0.73   0.03   -0.05   0.38        0.36    0.20     0.13
## INEXPFTE        1.00   0.15   -0.21   0.47        0.27    0.35    -0.05
## PFTFAC          0.15   1.00   -0.28   0.30        0.22    0.30    -0.04
## PCTPELL        -0.21  -0.28    1.00  -0.52       -0.03   -0.47     0.42
## C150_4          0.47   0.30   -0.52   1.00        0.43    0.58    -0.09
## PFTFTUG1_EF     0.27   0.22   -0.03   0.43        1.00    0.41     0.22
## RET_FT4         0.35   0.30   -0.47   0.58        0.41    1.00    -0.25
## PCTFLOAN       -0.05  -0.04    0.42  -0.09        0.22   -0.25     1.00
covmatrix<-cov(numvar, use = "p")
round(covmatrix,2)
##                    UNITID   CONTROL ADM_RATE    SAT_AVG          UGDS
## UNITID       4.312430e+13 672906.55  4534.40 -128150.47 -196709359.44
## CONTROL      6.729066e+05      0.70     0.03       7.83      -1936.43
## ADM_RATE     4.534400e+03      0.03     0.04      -9.15       -168.15
## SAT_AVG     -1.281505e+05      7.83    -9.15   17784.08     243791.76
## UGDS        -1.967094e+08  -1936.43  -168.15  243791.76   29581070.84
## UGDS_WHITE  -7.512580e+03     -0.06     0.01       6.37          6.76
## UGDS_BLACK   4.908170e+03      0.04     0.00     -11.63       -119.05
## UGDS_HISP    3.069760e+03      0.02     0.00      -0.31         36.36
## UGDS_ASIAN  -1.954100e+02      0.00     0.00       3.71         52.38
## UGDS_AIAN   -1.050000e+02     -0.01     0.00      -0.36        -14.31
## UGDS_NHPI    3.919000e+01      0.00     0.00      -0.07         -2.66
## UGDS_2MOR   -1.349000e+02      0.00     0.00       0.73         17.13
## UGDS_NRA    -8.503000e+02      0.00     0.00       2.26         30.74
## UGDS_UNKN    8.278300e+02      0.01     0.00      -0.70         -5.02
## PPTUG_EF    -2.356010e+03     -0.05     0.00      -5.87        217.06
## NPT4_PUB     8.555903e+06      0.00    22.29  154640.13    5346029.39
## NPT4_PRIV   -1.075273e+08   -641.66  -162.64  314374.72    3119630.40
## COSTT4_A    -5.270038e+07   4254.85  -746.51  925104.22  -13647207.02
## TUITFTE      1.028087e+08   1988.25  -215.48  467680.96   -4938152.92
## INEXPFTE    -1.691623e+08  -1558.02  -669.26  735007.62    2801231.37
## PFTFAC      -8.568160e+03     -0.06    -0.01       5.29         94.63
## PCTPELL      9.068690e+03      0.09     0.01     -13.75       -319.31
## C150_4      -5.018360e+03     -0.02    -0.01      18.62        212.98
## PFTFTUG1_EF -6.842000e+02      0.03     0.00      10.49       -113.24
## RET_FT4     -5.604270e+03     -0.04    -0.01      11.16        236.65
## PCTFLOAN     5.769150e+03      0.10     0.00     -11.55       -281.31
##             UGDS_WHITE UGDS_BLACK UGDS_HISP UGDS_ASIAN UGDS_AIAN UGDS_NHPI
## UNITID        -7512.58    4908.17   3069.76    -195.41   -105.00     39.19
## CONTROL          -0.06       0.04      0.02       0.00     -0.01      0.00
## ADM_RATE          0.01       0.00      0.00       0.00      0.00      0.00
## SAT_AVG           6.37     -11.63     -0.31       3.71     -0.36     -0.07
## UGDS              6.76    -119.05     36.36      52.38    -14.31     -2.66
## UGDS_WHITE        0.08      -0.03     -0.04       0.00      0.00      0.00
## UGDS_BLACK       -0.03       0.05     -0.01       0.00      0.00      0.00
## UGDS_HISP        -0.04      -0.01      0.05       0.00      0.00      0.00
## UGDS_ASIAN        0.00       0.00      0.00       0.01      0.00      0.00
## UGDS_AIAN         0.00       0.00      0.00       0.00      0.00      0.00
## UGDS_NHPI         0.00       0.00      0.00       0.00      0.00      0.00
## UGDS_2MOR         0.00       0.00      0.00       0.00      0.00      0.00
## UGDS_NRA          0.00       0.00      0.00       0.00      0.00      0.00
## UGDS_UNKN        -0.01       0.00      0.00       0.00      0.00      0.00
## PPTUG_EF          0.00       0.00      0.00       0.00      0.00      0.00
## NPT4_PUB        260.16     -24.66   -204.33       7.96    -50.33    -17.92
## NPT4_PRIV        81.21     -48.45   -322.35      44.37    -19.54     -0.09
## COSTT4_A        295.15    -189.04   -465.88     116.11   -120.30    -25.90
## TUITFTE         -53.86      55.26   -178.24      33.40    -53.98     -2.35
## INEXPFTE        228.72    -177.90   -210.80      59.56      8.01     -0.58
## PFTFAC            0.01      -0.01     -0.01       0.00      0.00      0.00
## PCTPELL          -0.02       0.02      0.01       0.00      0.00      0.00
## C150_4            0.01      -0.01      0.00       0.00      0.00      0.00
## PFTFTUG1_EF       0.01       0.00      0.00       0.00      0.00      0.00
## RET_FT4           0.01      -0.01      0.00       0.00      0.00      0.00
## PCTFLOAN          0.00       0.01     -0.01       0.00      0.00      0.00
##             UGDS_2MOR UGDS_NRA UGDS_UNKN PPTUG_EF    NPT4_PUB
## UNITID        -134.90  -850.30    827.83 -2356.01  8555903.25
## CONTROL          0.00     0.00      0.01    -0.05        0.00
## ADM_RATE         0.00     0.00      0.00     0.00       22.29
## SAT_AVG          0.73     2.26     -0.70    -5.87   154640.13
## UGDS            17.13    30.74     -5.02   217.06  5346029.39
## UGDS_WHITE       0.00     0.00     -0.01     0.00      260.16
## UGDS_BLACK       0.00     0.00      0.00     0.00      -24.66
## UGDS_HISP        0.00     0.00      0.00     0.00     -204.33
## UGDS_ASIAN       0.00     0.00      0.00     0.00        7.96
## UGDS_AIAN        0.00     0.00      0.00     0.00      -50.33
## UGDS_NHPI        0.00     0.00      0.00     0.00      -17.92
## UGDS_2MOR        0.00     0.00      0.00     0.00        5.16
## UGDS_NRA         0.00     0.00      0.00     0.00       21.82
## UGDS_UNKN        0.00     0.00      0.01     0.00        2.14
## PPTUG_EF         0.00     0.00      0.00     0.06     -494.75
## NPT4_PUB         5.16    21.82      2.14  -494.75 21805832.12
## NPT4_PRIV       43.83    92.25    127.96   -33.15          NA
## COSTT4_A        38.59   213.37    133.50 -1464.04 20420278.27
## TUITFTE         24.17    74.09     97.82  -214.98 11215184.61
## INEXPFTE        19.21    73.98     -0.92   -79.92  6239926.77
## PFTFAC           0.00     0.00      0.00    -0.02      292.43
## PCTPELL          0.00     0.00      0.00    -0.01      -82.79
## C150_4           0.00     0.00      0.00    -0.02      450.90
## PFTFTUG1_EF      0.00     0.00      0.00    -0.04      359.35
## RET_FT4          0.00     0.00      0.00    -0.01      161.13
## PCTFLOAN         0.00     0.00      0.00    -0.02      729.64
##                 NPT4_PRIV     COSTT4_A      TUITFTE      INEXPFTE   PFTFAC
## UNITID      -107527276.60 -52700381.15 102808725.53 -169162321.16 -8568.16
## CONTROL           -641.66      4254.85      1988.25      -1558.02    -0.06
## ADM_RATE          -162.64      -746.51      -215.48       -669.26    -0.01
## SAT_AVG         314374.72    925104.22    467680.96     735007.62     5.29
## UGDS           3119630.40 -13647207.02  -4938152.92    2801231.37    94.63
## UGDS_WHITE          81.21       295.15       -53.86        228.72     0.01
## UGDS_BLACK         -48.45      -189.04        55.26       -177.90    -0.01
## UGDS_HISP         -322.35      -465.88      -178.24       -210.80    -0.01
## UGDS_ASIAN          44.37       116.11        33.40         59.56     0.00
## UGDS_AIAN          -19.54      -120.30       -53.98          8.01     0.00
## UGDS_NHPI           -0.09       -25.90        -2.35         -0.58     0.00
## UGDS_2MOR           43.83        38.59        24.17         19.21     0.00
## UGDS_NRA            92.25       213.37        74.09         73.98     0.00
## UGDS_UNKN          127.96       133.50        97.82         -0.92     0.00
## PPTUG_EF           -33.15     -1464.04      -214.98        -79.92    -0.02
## NPT4_PUB               NA  20420278.27  11215184.61    6239926.77   292.43
## NPT4_PRIV     52883812.83  60259561.82  29011477.66   12658912.32   -69.25
## COSTT4_A      60259561.82 162884718.94  75891018.52   38078362.82   498.66
## TUITFTE       29011477.66  75891018.52 301920777.62  161489240.07   202.85
## INEXPFTE      12658912.32  38078362.82 161489240.07  161959774.00   732.13
## PFTFAC             -69.25       498.66       202.85        732.13     0.09
## PCTPELL           -499.56      -686.43      -208.65       -566.61    -0.02
## C150_4             520.95      1501.59       555.92        763.66     0.02
## PFTFTUG1_EF        236.91      1522.75       746.50        450.68     0.02
## RET_FT4            293.78       809.59       266.67        530.98     0.02
## PCTFLOAN           525.87      1551.44       664.30       -178.50     0.00
##             PCTPELL   C150_4 PFTFTUG1_EF  RET_FT4 PCTFLOAN
## UNITID      9068.69 -5018.36     -684.20 -5604.27  5769.15
## CONTROL        0.09    -0.02        0.03    -0.04     0.10
## ADM_RATE       0.01    -0.01        0.00    -0.01     0.00
## SAT_AVG      -13.75    18.62       10.49    11.16   -11.55
## UGDS        -319.31   212.98     -113.24   236.65  -281.31
## UGDS_WHITE    -0.02     0.01        0.01     0.01     0.00
## UGDS_BLACK     0.02    -0.01        0.00    -0.01     0.01
## UGDS_HISP      0.01     0.00        0.00     0.00    -0.01
## UGDS_ASIAN     0.00     0.00        0.00     0.00     0.00
## UGDS_AIAN      0.00     0.00        0.00     0.00     0.00
## UGDS_NHPI      0.00     0.00        0.00     0.00     0.00
## UGDS_2MOR      0.00     0.00        0.00     0.00     0.00
## UGDS_NRA       0.00     0.00        0.00     0.00     0.00
## UGDS_UNKN      0.00     0.00        0.00     0.00     0.00
## PPTUG_EF      -0.01    -0.02       -0.04    -0.01    -0.02
## NPT4_PUB     -82.79   450.90      359.35   161.13   729.64
## NPT4_PRIV   -499.56   520.95      236.91   293.78   525.87
## COSTT4_A    -686.43  1501.59     1522.75   809.59  1551.44
## TUITFTE     -208.65   555.92      746.50   266.67   664.30
## INEXPFTE    -566.61   763.66      450.68   530.98  -178.50
## PFTFAC        -0.02     0.02        0.02     0.02     0.00
## PCTPELL        0.05    -0.02        0.00    -0.02     0.03
## C150_4        -0.02     0.05        0.02     0.02     0.00
## PFTFTUG1_EF    0.00     0.02        0.07     0.02     0.02
## RET_FT4       -0.02     0.02        0.02     0.04    -0.01
## PCTFLOAN       0.03     0.00        0.02    -0.01     0.08
cormatrix
##                   UNITID      CONTROL    ADM_RATE     SAT_AVG         UGDS
## UNITID       1.000000000  0.122493538  0.20473480 -0.01784718 -0.270589310
## CONTROL      0.122493538  1.000000000  0.18070848  0.11800425 -0.418104977
## ADM_RATE     0.204734804  0.180708478  1.00000000 -0.35436240 -0.127279600
## SAT_AVG     -0.017847180  0.118004254 -0.35436240  1.00000000  0.249611095
## UGDS        -0.270589310 -0.418104977 -0.12727960  0.24961110  1.000000000
## UGDS_WHITE  -0.195619430 -0.243593789  0.11168300  0.21669481  0.004327530
## UGDS_BLACK   0.163418149  0.204666634 -0.02905491 -0.46948461 -0.097413802
## UGDS_HISP    0.103175200  0.126711295  0.02035797 -0.02071523  0.030035380
## UGDS_ASIAN  -0.019442350 -0.020901768 -0.21854922  0.46573435  0.128072682
## UGDS_AIAN   -0.011277686 -0.104279399  0.04655114 -0.08358082 -0.037780869
## UGDS_NHPI    0.008920492 -0.007020125  0.03126768 -0.07271551 -0.014876220
## UGDS_2MOR   -0.032364464 -0.047418500 -0.07123272  0.24376903  0.101022286
## UGDS_NRA    -0.127427432 -0.110436022 -0.22611922  0.36099040  0.113219624
## UGDS_UNKN    0.066367027  0.125956281 -0.01531579 -0.10440877 -0.009889212
## PPTUG_EF    -0.071567424 -0.257447472  0.07903904 -0.34703695  0.161777200
## NPT4_PUB     0.019814892           NA  0.02782553  0.34169792  0.146803909
## NPT4_PRIV   -0.108358313 -0.189920428 -0.10542663  0.36292252  0.132046190
## COSTT4_A    -0.035760281  0.419594213 -0.27750228  0.52117126 -0.159172846
## TUITFTE      0.044338873  0.136384564 -0.14143032  0.52528127 -0.052316407
## INEXPFTE    -0.099609609 -0.145919005 -0.40898646  0.63510957  0.042658066
## PFTFAC      -0.250730186 -0.261382636 -0.17256667  0.16899071  0.045408404
## PCTPELL      0.300552253  0.458089115  0.24488347 -0.71224956 -0.259438971
## C150_4      -0.223423621 -0.119431120 -0.32018650  0.80147835  0.138243362
## PFTFTUG1_EF -0.024619288  0.172711873 -0.05908279  0.39928761 -0.068835200
## RET_FT4     -0.266782598 -0.294291957 -0.21026497  0.74199292  0.168248801
## PCTFLOAN     0.152064822  0.432246118  0.10762420 -0.51033746 -0.181782462
##              UGDS_WHITE  UGDS_BLACK    UGDS_HISP  UGDS_ASIAN    UGDS_AIAN
## UNITID      -0.19561943  0.16341815  0.103175200 -0.01944235 -0.011277686
## CONTROL     -0.24359379  0.20466663  0.126711295 -0.02090177 -0.104279399
## ADM_RATE     0.11168300 -0.02905491  0.020357973 -0.21854922  0.046551139
## SAT_AVG      0.21669481 -0.46948461 -0.020715225  0.46573435 -0.083580819
## UGDS         0.00432753 -0.09741380  0.030035380  0.12807268 -0.037780869
## UGDS_WHITE   1.00000000 -0.50797351 -0.554214097 -0.21488201 -0.089845323
## UGDS_BLACK  -0.50797351  1.00000000 -0.205057081 -0.12934209 -0.094355778
## UGDS_HISP   -0.55421410 -0.20505708  1.000000000  0.03300474 -0.059500100
## UGDS_ASIAN  -0.21488201 -0.12934209  0.033004738  1.00000000 -0.048742363
## UGDS_AIAN   -0.08984532 -0.09435578 -0.059500100 -0.04874236  1.000000000
## UGDS_NHPI   -0.09278148 -0.05040789 -0.015921018  0.10448779 -0.005356698
## UGDS_2MOR   -0.02373690 -0.09685375 -0.088686490  0.10686212 -0.017235613
## UGDS_NRA    -0.06773875 -0.12133509 -0.057275382  0.16235768 -0.033947517
## UGDS_UNKN   -0.19766756 -0.05601727 -0.093683489 -0.02961362 -0.033446091
## PPTUG_EF    -0.02627129  0.02617678 -0.006598368  0.03911231  0.040875506
## NPT4_PUB     0.21739600 -0.02981708 -0.241453843  0.02942431 -0.097819687
## NPT4_PRIV    0.03835043 -0.02783919 -0.184949487  0.08242557 -0.060588083
## COSTT4_A     0.08629270 -0.07155682 -0.184253125  0.15825161 -0.110773604
## TUITFTE     -0.01081433  0.01418705 -0.046209138  0.02573125 -0.044648018
## INEXPFTE     0.06601190 -0.06565252 -0.078554714  0.06596620  0.009526498
## PFTFAC       0.17884731 -0.14709910 -0.103257065 -0.01930712  0.038011980
## PCTPELL     -0.35141655  0.35406587  0.206144339 -0.15227313  0.011845852
## C150_4       0.23617301 -0.31723700 -0.061069463  0.28881316 -0.108272207
## PFTFTUG1_EF  0.07690362 -0.06455469 -0.040664601 -0.02466865 -0.018650118
## RET_FT4      0.21713437 -0.30534227 -0.021287767  0.25243281 -0.062629180
## PCTFLOAN     0.01091330  0.21392771 -0.176685789 -0.15651302 -0.143278570
##                 UGDS_NHPI    UGDS_2MOR     UGDS_NRA    UGDS_UNKN
## UNITID       0.0089204924 -0.032364464 -0.127427432  0.066367027
## CONTROL     -0.0070201252 -0.047418500 -0.110436022  0.125956281
## ADM_RATE     0.0312676828 -0.071232721 -0.226119217 -0.015315791
## SAT_AVG     -0.0727155062  0.243769032  0.360990396 -0.104408770
## UGDS        -0.0148762197  0.101022286  0.113219624 -0.009889212
## UGDS_WHITE  -0.0927814754 -0.023736905 -0.067738747 -0.197667558
## UGDS_BLACK  -0.0504078890 -0.096853749 -0.121335087 -0.056017266
## UGDS_HISP   -0.0159210182 -0.088686490 -0.057275382 -0.093683489
## UGDS_ASIAN   0.1044877932  0.106862123  0.162357684 -0.029613622
## UGDS_AIAN   -0.0053566981 -0.017235613 -0.033947517 -0.033446091
## UGDS_NHPI    1.0000000000  0.065829028 -0.006349936 -0.004536746
## UGDS_2MOR    0.0658290276  1.000000000  0.030016915  0.079404465
## UGDS_NRA    -0.0063499361  0.030016915  1.000000000 -0.007450126
## UGDS_UNKN   -0.0045367463  0.079404465 -0.007450126  1.000000000
## PPTUG_EF     0.0115346411  0.027110947 -0.082805633  0.001477585
## NPT4_PUB    -0.0775838548  0.036636685  0.185913387  0.011981654
## NPT4_PRIV   -0.0005016322  0.195815154  0.247282716  0.166799674
## COSTT4_A    -0.0506290598  0.109832770  0.316150288  0.115186024
## TUITFTE     -0.0041143183  0.044680524  0.085506622  0.060405858
## INEXPFTE    -0.0014588486  0.051045871  0.122737340 -0.000812433
## PFTFAC      -0.0013181112  0.020749553  0.114592948 -0.076987123
## PCTPELL      0.0397068837 -0.105559574 -0.286928245  0.021042973
## C150_4      -0.0071144668  0.120511722  0.231923005 -0.144386225
## PFTFTUG1_EF -0.0034444230 -0.007921633  0.158242941 -0.063471918
## RET_FT4     -0.0189494872  0.097342561  0.216751275 -0.193997676
## PCTFLOAN    -0.0468500875  0.051206998 -0.099518215  0.161087155
##                 PPTUG_EF    NPT4_PUB     NPT4_PRIV    COSTT4_A
## UNITID      -0.071567424  0.01981489 -0.1083583130 -0.03576028
## CONTROL     -0.257447472          NA -0.1899204277  0.41959421
## ADM_RATE     0.079039043  0.02782553 -0.1054266300 -0.27750228
## SAT_AVG     -0.347036949  0.34169792  0.3629225157  0.52117126
## UGDS         0.161777200  0.14680391  0.1320461898 -0.15917285
## UGDS_WHITE  -0.026271288  0.21739600  0.0383504318  0.08629270
## UGDS_BLACK   0.026176782 -0.02981708 -0.0278391861 -0.07155682
## UGDS_HISP   -0.006598368 -0.24145384 -0.1849494872 -0.18425313
## UGDS_ASIAN   0.039112309  0.02942431  0.0824255714  0.15825161
## UGDS_AIAN    0.040875506 -0.09781969 -0.0605880829 -0.11077360
## UGDS_NHPI    0.011534641 -0.07758385 -0.0005016322 -0.05062906
## UGDS_2MOR    0.027110947  0.03663669  0.1958151537  0.10983277
## UGDS_NRA    -0.082805633  0.18591339  0.2472827156  0.31615029
## UGDS_UNKN    0.001477585  0.01198165  0.1667996735  0.11518602
## PPTUG_EF     1.000000000 -0.45579731 -0.0220192177 -0.48886305
## NPT4_PUB    -0.455797314  1.00000000            NA  0.92270809
## NPT4_PRIV   -0.022019218          NA  1.0000000000  0.70825343
## COSTT4_A    -0.488863052  0.92270809  0.7082534292  1.00000000
## TUITFTE     -0.050285077  0.58069767  0.5520262828  0.76021421
## INEXPFTE    -0.026849302  0.29990739  0.2690729864  0.45545444
## PFTFAC      -0.239224901  0.23484204 -0.0315218723  0.12116344
## PCTPELL     -0.132243427 -0.10602216 -0.3084972542 -0.25278323
## C150_4      -0.404749586  0.56798052  0.3361351988  0.55089376
## PFTFTUG1_EF -0.715559140  0.40004087  0.1212472822  0.45002045
## RET_FT4     -0.361639649  0.32386032  0.1901486530  0.32089387
## PCTFLOAN    -0.229862175  0.61339790  0.2918746434  0.43468955
##                  TUITFTE     INEXPFTE       PFTFAC     PCTPELL
## UNITID       0.044338873 -0.099609609 -0.250730186  0.30055225
## CONTROL      0.136384564 -0.145919005 -0.261382636  0.45808912
## ADM_RATE    -0.141430320 -0.408986460 -0.172566672  0.24488347
## SAT_AVG      0.525281272  0.635109575  0.168990712 -0.71224956
## UGDS        -0.052316407  0.042658066  0.045408404 -0.25943897
## UGDS_WHITE  -0.010814333  0.066011899  0.178847305 -0.35141655
## UGDS_BLACK   0.014187051 -0.065652524 -0.147099101  0.35406587
## UGDS_HISP   -0.046209138 -0.078554714 -0.103257065  0.20614434
## UGDS_ASIAN   0.025731249  0.065966199 -0.019307120 -0.15227313
## UGDS_AIAN   -0.044648018  0.009526498  0.038011980  0.01184585
## UGDS_NHPI   -0.004114318 -0.001458849 -0.001318111  0.03970688
## UGDS_2MOR    0.044680524  0.051045871  0.020749553 -0.10555957
## UGDS_NRA     0.085506622  0.122737340  0.114592948 -0.28692824
## UGDS_UNKN    0.060405858 -0.000812433 -0.076987123  0.02104297
## PPTUG_EF    -0.050285077 -0.026849302 -0.239224901 -0.13224343
## NPT4_PUB     0.580697669  0.299907392  0.234842040 -0.10602216
## NPT4_PRIV    0.552026283  0.269072986 -0.031521872 -0.30849725
## COSTT4_A     0.760214212  0.455454439  0.121163437 -0.25278323
## TUITFTE      1.000000000  0.730286898  0.030241874 -0.05326752
## INEXPFTE     0.730286898  1.000000000  0.153370047 -0.20771511
## PFTFAC       0.030241874  0.153370047  1.000000000 -0.27734550
## PCTPELL     -0.053267516 -0.207715114 -0.277345505  1.00000000
## C150_4       0.376892532  0.470649399  0.297374790 -0.51969735
## PFTFTUG1_EF  0.361734037  0.266256095  0.223710454 -0.02825530
## RET_FT4      0.197837071  0.350911976  0.302443892 -0.46616866
## PCTFLOAN     0.134898657 -0.052051315 -0.043993666  0.41861098
##                   C150_4  PFTFTUG1_EF     RET_FT4    PCTFLOAN
## UNITID      -0.223423621 -0.024619288 -0.26678260  0.15206482
## CONTROL     -0.119431120  0.172711873 -0.29429196  0.43224612
## ADM_RATE    -0.320186498 -0.059082790 -0.21026497  0.10762420
## SAT_AVG      0.801478347  0.399287605  0.74199292 -0.51033746
## UGDS         0.138243362 -0.068835200  0.16824880 -0.18178246
## UGDS_WHITE   0.236173010  0.076903624  0.21713437  0.01091330
## UGDS_BLACK  -0.317237000 -0.064554686 -0.30534227  0.21392771
## UGDS_HISP   -0.061069463 -0.040664601 -0.02128777 -0.17668579
## UGDS_ASIAN   0.288813159 -0.024668650  0.25243281 -0.15651302
## UGDS_AIAN   -0.108272207 -0.018650118 -0.06262918 -0.14327857
## UGDS_NHPI   -0.007114467 -0.003444423 -0.01894949 -0.04685009
## UGDS_2MOR    0.120511722 -0.007921633  0.09734256  0.05120700
## UGDS_NRA     0.231923005  0.158242941  0.21675128 -0.09951822
## UGDS_UNKN   -0.144386225 -0.063471918 -0.19399768  0.16108716
## PPTUG_EF    -0.404749586 -0.715559140 -0.36163965 -0.22986218
## NPT4_PUB     0.567980524  0.400040873  0.32386032  0.61339790
## NPT4_PRIV    0.336135199  0.121247282  0.19014865  0.29187464
## COSTT4_A     0.550893756  0.450020453  0.32089387  0.43468955
## TUITFTE      0.376892532  0.361734037  0.19783707  0.13489866
## INEXPFTE     0.470649399  0.266256095  0.35091198 -0.05205132
## PFTFAC       0.297374790  0.223710454  0.30244389 -0.04399367
## PCTPELL     -0.519697353 -0.028255301 -0.46616866  0.41861098
## C150_4       1.000000000  0.426461668  0.58103449 -0.09340366
## PFTFTUG1_EF  0.426461668  1.000000000  0.41358619  0.21710522
## RET_FT4      0.581034494  0.413586189  1.00000000 -0.25435596
## PCTFLOAN    -0.093403664  0.217105223 -0.25435596  1.00000000
covmatrix
##                    UNITID       CONTROL      ADM_RATE       SAT_AVG
## UNITID       4.312430e+13  6.729066e+05  4.534404e+03 -1.281505e+05
## CONTROL      6.729066e+05  6.997793e-01  2.537410e-02  7.829443e+00
## ADM_RATE     4.534404e+03  2.537410e-02  4.365108e-02 -9.152082e+00
## SAT_AVG     -1.281505e+05  7.829443e+00 -9.152082e+00  1.778408e+04
## UGDS        -1.967094e+08 -1.936429e+03 -1.681531e+02  2.437918e+05
## UGDS_WHITE  -7.512578e+03 -5.959982e-02  5.891843e-03  6.366863e+00
## UGDS_BLACK   4.908173e+03  3.916232e-02 -1.159646e-03 -1.162703e+01
## UGDS_HISP    3.069763e+03  2.401854e-02  7.547608e-04 -3.110483e-01
## UGDS_ASIAN  -1.954065e+02 -1.338366e-03 -2.837813e-03  3.711274e+00
## UGDS_AIAN   -1.049952e+02 -6.185145e-03  3.201771e-04 -3.600650e-01
## UGDS_NHPI    3.919438e+01 -1.965086e-04  2.497858e-04 -7.126132e-02
## UGDS_2MOR   -1.349023e+02 -1.259217e-03 -3.800944e-04  7.298147e-01
## UGDS_NRA    -8.502974e+02 -4.694836e-03 -2.637014e-03  2.263840e+00
## UGDS_UNKN    8.278347e+02  1.000951e-02 -2.024596e-04 -7.023401e-01
## PPTUG_EF    -2.356012e+03 -5.406731e-02  2.788057e-03 -5.866310e+00
## NPT4_PUB     8.555903e+06  0.000000e+00  2.228791e+01  1.546401e+05
## NPT4_PRIV   -1.075273e+08 -6.416559e+02 -1.626399e+02  3.143747e+05
## COSTT4_A    -5.270038e+07  4.254855e+03 -7.465148e+02  9.251042e+05
## TUITFTE      1.028087e+08  1.988247e+03 -2.154816e+02  4.676810e+05
## INEXPFTE    -1.691623e+08 -1.558023e+03 -6.692570e+02  7.350076e+05
## PFTFAC      -8.568158e+03 -6.157043e-02 -1.018346e-02  5.287238e+00
## PCTPELL      9.068688e+03  8.820822e-02  1.032733e-02 -1.375176e+01
## C150_4      -5.018359e+03 -1.776217e-02 -1.229116e-02  1.862141e+01
## PFTFTUG1_EF -6.841997e+02  3.398633e-02 -2.831299e-03  1.049133e+01
## RET_FT4     -5.604272e+03 -3.800316e-02 -6.093242e-03  1.115780e+01
## PCTFLOAN     5.769146e+03  1.046522e-01  4.891957e-03 -1.155212e+01
##                      UGDS    UGDS_WHITE    UGDS_BLACK     UGDS_HISP
## UNITID      -1.967094e+08 -7.512578e+03  4.908173e+03  3.069763e+03
## CONTROL     -1.936429e+03 -5.959982e-02  3.916232e-02  2.401854e-02
## ADM_RATE    -1.681531e+02  5.891843e-03 -1.159646e-03  7.547608e-04
## SAT_AVG      2.437918e+05  6.366863e+00 -1.162703e+01 -3.110483e-01
## UGDS         2.958107e+07  6.762645e+00 -1.190528e+02  3.636321e+01
## UGDS_WHITE   6.762645e+00  8.255418e-02 -3.279614e-02 -3.544616e-02
## UGDS_BLACK  -1.190528e+02 -3.279614e-02  5.049219e-02 -1.025673e-02
## UGDS_HISP    3.636321e+01 -3.544616e-02 -1.025673e-02  4.955006e-02
## UGDS_ASIAN   5.237768e+01 -4.642505e-03 -2.185419e-03  5.524350e-04
## UGDS_AIAN   -1.431268e+01 -1.798072e-03 -1.476804e-03 -9.225330e-04
## UGDS_NHPI   -2.659666e+00 -8.763112e-04 -3.723387e-04 -1.164985e-04
## UGDS_2MOR    1.713435e+01 -2.126852e-04 -6.786910e-04 -6.156348e-04
## UGDS_NRA     3.074179e+01 -9.716440e-04 -1.361128e-03 -6.364885e-04
## UGDS_UNKN   -5.019408e+00 -5.300157e-03 -1.174675e-03 -1.946117e-03
## PPTUG_EF     2.170634e+02 -1.857259e-03  1.450254e-03 -3.621910e-04
## NPT4_PUB     5.346029e+06  2.601627e+02 -2.465739e+01 -2.043260e+02
## NPT4_PRIV    3.119630e+06  8.120708e+01 -4.845459e+01 -3.223476e+02
## COSTT4_A    -1.364721e+07  2.951488e+02 -1.890390e+02 -4.658808e+02
## TUITFTE     -4.938153e+06 -5.386015e+01  5.525877e+01 -1.782413e+02
## INEXPFTE     2.801231e+06  2.287237e+02 -1.779024e+02 -2.108016e+02
## PFTFAC       9.463431e+01  1.426599e-02 -8.998135e-03 -6.329072e-03
## PCTPELL     -3.193147e+02 -2.280271e-02  1.799104e-02  1.037559e-02
## C150_4       2.129771e+02  1.337822e-02 -1.375469e-02 -2.437542e-03
## PFTFTUG1_EF -1.132397e+02  5.217475e-03 -3.383117e-03 -1.987702e-03
## RET_FT4      2.366524e+02  1.138734e-02 -1.226377e-02 -7.882165e-04
## PCTFLOAN    -2.813073e+02  8.903602e-04  1.366736e-02 -1.118120e-02
##                UGDS_ASIAN     UGDS_AIAN     UGDS_NHPI     UGDS_2MOR
## UNITID      -1.954065e+02 -1.049952e+02  3.919438e+01 -1.349023e+02
## CONTROL     -1.338366e-03 -6.185145e-03 -1.965086e-04 -1.259217e-03
## ADM_RATE    -2.837813e-03  3.201771e-04  2.497858e-04 -3.800944e-04
## SAT_AVG      3.711274e+00 -3.600650e-01 -7.126132e-02  7.298147e-01
## UGDS         5.237768e+01 -1.431268e+01 -2.659666e+00  1.713435e+01
## UGDS_WHITE  -4.642505e-03 -1.798072e-03 -8.763112e-04 -2.126852e-04
## UGDS_BLACK  -2.185419e-03 -1.476804e-03 -3.723387e-04 -6.786910e-04
## UGDS_HISP    5.524350e-04 -9.225330e-04 -1.164985e-04 -6.156348e-04
## UGDS_ASIAN   5.654128e-03 -2.552887e-04  2.582712e-04  2.505822e-04
## UGDS_AIAN   -2.552887e-04  4.851592e-03 -1.226498e-05 -3.743798e-05
## UGDS_NHPI    2.582712e-04 -1.226498e-05  1.080576e-03  6.748210e-05
## UGDS_2MOR    2.505822e-04 -3.743798e-05  6.748210e-05  9.724945e-04
## UGDS_NRA     6.094753e-04 -1.180458e-04 -1.042071e-05  4.673154e-05
## UGDS_UNKN   -2.078060e-04 -2.174059e-04 -1.391733e-05  2.310853e-04
## PPTUG_EF     7.184478e-04  7.024979e-04  9.356161e-05  2.083970e-04
## NPT4_PUB     7.956598e+00 -5.032745e+01 -1.792213e+01  5.157079e+00
## NPT4_PRIV    4.436821e+01 -1.953968e+01 -8.932016e-02  4.382842e+01
## COSTT4_A     1.161101e+02 -1.202998e+02 -2.589760e+01  3.858757e+01
## TUITFTE      3.339505e+01 -5.397685e+01 -2.347438e+00  2.416997e+01
## INEXPFTE     5.956125e+01  8.012348e+00 -5.790654e-01  1.921055e+01
## PFTFAC      -3.399748e-04  1.005123e-03 -1.511376e-05  1.831850e-04
## PCTPELL     -2.565856e-03  1.867542e-04  2.954484e-04 -7.441574e-04
## C150_4       3.741012e-03 -1.613990e-03 -5.271869e-05  6.519264e-04
## PFTFTUG1_EF -3.710226e-04 -4.316542e-04 -3.650252e-05 -5.498730e-05
## RET_FT4      2.978017e-03 -8.138075e-04 -1.330618e-04  4.767810e-04
## PCTFLOAN    -3.315926e-03 -2.840080e-03 -4.383001e-04  4.538808e-04
##                  UGDS_NRA     UGDS_UNKN      PPTUG_EF      NPT4_PUB
## UNITID      -8.502974e+02  8.278347e+02 -2.356012e+03  8.555903e+06
## CONTROL     -4.694836e-03  1.000951e-02 -5.406731e-02  0.000000e+00
## ADM_RATE    -2.637014e-03 -2.024596e-04  2.788057e-03  2.228791e+01
## SAT_AVG      2.263840e+00 -7.023401e-01 -5.866310e+00  1.546401e+05
## UGDS         3.074179e+01 -5.019408e+00  2.170634e+02  5.346029e+06
## UGDS_WHITE  -9.716440e-04 -5.300157e-03 -1.857259e-03  2.601627e+02
## UGDS_BLACK  -1.361128e-03 -1.174675e-03  1.450254e-03 -2.465739e+01
## UGDS_HISP   -6.364885e-04 -1.946117e-03 -3.621910e-04 -2.043260e+02
## UGDS_ASIAN   6.094753e-04 -2.078060e-04  7.184478e-04  7.956598e+00
## UGDS_AIAN   -1.180458e-04 -2.174059e-04  7.024979e-04 -5.032745e+01
## UGDS_NHPI   -1.042071e-05 -1.391733e-05  9.356161e-05 -1.792213e+01
## UGDS_2MOR    4.673154e-05  2.310853e-04  2.083970e-04  5.157079e+00
## UGDS_NRA     2.492304e-03 -3.470947e-05 -9.876967e-04  2.182463e+01
## UGDS_UNKN   -3.470947e-05  8.708988e-03  3.399619e-05  2.137406e+00
## PPTUG_EF    -9.876967e-04  3.399619e-05  6.070846e-02 -4.947463e+02
## NPT4_PUB     2.182463e+01  2.137406e+00 -4.947463e+02  2.180583e+07
## NPT4_PRIV    9.224635e+01  1.279576e+02 -3.315144e+01            NA
## COSTT4_A     2.133744e+02  1.334981e+02 -1.464035e+03  2.042028e+07
## TUITFTE      7.408646e+01  9.782208e+01 -2.149797e+02  1.121518e+07
## INEXPFTE     7.398386e+01 -9.153065e-01 -7.992215e+01  6.239927e+06
## PFTFAC       1.925859e-03 -1.779038e-03 -1.754014e-02  2.924302e+02
## PCTPELL     -3.139439e-03  4.440981e-04 -7.358276e-03 -8.278810e+01
## C150_4       2.900199e-03 -2.949484e-03 -1.715897e-02  4.508953e+02
## PFTFTUG1_EF  2.314861e-03 -1.267634e-03 -4.279065e-02  3.593479e+02
## RET_FT4      2.665523e-03 -3.509056e-03 -1.376131e-02  1.611303e+02
## PCTFLOAN    -1.369073e-03  4.274429e-03 -1.607461e-02  7.296435e+02
##                 NPT4_PRIV      COSTT4_A       TUITFTE      INEXPFTE
## UNITID      -1.075273e+08 -5.270038e+07  1.028087e+08 -1.691623e+08
## CONTROL     -6.416559e+02  4.254855e+03  1.988247e+03 -1.558023e+03
## ADM_RATE    -1.626399e+02 -7.465148e+02 -2.154816e+02 -6.692570e+02
## SAT_AVG      3.143747e+05  9.251042e+05  4.676810e+05  7.350076e+05
## UGDS         3.119630e+06 -1.364721e+07 -4.938153e+06  2.801231e+06
## UGDS_WHITE   8.120708e+01  2.951488e+02 -5.386015e+01  2.287237e+02
## UGDS_BLACK  -4.845459e+01 -1.890390e+02  5.525877e+01 -1.779024e+02
## UGDS_HISP   -3.223476e+02 -4.658808e+02 -1.782413e+02 -2.108016e+02
## UGDS_ASIAN   4.436821e+01  1.161101e+02  3.339505e+01  5.956125e+01
## UGDS_AIAN   -1.953968e+01 -1.202998e+02 -5.397685e+01  8.012348e+00
## UGDS_NHPI   -8.932016e-02 -2.589760e+01 -2.347438e+00 -5.790654e-01
## UGDS_2MOR    4.382842e+01  3.858757e+01  2.416997e+01  1.921055e+01
## UGDS_NRA     9.224635e+01  2.133744e+02  7.408646e+01  7.398386e+01
## UGDS_UNKN    1.279576e+02  1.334981e+02  9.782208e+01 -9.153065e-01
## PPTUG_EF    -3.315144e+01 -1.464035e+03 -2.149797e+02 -7.992215e+01
## NPT4_PUB               NA  2.042028e+07  1.121518e+07  6.239927e+06
## NPT4_PRIV    5.288381e+07  6.025956e+07  2.901148e+07  1.265891e+07
## COSTT4_A     6.025956e+07  1.628847e+08  7.589102e+07  3.807836e+07
## TUITFTE      2.901148e+07  7.589102e+07  3.019208e+08  1.614892e+08
## INEXPFTE     1.265891e+07  3.807836e+07  1.614892e+08  1.619598e+08
## PFTFAC      -6.924581e+01  4.986624e+02  2.028547e+02  7.321315e+02
## PCTPELL     -4.995591e+02 -6.864275e+02 -2.086541e+02 -5.666061e+02
## C150_4       5.209488e+02  1.501587e+03  5.559162e+02  7.636612e+02
## PFTFTUG1_EF  2.369126e+02  1.522746e+03  7.464979e+02  4.506753e+02
## RET_FT4      2.937806e+02  8.095945e+02  2.666704e+02  5.309794e+02
## PCTFLOAN     5.258666e+02  1.551442e+03  6.643038e+02 -1.785005e+02
##                    PFTFAC       PCTPELL        C150_4   PFTFTUG1_EF
## UNITID      -8.568158e+03  9.068688e+03 -5.018359e+03 -6.841997e+02
## CONTROL     -6.157043e-02  8.820822e-02 -1.776217e-02  3.398633e-02
## ADM_RATE    -1.018346e-02  1.032733e-02 -1.229116e-02 -2.831299e-03
## SAT_AVG      5.287238e+00 -1.375176e+01  1.862141e+01  1.049133e+01
## UGDS         9.463431e+01 -3.193147e+02  2.129771e+02 -1.132397e+02
## UGDS_WHITE   1.426599e-02 -2.280271e-02  1.337822e-02  5.217475e-03
## UGDS_BLACK  -8.998135e-03  1.799104e-02 -1.375469e-02 -3.383117e-03
## UGDS_HISP   -6.329072e-03  1.037559e-02 -2.437542e-03 -1.987702e-03
## UGDS_ASIAN  -3.399748e-04 -2.565856e-03  3.741012e-03 -3.710226e-04
## UGDS_AIAN    1.005123e-03  1.867542e-04 -1.613990e-03 -4.316542e-04
## UGDS_NHPI   -1.511376e-05  2.954484e-04 -5.271869e-05 -3.650252e-05
## UGDS_2MOR    1.831850e-04 -7.441574e-04  6.519264e-04 -5.498730e-05
## UGDS_NRA     1.925859e-03 -3.139439e-03  2.900199e-03  2.314861e-03
## UGDS_UNKN   -1.779038e-03  4.440981e-04 -2.949484e-03 -1.267634e-03
## PPTUG_EF    -1.754014e-02 -7.358276e-03 -1.715897e-02 -4.279065e-02
## NPT4_PUB     2.924302e+02 -8.278810e+01  4.508953e+02  3.593479e+02
## NPT4_PRIV   -6.924581e+01 -4.995591e+02  5.209488e+02  2.369126e+02
## COSTT4_A     4.986624e+02 -6.864275e+02  1.501587e+03  1.522746e+03
## TUITFTE      2.028547e+02 -2.086541e+02  5.559162e+02  7.464979e+02
## INEXPFTE     7.321315e+02 -5.666061e+02  7.636612e+02  4.506753e+02
## PFTFAC       9.379814e-02 -1.725719e-02  1.863125e-02  1.708395e-02
## PCTPELL     -1.725719e-02  5.104940e-02 -2.292341e-02 -1.498526e-03
## C150_4       1.863125e-02 -2.292341e-02  4.570058e-02  2.178981e-02
## PFTFTUG1_EF  1.708395e-02 -1.498526e-03  2.178981e-02  6.611554e-02
## RET_FT4      1.593969e-02 -1.823553e-02  2.320601e-02  1.861752e-02
## PCTFLOAN    -3.634241e-03  2.686950e-02 -4.459163e-03  1.560087e-02
##                   RET_FT4      PCTFLOAN
## UNITID      -5.604272e+03  5.769146e+03
## CONTROL     -3.800316e-02  1.046522e-01
## ADM_RATE    -6.093242e-03  4.891957e-03
## SAT_AVG      1.115780e+01 -1.155212e+01
## UGDS         2.366524e+02 -2.813073e+02
## UGDS_WHITE   1.138734e-02  8.903602e-04
## UGDS_BLACK  -1.226377e-02  1.366736e-02
## UGDS_HISP   -7.882165e-04 -1.118120e-02
## UGDS_ASIAN   2.978017e-03 -3.315926e-03
## UGDS_AIAN   -8.138075e-04 -2.840080e-03
## UGDS_NHPI   -1.330618e-04 -4.383001e-04
## UGDS_2MOR    4.767810e-04  4.538808e-04
## UGDS_NRA     2.665523e-03 -1.369073e-03
## UGDS_UNKN   -3.509056e-03  4.274429e-03
## PPTUG_EF    -1.376131e-02 -1.607461e-02
## NPT4_PUB     1.611303e+02  7.296435e+02
## NPT4_PRIV    2.937806e+02  5.258666e+02
## COSTT4_A     8.095945e+02  1.551442e+03
## TUITFTE      2.666704e+02  6.643038e+02
## INEXPFTE     5.309794e+02 -1.785005e+02
## PFTFAC       1.593969e-02 -3.634241e-03
## PCTPELL     -1.823553e-02  2.686950e-02
## C150_4       2.320601e-02 -4.459163e-03
## PFTFTUG1_EF  1.861752e-02  1.560087e-02
## RET_FT4      3.827693e-02 -1.095776e-02
## PCTFLOAN    -1.095776e-02  8.070627e-02
public<-subset(numvar, CONTROL==1)
nonprofit<-subset(numvar, CONTROL==2)
forprofit<-subset(numvar, CONTROL==3)

describe(public)
## Warning in FUN(newX[, i], ...): no non-missing arguments to min; returning
## Inf
## Warning in FUN(newX[, i], ...): no non-missing arguments to max; returning
## -Inf
describe(nonprofit)
## Warning in FUN(newX[, i], ...): no non-missing arguments to min; returning
## Inf

## Warning in FUN(newX[, i], ...): no non-missing arguments to max; returning
## -Inf
describe(forprofit)
## Warning in FUN(newX[, i], ...): no non-missing arguments to min; returning
## Inf

## Warning in FUN(newX[, i], ...): no non-missing arguments to max; returning
## -Inf
cormatrix1<-cor(public, use = "p")
## Warning in cor(public, use = "p"): the standard deviation is zero
cormatrix2<-cor(nonprofit, use = "p")
## Warning in cor(nonprofit, use = "p"): the standard deviation is zero
cormatrix3<-cor(forprofit, use = "p")
## Warning in cor(forprofit, use = "p"): the standard deviation is zero
cormatrix1
##                  UNITID CONTROL     ADM_RATE      SAT_AVG        UGDS
## UNITID       1.00000000      NA  0.034113410 -0.030812363 -0.27986350
## CONTROL              NA      NA           NA           NA          NA
## ADM_RATE     0.03411341      NA  1.000000000 -0.196549127 -0.12893924
## SAT_AVG     -0.03081236      NA -0.196549127  1.000000000  0.53706595
## UGDS        -0.27986350      NA -0.128939240  0.537065949  1.00000000
## UGDS_WHITE   0.12159511      NA  0.260910123  0.290783296 -0.20305873
## UGDS_BLACK  -0.07145822      NA -0.206742875 -0.494207233 -0.05160032
## UGDS_HISP   -0.06528820      NA -0.049544292 -0.003580806  0.21789188
## UGDS_ASIAN  -0.15374752      NA -0.283453456  0.392899181  0.36443071
## UGDS_AIAN    0.10284681      NA  0.072378882 -0.098191053 -0.12512850
## UGDS_NHPI    0.02945032      NA  0.066398765 -0.046548752 -0.03219361
## UGDS_2MOR   -0.08808565      NA  0.051157507  0.124410094  0.13260237
## UGDS_NRA    -0.16068414      NA -0.082449671  0.383711210  0.39783997
## UGDS_UNKN   -0.10489126      NA -0.126345348 -0.111527221  0.05302130
## PPTUG_EF    -0.13200051      NA  0.003671783 -0.326174875  0.04884913
## NPT4_PUB     0.01981489      NA  0.027825533  0.341697915  0.14680391
## NPT4_PRIV            NA      NA           NA           NA          NA
## COSTT4_A    -0.02169922      NA -0.127426211  0.483181708  0.28026738
## TUITFTE      0.03622683      NA -0.012003746  0.589397258  0.19447995
## INEXPFTE     0.04842383      NA -0.204854369  0.549448824 -0.02179121
## PFTFAC       0.07685487      NA  0.049534179  0.122496659 -0.01946888
## PCTPELL      0.12322085      NA -0.017770642 -0.654831191 -0.21611950
## C150_4      -0.04297910      NA -0.183901699  0.784058906  0.46309209
## PFTFTUG1_EF  0.02171617      NA  0.037258452  0.279297520  0.11161795
## RET_FT4     -0.02610264      NA -0.255870345  0.730792609  0.47655536
## PCTFLOAN     0.05888115      NA  0.044802604 -0.397184388  0.04576884
##              UGDS_WHITE   UGDS_BLACK    UGDS_HISP  UGDS_ASIAN   UGDS_AIAN
## UNITID       0.12159511 -0.071458225 -0.065288204 -0.15374752  0.10284681
## CONTROL              NA           NA           NA          NA          NA
## ADM_RATE     0.26091012 -0.206742875 -0.049544292 -0.28345346  0.07237888
## SAT_AVG      0.29078330 -0.494207233 -0.003580806  0.39289918 -0.09819105
## UGDS        -0.20305873 -0.051600325  0.217891879  0.36443071 -0.12512850
## UGDS_WHITE   1.00000000 -0.462318808 -0.598192056 -0.37406339 -0.23342806
## UGDS_BLACK  -0.46231881  1.000000000 -0.160179119 -0.09826229 -0.12626966
## UGDS_HISP   -0.59819206 -0.160179119  1.000000000  0.21324672 -0.09339752
## UGDS_ASIAN  -0.37406339 -0.098262294  0.213246716  1.00000000 -0.09655542
## UGDS_AIAN   -0.23342806 -0.126269656 -0.093397521 -0.09655542  1.00000000
## UGDS_NHPI   -0.15363179 -0.056415271 -0.033890991  0.12271002 -0.01416123
## UGDS_2MOR   -0.12184468 -0.108435880 -0.013987712  0.37654021 -0.05702537
## UGDS_NRA    -0.14187030 -0.069031163  0.024226253  0.34376150 -0.07593759
## UGDS_UNKN   -0.11095337 -0.029174309 -0.001782806  0.03190845 -0.05521507
## PPTUG_EF    -0.16627397 -0.008291912  0.192264353  0.07037155  0.02505567
## NPT4_PUB     0.21739600 -0.029817078 -0.241453843  0.02942431 -0.09781969
## NPT4_PRIV            NA           NA           NA          NA          NA
## COSTT4_A     0.13585999 -0.040832193 -0.185041840  0.17247857 -0.09394066
## TUITFTE      0.17457550 -0.082030288 -0.177996422  0.10822037 -0.09296081
## INEXPFTE     0.02118460 -0.023331195 -0.041765259  0.08072318  0.01454237
## PFTFAC       0.08333716 -0.015648027 -0.128195765 -0.07124724  0.04341494
## PCTPELL     -0.15169159  0.347603069 -0.045072795 -0.19172018  0.06310760
## C150_4       0.25605456 -0.292738371 -0.061915217  0.31053613 -0.18777934
## PFTFTUG1_EF  0.09241724 -0.030071324 -0.086226504 -0.09345391  0.02577786
## RET_FT4      0.01345870 -0.241704363  0.118139791  0.37938685 -0.10301830
## PCTFLOAN     0.24070712  0.119752693 -0.312212514 -0.09513772 -0.18640733
##                UGDS_NHPI     UGDS_2MOR    UGDS_NRA    UGDS_UNKN
## UNITID       0.029450316 -0.0880856481 -0.16068414 -0.104891257
## CONTROL               NA            NA          NA           NA
## ADM_RATE     0.066398765  0.0511575070 -0.08244967 -0.126345348
## SAT_AVG     -0.046548752  0.1244100941  0.38371121 -0.111527221
## UGDS        -0.032193611  0.1326023689  0.39783997  0.053021301
## UGDS_WHITE  -0.153631792 -0.1218446776 -0.14187030 -0.110953367
## UGDS_BLACK  -0.056415271 -0.1084358797 -0.06903116 -0.029174309
## UGDS_HISP   -0.033890991 -0.0139877117  0.02422625 -0.001782806
## UGDS_ASIAN   0.122710024  0.3765402078  0.34376150  0.031908454
## UGDS_AIAN   -0.014161231 -0.0570253688 -0.07593759 -0.055215073
## UGDS_NHPI    1.000000000  0.0554579646  0.02037714 -0.028248864
## UGDS_2MOR    0.055457965  1.0000000000  0.16785069  0.008642035
## UGDS_NRA     0.020377141  0.1678506936  1.00000000  0.040883518
## UGDS_UNKN   -0.028248864  0.0086420347  0.04088352  1.000000000
## PPTUG_EF     0.008464356  0.0363518108 -0.19002131  0.147253941
## NPT4_PUB    -0.077583855  0.0366366855  0.18591339  0.011981654
## NPT4_PRIV             NA            NA          NA           NA
## COSTT4_A    -0.088582801  0.0894954524  0.33557284  0.013786069
## TUITFTE     -0.031013225  0.0219852856  0.26644025  0.004099335
## INEXPFTE    -0.009645051 -0.0123834142  0.06087213 -0.019596007
## PFTFAC       0.019686831  0.0075930583  0.16966860 -0.020488273
## PCTPELL      0.118538114 -0.1826965435 -0.18519928 -0.148982271
## C150_4      -0.095539028  0.0472677289  0.28710603 -0.110576014
## PFTFTUG1_EF  0.071825407 -0.0842437625  0.17382764 -0.139717299
## RET_FT4      0.038125901  0.0211515844  0.26888057 -0.088740300
## PCTFLOAN    -0.074566228  0.0005894428  0.11832784  0.016975399
##                 PPTUG_EF    NPT4_PUB NPT4_PRIV    COSTT4_A      TUITFTE
## UNITID      -0.132000514  0.01981489        NA -0.02169922  0.036226828
## CONTROL               NA          NA        NA          NA           NA
## ADM_RATE     0.003671783  0.02782553        NA -0.12742621 -0.012003746
## SAT_AVG     -0.326174875  0.34169792        NA  0.48318171  0.589397258
## UGDS         0.048849131  0.14680391        NA  0.28026738  0.194479949
## UGDS_WHITE  -0.166273975  0.21739600        NA  0.13585999  0.174575498
## UGDS_BLACK  -0.008291912 -0.02981708        NA -0.04083219 -0.082030288
## UGDS_HISP    0.192264353 -0.24145384        NA -0.18504184 -0.177996422
## UGDS_ASIAN   0.070371545  0.02942431        NA  0.17247857  0.108220365
## UGDS_AIAN    0.025055667 -0.09781969        NA -0.09394066 -0.092960814
## UGDS_NHPI    0.008464356 -0.07758385        NA -0.08858280 -0.031013225
## UGDS_2MOR    0.036351811  0.03663669        NA  0.08949545  0.021985286
## UGDS_NRA    -0.190021308  0.18591339        NA  0.33557284  0.266440249
## UGDS_UNKN    0.147253941  0.01198165        NA  0.01378607  0.004099335
## PPTUG_EF     1.000000000 -0.45579731        NA -0.60014713 -0.401579782
## NPT4_PUB    -0.455797314  1.00000000        NA  0.92270809  0.580697669
## NPT4_PRIV             NA          NA        NA          NA           NA
## COSTT4_A    -0.600147130  0.92270809        NA  1.00000000  0.787421762
## TUITFTE     -0.401579782  0.58069767        NA  0.78742176  1.000000000
## INEXPFTE    -0.183387828  0.29990739        NA  0.49775812  0.400870338
## PFTFAC      -0.413172504  0.23484204        NA  0.26572184  0.230989769
## PCTPELL     -0.187062897 -0.10602216        NA -0.20918041 -0.138503259
## C150_4      -0.594225893  0.56798052        NA  0.68722942  0.650967800
## PFTFTUG1_EF -0.737679932  0.40004087        NA  0.44439713  0.471930103
## RET_FT4     -0.480680261  0.32386032        NA  0.47831377  0.478334867
## PCTFLOAN    -0.446474665  0.61339790        NA  0.62528417  0.446062843
##                 INEXPFTE       PFTFAC      PCTPELL      C150_4 PFTFTUG1_EF
## UNITID       0.048423828  0.076854874  0.123220852 -0.04297910  0.02171617
## CONTROL               NA           NA           NA          NA          NA
## ADM_RATE    -0.204854369  0.049534179 -0.017770642 -0.18390170  0.03725845
## SAT_AVG      0.549448824  0.122496659 -0.654831191  0.78405891  0.27929752
## UGDS        -0.021791206 -0.019468884 -0.216119497  0.46309209  0.11161795
## UGDS_WHITE   0.021184598  0.083337162 -0.151691595  0.25605456  0.09241724
## UGDS_BLACK  -0.023331195 -0.015648027  0.347603069 -0.29273837 -0.03007132
## UGDS_HISP   -0.041765259 -0.128195765 -0.045072795 -0.06191522 -0.08622650
## UGDS_ASIAN   0.080723180 -0.071247243 -0.191720180  0.31053613 -0.09345391
## UGDS_AIAN    0.014542370  0.043414939  0.063107596 -0.18777934  0.02577786
## UGDS_NHPI   -0.009645051  0.019686831  0.118538114 -0.09553903  0.07182541
## UGDS_2MOR   -0.012383414  0.007593058 -0.182696543  0.04726773 -0.08424376
## UGDS_NRA     0.060872129  0.169668602 -0.185199280  0.28710603  0.17382764
## UGDS_UNKN   -0.019596007 -0.020488273 -0.148982271 -0.11057601 -0.13971730
## PPTUG_EF    -0.183387828 -0.413172504 -0.187062897 -0.59422589 -0.73767993
## NPT4_PUB     0.299907392  0.234842040 -0.106022161  0.56798052  0.40004087
## NPT4_PRIV             NA           NA           NA          NA          NA
## COSTT4_A     0.497758120  0.265721840 -0.209180412  0.68722942  0.44439713
## TUITFTE      0.400870338  0.230989769 -0.138503259  0.65096780  0.47193010
## INEXPFTE     1.000000000  0.111648388 -0.093488536  0.51615425  0.30866292
## PFTFAC       0.111648388  1.000000000 -0.002407912  0.15561680  0.29140123
## PCTPELL     -0.093488536 -0.002407912  1.000000000 -0.54165168  0.09639879
## C150_4       0.516154250  0.155616803 -0.541651680  1.00000000  0.46312136
## PFTFTUG1_EF  0.308662924  0.291401229  0.096398789  0.46312136  1.00000000
## RET_FT4      0.468125258  0.099687702 -0.396603967  0.79117380  0.37299361
## PCTFLOAN     0.140150643  0.306340546  0.241036669  0.12327819  0.41929344
##                 RET_FT4      PCTFLOAN
## UNITID      -0.02610264  0.0588811457
## CONTROL              NA            NA
## ADM_RATE    -0.25587034  0.0448026040
## SAT_AVG      0.73079261 -0.3971843881
## UGDS         0.47655536  0.0457688413
## UGDS_WHITE   0.01345870  0.2407071192
## UGDS_BLACK  -0.24170436  0.1197526927
## UGDS_HISP    0.11813979 -0.3122125138
## UGDS_ASIAN   0.37938685 -0.0951377216
## UGDS_AIAN   -0.10301830 -0.1864073272
## UGDS_NHPI    0.03812590 -0.0745662277
## UGDS_2MOR    0.02115158  0.0005894428
## UGDS_NRA     0.26888057  0.1183278417
## UGDS_UNKN   -0.08874030  0.0169753989
## PPTUG_EF    -0.48068026 -0.4464746646
## NPT4_PUB     0.32386032  0.6133979006
## NPT4_PRIV            NA            NA
## COSTT4_A     0.47831377  0.6252841688
## TUITFTE      0.47833487  0.4460628429
## INEXPFTE     0.46812526  0.1401506434
## PFTFAC       0.09968770  0.3063405461
## PCTPELL     -0.39660397  0.2410366691
## C150_4       0.79117380  0.1232781901
## PFTFTUG1_EF  0.37299361  0.4192934377
## RET_FT4      1.00000000 -0.1392659607
## PCTFLOAN    -0.13926596  1.0000000000
cormatrix2
##                    UNITID CONTROL     ADM_RATE       SAT_AVG         UGDS
## UNITID       1.0000000000      NA  0.088915795 -0.0009228586 -0.148072002
## CONTROL                NA      NA           NA            NA           NA
## ADM_RATE     0.0889157951      NA  1.000000000 -0.4081278436 -0.175628697
## SAT_AVG     -0.0009228586      NA -0.408127844  1.0000000000  0.342359411
## UGDS        -0.1480720024      NA -0.175628697  0.3423594115  1.000000000
## UGDS_WHITE  -0.1308375757      NA  0.251715155  0.1711591056 -0.024208879
## UGDS_BLACK   0.0638877522      NA -0.082746919 -0.4666495936 -0.064646402
## UGDS_HISP    0.1792106552      NA -0.071689501 -0.0103185721  0.018048908
## UGDS_ASIAN  -0.0015194911      NA -0.251057723  0.5559889686  0.101165321
## UGDS_AIAN    0.0373785455      NA -0.030566908 -0.1035241635 -0.044942908
## UGDS_NHPI    0.0542958146      NA -0.007819085 -0.0873136068 -0.022314097
## UGDS_2MOR   -0.1526143506      NA -0.187934677  0.3417967822  0.109034840
## UGDS_NRA    -0.0993397891      NA -0.204726864  0.3520770499  0.067814998
## UGDS_UNKN   -0.0790289376      NA -0.017301084 -0.1460292771  0.091303173
## PPTUG_EF     0.0916395217      NA  0.046444198 -0.3340795205 -0.006011162
## NPT4_PUB               NA      NA           NA            NA           NA
## NPT4_PRIV   -0.2666166760      NA -0.116023079  0.3736482303  0.222921292
## COSTT4_A    -0.3556267437      NA -0.297944933  0.7097194962  0.249217431
## TUITFTE      0.0060454800      NA -0.270895755  0.5726043352  0.032415995
## INEXPFTE    -0.0159471163      NA -0.416326228  0.6722936709  0.057004507
## PFTFAC      -0.0875249023      NA -0.060604720  0.2013073371  0.026799690
## PCTPELL      0.2832617834      NA  0.137607661 -0.7355873183 -0.186697955
## C150_4      -0.1417165296      NA -0.323043933  0.8121477946  0.192804112
## PFTFTUG1_EF -0.0981008034      NA -0.157450500  0.4259549225  0.102128314
## RET_FT4     -0.0823184633      NA -0.186209082  0.7568600685  0.178786053
## PCTFLOAN    -0.1859263068      NA  0.062769595 -0.6526462221 -0.020818543
##               UGDS_WHITE  UGDS_BLACK    UGDS_HISP   UGDS_ASIAN
## UNITID      -0.130837576  0.06388775  0.179210655 -0.001519491
## CONTROL               NA          NA           NA           NA
## ADM_RATE     0.251715155 -0.08274692 -0.071689501 -0.251057723
## SAT_AVG      0.171159106 -0.46664959 -0.010318572  0.555988969
## UGDS        -0.024208879 -0.06464640  0.018048908  0.101165321
## UGDS_WHITE   1.000000000 -0.52324468 -0.565814104 -0.216217594
## UGDS_BLACK  -0.523244680  1.00000000 -0.131189567 -0.128796005
## UGDS_HISP   -0.565814104 -0.13118957  1.000000000 -0.011600198
## UGDS_ASIAN  -0.216217594 -0.12879601 -0.011600198  1.000000000
## UGDS_AIAN   -0.135607696 -0.05078120 -0.048074696 -0.051238822
## UGDS_NHPI   -0.077521191 -0.03589744 -0.007718325  0.066485561
## UGDS_2MOR   -0.018073365 -0.10574307 -0.079777036  0.188275789
## UGDS_NRA    -0.177529090 -0.12438104 -0.078580895  0.248586112
## UGDS_UNKN   -0.117725028 -0.04000695 -0.122503872 -0.002011410
## PPTUG_EF    -0.117369249  0.13905951  0.045376150 -0.081367099
## NPT4_PUB              NA          NA           NA           NA
## NPT4_PRIV    0.122628264 -0.12553620 -0.250108027  0.227248190
## COSTT4_A     0.163310193 -0.23390664 -0.233255342  0.331733696
## TUITFTE     -0.010727178  0.00567438 -0.030220316  0.043470905
## INEXPFTE     0.008634152 -0.03484281 -0.048514254  0.125669807
## PFTFAC       0.096429358 -0.02573481 -0.058845979 -0.032135458
## PCTPELL     -0.398670840  0.39103271  0.325416264 -0.184648300
## C150_4       0.177720575 -0.29202472 -0.119254991  0.321509189
## PFTFTUG1_EF  0.067785340 -0.12121931 -0.014488505  0.094893379
## RET_FT4      0.166637768 -0.29896125 -0.043182676  0.276783615
## PCTFLOAN     0.026846977  0.26742511 -0.192130148 -0.149464585
##                UGDS_AIAN    UGDS_NHPI   UGDS_2MOR     UGDS_NRA
## UNITID       0.037378545  0.054295815 -0.15261435 -0.099339789
## CONTROL               NA           NA          NA           NA
## ADM_RATE    -0.030566908 -0.007819085 -0.18793468 -0.204726864
## SAT_AVG     -0.103524164 -0.087313607  0.34179678  0.352077050
## UGDS        -0.044942908 -0.022314097  0.10903484  0.067814998
## UGDS_WHITE  -0.135607696 -0.077521191 -0.01807336 -0.177529090
## UGDS_BLACK  -0.050781205 -0.035897436 -0.10574307 -0.124381041
## UGDS_HISP   -0.048074696 -0.007718325 -0.07977704 -0.078580895
## UGDS_ASIAN  -0.051238822  0.066485561  0.18827579  0.248586112
## UGDS_AIAN    1.000000000  0.001338006 -0.05179418 -0.044622837
## UGDS_NHPI    0.001338006  1.000000000  0.07614773 -0.015962989
## UGDS_2MOR   -0.051794179  0.076147732  1.00000000  0.076574884
## UGDS_NRA    -0.044622837 -0.015962989  0.07657488  1.000000000
## UGDS_UNKN   -0.024041179 -0.014202881  0.01123435  0.001466837
## PPTUG_EF     0.021853144  0.014430156 -0.08252155 -0.120515374
## NPT4_PUB              NA           NA          NA           NA
## NPT4_PRIV   -0.118882303 -0.018294071  0.34929921  0.221142091
## COSTT4_A    -0.136786715 -0.057354712  0.41638654  0.250164850
## TUITFTE     -0.029882634 -0.011892369  0.09054137  0.035034414
## INEXPFTE    -0.011307427 -0.013461767  0.11071416  0.075095356
## PFTFAC       0.007472747 -0.020766117 -0.01082051 -0.032144057
## PCTPELL      0.125162303  0.064603845 -0.20485068 -0.301623991
## C150_4      -0.089352017  0.046260298  0.28492569  0.188910609
## PFTFTUG1_EF -0.030642543 -0.044171186  0.14226594  0.119824861
## RET_FT4     -0.114049946 -0.056127146  0.15851817  0.198332957
## PCTFLOAN    -0.094320484 -0.049034356  0.12349793 -0.197873316
##                UGDS_UNKN     PPTUG_EF NPT4_PUB   NPT4_PRIV    COSTT4_A
## UNITID      -0.079028938  0.091639522       NA -0.26661668 -0.35562674
## CONTROL               NA           NA       NA          NA          NA
## ADM_RATE    -0.017301084  0.046444198       NA -0.11602308 -0.29794493
## SAT_AVG     -0.146029277 -0.334079521       NA  0.37364823  0.70971950
## UGDS         0.091303173 -0.006011162       NA  0.22292129  0.24921743
## UGDS_WHITE  -0.117725028 -0.117369249       NA  0.12262826  0.16331019
## UGDS_BLACK  -0.040006947  0.139059506       NA -0.12553620 -0.23390664
## UGDS_HISP   -0.122503872  0.045376150       NA -0.25010803 -0.23325534
## UGDS_ASIAN  -0.002011410 -0.081367099       NA  0.22724819  0.33173370
## UGDS_AIAN   -0.024041179  0.021853144       NA -0.11888230 -0.13678672
## UGDS_NHPI   -0.014202881  0.014430156       NA -0.01829407 -0.05735471
## UGDS_2MOR    0.011234345 -0.082521552       NA  0.34929921  0.41638654
## UGDS_NRA     0.001466837 -0.120515374       NA  0.22114209  0.25016485
## UGDS_UNKN    1.000000000  0.138693133       NA  0.21745762  0.16772262
## PPTUG_EF     0.138693133  1.000000000       NA -0.16919218 -0.37104040
## NPT4_PUB              NA           NA       NA          NA          NA
## NPT4_PRIV    0.217457623 -0.169192184       NA  1.00000000  0.77174590
## COSTT4_A     0.167722622 -0.371040405       NA  0.77174590  1.00000000
## TUITFTE      0.030688794  0.072661687       NA  0.67399569  0.73577001
## INEXPFTE    -0.020415710  0.017091403       NA  0.27702619  0.50867706
## PFTFAC      -0.073020972 -0.161089513       NA -0.03587016  0.08439357
## PCTPELL     -0.101643102  0.084938607       NA -0.51689062 -0.67495495
## C150_4      -0.054689764 -0.338111891       NA  0.44871639  0.64051164
## PFTFTUG1_EF -0.097692525 -0.691499717       NA  0.22615558  0.44784248
## RET_FT4     -0.048513028 -0.286696462       NA  0.27533609  0.47446944
## PCTFLOAN     0.139123229  0.052977625       NA  0.27654898  0.12925877
##                 TUITFTE     INEXPFTE       PFTFAC     PCTPELL      C150_4
## UNITID       0.00604548 -0.015947116 -0.087524902  0.28326178 -0.14171653
## CONTROL              NA           NA           NA          NA          NA
## ADM_RATE    -0.27089575 -0.416326228 -0.060604720  0.13760766 -0.32304393
## SAT_AVG      0.57260434  0.672293671  0.201307337 -0.73558732  0.81214779
## UGDS         0.03241599  0.057004507  0.026799690 -0.18669795  0.19280411
## UGDS_WHITE  -0.01072718  0.008634152  0.096429358 -0.39867084  0.17772058
## UGDS_BLACK   0.00567438 -0.034842812 -0.025734807  0.39103271 -0.29202472
## UGDS_HISP   -0.03022032 -0.048514254 -0.058845979  0.32541626 -0.11925499
## UGDS_ASIAN   0.04347091  0.125669807 -0.032135458 -0.18464830  0.32150919
## UGDS_AIAN   -0.02988263 -0.011307427  0.007472747  0.12516230 -0.08935202
## UGDS_NHPI   -0.01189237 -0.013461767 -0.020766117  0.06460384  0.04626030
## UGDS_2MOR    0.09054137  0.110714156 -0.010820508 -0.20485068  0.28492569
## UGDS_NRA     0.03503441  0.075095356 -0.032144057 -0.30162399  0.18891061
## UGDS_UNKN    0.03068879 -0.020415710 -0.073020972 -0.10164310 -0.05468976
## PPTUG_EF     0.07266169  0.017091403 -0.161089513  0.08493861 -0.33811189
## NPT4_PUB             NA           NA           NA          NA          NA
## NPT4_PRIV    0.67399569  0.277026191 -0.035870157 -0.51689062  0.44871639
## COSTT4_A     0.73577001  0.508677055  0.084393565 -0.67495495  0.64051164
## TUITFTE      1.00000000  0.865169428  0.030280482 -0.12795475  0.48939824
## INEXPFTE     0.86516943  1.000000000  0.094676234 -0.20575025  0.47243477
## PFTFAC       0.03028048  0.094676234  1.000000000 -0.13350079  0.18015840
## PCTPELL     -0.12795475 -0.205750250 -0.133500789  1.00000000 -0.56723503
## C150_4       0.48939824  0.472434771  0.180158397 -0.56723503  1.00000000
## PFTFTUG1_EF  0.29162092  0.292481562  0.206484846 -0.25280920  0.41628877
## RET_FT4      0.35959455  0.351409110  0.150851461 -0.47694153  0.56658786
## PCTFLOAN    -0.02923821 -0.132904681 -0.068084581  0.17968369 -0.10121207
##             PFTFTUG1_EF     RET_FT4    PCTFLOAN
## UNITID      -0.09810080 -0.08231846 -0.18592631
## CONTROL              NA          NA          NA
## ADM_RATE    -0.15745050 -0.18620908  0.06276960
## SAT_AVG      0.42595492  0.75686007 -0.65264622
## UGDS         0.10212831  0.17878605 -0.02081854
## UGDS_WHITE   0.06778534  0.16663777  0.02684698
## UGDS_BLACK  -0.12121931 -0.29896125  0.26742511
## UGDS_HISP   -0.01448851 -0.04318268 -0.19213015
## UGDS_ASIAN   0.09489338  0.27678361 -0.14946458
## UGDS_AIAN   -0.03064254 -0.11404995 -0.09432048
## UGDS_NHPI   -0.04417119 -0.05612715 -0.04903436
## UGDS_2MOR    0.14226594  0.15851817  0.12349793
## UGDS_NRA     0.11982486  0.19833296 -0.19787332
## UGDS_UNKN   -0.09769252 -0.04851303  0.13912323
## PPTUG_EF    -0.69149972 -0.28669646  0.05297763
## NPT4_PUB             NA          NA          NA
## NPT4_PRIV    0.22615558  0.27533609  0.27654898
## COSTT4_A     0.44784248  0.47446944  0.12925877
## TUITFTE      0.29162092  0.35959455 -0.02923821
## INEXPFTE     0.29248156  0.35140911 -0.13290468
## PFTFAC       0.20648485  0.15085146 -0.06808458
## PCTPELL     -0.25280920 -0.47694153  0.17968369
## C150_4       0.41628877  0.56658786 -0.10121207
## PFTFTUG1_EF  1.00000000  0.40104019 -0.08138818
## RET_FT4      0.40104019  1.00000000 -0.26479716
## PCTFLOAN    -0.08138818 -0.26479716  1.00000000
cormatrix3
##                   UNITID CONTROL     ADM_RATE     SAT_AVG          UGDS
## UNITID       1.000000000      NA -0.007927216  0.92478693 -1.449278e-02
## CONTROL               NA      NA           NA          NA            NA
## ADM_RATE    -0.007927216      NA  1.000000000 -0.55689691 -1.139368e-01
## SAT_AVG      0.924786931      NA -0.556896914  1.00000000 -5.145799e-01
## UGDS        -0.014492781      NA -0.113936787 -0.51457990  1.000000e+00
## UGDS_WHITE  -0.132547999      NA -0.045495357 -0.04815596 -3.804176e-02
## UGDS_BLACK   0.094659029      NA -0.016570520 -0.92728173  2.219894e-05
## UGDS_HISP    0.018808533      NA  0.078187815 -0.44838718  1.461741e-03
## UGDS_ASIAN   0.034444358      NA -0.130886313  0.37124112 -9.224145e-03
## UGDS_AIAN   -0.061891317      NA  0.076077857 -0.41421026 -1.570980e-03
## UGDS_NHPI   -0.024821119      NA  0.053277614 -0.24077025  6.868353e-03
## UGDS_2MOR    0.052423488      NA  0.068126495  0.62100396  4.821561e-02
## UGDS_NRA     0.041135562      NA -0.073465314  0.48271470  1.494656e-02
## UGDS_UNKN    0.051124905      NA  0.057024811  0.13613918  7.640572e-02
## PPTUG_EF     0.045584911      NA -0.099272758 -0.52846604  4.364624e-02
## NPT4_PUB              NA      NA           NA          NA            NA
## NPT4_PRIV    0.064982726      NA -0.245108937  0.06097363  4.171311e-02
## COSTT4_A    -0.042228893      NA -0.290367647  0.08166823 -3.066538e-02
## TUITFTE      0.054380685      NA -0.051322977  0.28894473  1.380408e-02
## INEXPFTE    -0.019382546      NA -0.128304878  0.60526858 -3.395162e-02
## PFTFAC      -0.176948964      NA -0.080063593  0.41055943 -3.985584e-02
## PCTPELL     -0.048612995      NA  0.216345286 -0.53513378 -1.598827e-02
## C150_4      -0.112515895      NA -0.083829278  0.63118477 -6.373338e-02
## PFTFTUG1_EF -0.028452245      NA  0.317193726  0.57184638 -1.658425e-01
## RET_FT4     -0.104212648      NA -0.173563953  0.60742201 -4.628135e-02
## PCTFLOAN    -0.012044042      NA -0.027607175 -0.34797080  4.132152e-03
##                UGDS_WHITE    UGDS_BLACK    UGDS_HISP    UGDS_ASIAN
## UNITID      -0.1325479995  9.465903e-02  0.018808533  3.444436e-02
## CONTROL                NA            NA           NA            NA
## ADM_RATE    -0.0454953566 -1.657052e-02  0.078187815 -1.308863e-01
## SAT_AVG     -0.0481559613 -9.272817e-01 -0.448387181  3.712411e-01
## UGDS        -0.0380417576  2.219894e-05  0.001461741 -9.224145e-03
## UGDS_WHITE   1.0000000000 -4.693707e-01 -0.512101240 -1.879667e-01
## UGDS_BLACK  -0.4693707255  1.000000e+00 -0.313946438 -1.332359e-01
## UGDS_HISP   -0.5121012404 -3.139464e-01  1.000000000  3.186609e-03
## UGDS_ASIAN  -0.1879666569 -1.332359e-01  0.003186609  1.000000e+00
## UGDS_AIAN    0.0767498729 -1.311689e-01 -0.028907157 -3.415019e-02
## UGDS_NHPI   -0.0639596274 -7.200464e-02 -0.010027533  1.405919e-01
## UGDS_2MOR   -0.0003193679 -8.189886e-02 -0.115558055 -1.334437e-02
## UGDS_NRA    -0.0971217458 -6.195832e-02 -0.001536588  8.205791e-02
## UGDS_UNKN   -0.2195269794 -1.028306e-01 -0.127280870 -4.188757e-02
## PPTUG_EF    -0.0148344852  6.866402e-02 -0.077342418  6.862224e-02
## NPT4_PUB               NA            NA           NA            NA
## NPT4_PRIV   -0.0623264035  6.735264e-02 -0.127486633  1.254858e-02
## COSTT4_A     0.0869257682  7.707457e-02 -0.289114733  2.417903e-01
## TUITFTE      0.0108792982  1.476538e-02 -0.114227297  7.033817e-03
## INEXPFTE     0.0544697508 -2.718023e-02 -0.108585206 -4.708250e-03
## PFTFAC       0.0555373300 -1.453902e-01  0.054851108 -8.563675e-05
## PCTPELL     -0.2483280185  2.206886e-01  0.154652199 -1.430377e-01
## C150_4       0.0551750204 -2.216001e-01  0.206690405  2.190672e-01
## PFTFTUG1_EF  0.0426910995 -1.501930e-02  0.061021468 -8.584166e-02
## RET_FT4      0.1219763951 -2.041337e-01  0.064552558  1.548142e-01
## PCTFLOAN     0.1011309617  1.367613e-01 -0.252342682 -2.096348e-01
##                UGDS_AIAN     UGDS_NHPI     UGDS_2MOR     UGDS_NRA
## UNITID      -0.061891317 -0.0248211188  0.0524234882  0.041135562
## CONTROL               NA            NA            NA           NA
## ADM_RATE     0.076077857  0.0532776143  0.0681264951 -0.073465314
## SAT_AVG     -0.414210264 -0.2407702451  0.6210039569  0.482714698
## UGDS        -0.001570980  0.0068683531  0.0482156090  0.014946565
## UGDS_WHITE   0.076749873 -0.0639596274 -0.0003193679 -0.097121746
## UGDS_BLACK  -0.131168921 -0.0720046366 -0.0818988554 -0.061958316
## UGDS_HISP   -0.028907157 -0.0100275326 -0.1155580555 -0.001536588
## UGDS_ASIAN  -0.034150190  0.1405918832 -0.0133443745  0.082057905
## UGDS_AIAN    1.000000000  0.0226081145  0.0753714491 -0.029334920
## UGDS_NHPI    0.022608115  1.0000000000  0.0844674117 -0.007478147
## UGDS_2MOR    0.075371449  0.0844674117  1.0000000000 -0.041498615
## UGDS_NRA    -0.029334920 -0.0074781475 -0.0414986155  1.000000000
## UGDS_UNKN   -0.026374381  0.0084636095  0.1248319211 -0.004155127
## PPTUG_EF    -0.057900285  0.0004669291  0.0321020903  0.010432075
## NPT4_PUB              NA            NA            NA           NA
## NPT4_PRIV   -0.010581561  0.0163730753  0.1472305938  0.211582130
## COSTT4_A     0.059352356 -0.0003371757  0.0841086684  0.297864383
## TUITFTE     -0.003246465  0.0476682591  0.0760837939  0.146919382
## INEXPFTE    -0.021295683  0.0606406709  0.0568981529  0.123544593
## PFTFAC       0.076498696 -0.0148801326  0.0259237181  0.111409652
## PCTPELL      0.026041206 -0.0335172109 -0.0232161290 -0.172685703
## C150_4      -0.020372343  0.0565600379 -0.0559086519  0.034383230
## PFTFTUG1_EF  0.007382187 -0.0977993949  0.0140817285 -0.005822726
## RET_FT4      0.023269986  0.0253165900 -0.0133548794  0.119087370
## PCTFLOAN     0.014122556 -0.0164465512  0.1134283354 -0.105398310
##                 UGDS_UNKN      PPTUG_EF NPT4_PUB   NPT4_PRIV      COSTT4_A
## UNITID       0.0511249054  0.0455849110       NA  0.06498273 -0.0422288932
## CONTROL                NA            NA       NA          NA            NA
## ADM_RATE     0.0570248108 -0.0992727577       NA -0.24510894 -0.2903676475
## SAT_AVG      0.1361391767 -0.5284660370       NA  0.06097363  0.0816682281
## UGDS         0.0764057197  0.0436462386       NA  0.04171311 -0.0306653773
## UGDS_WHITE  -0.2195269794 -0.0148344852       NA -0.06232640  0.0869257682
## UGDS_BLACK  -0.1028306291  0.0686640249       NA  0.06735264  0.0770745745
## UGDS_HISP   -0.1272808705 -0.0773424180       NA -0.12748663 -0.2891147329
## UGDS_ASIAN  -0.0418875729  0.0686222379       NA  0.01254858  0.2417902780
## UGDS_AIAN   -0.0263743810 -0.0579002846       NA -0.01058156  0.0593523562
## UGDS_NHPI    0.0084636095  0.0004669291       NA  0.01637308 -0.0003371757
## UGDS_2MOR    0.1248319211  0.0321020903       NA  0.14723059  0.0841086684
## UGDS_NRA    -0.0041551266  0.0104320746       NA  0.21158213  0.2978643829
## UGDS_UNKN    1.0000000000  0.0019694715       NA  0.17545546  0.0007459633
## PPTUG_EF     0.0019694715  1.0000000000       NA  0.06322685  0.0560070565
## NPT4_PUB               NA            NA       NA          NA            NA
## NPT4_PRIV    0.1754554566  0.0632268456       NA  1.00000000  0.9673575565
## COSTT4_A     0.0007459633  0.0560070565       NA  0.96735756  1.0000000000
## TUITFTE      0.0944554921  0.0889486299       NA  0.45727302  0.4020430241
## INEXPFTE     0.0859744766  0.0200755142       NA  0.18241881  0.3196399732
## PFTFAC      -0.0013786304 -0.2582199178       NA -0.01507695  0.1019986964
## PCTPELL     -0.0040282670 -0.0827031681       NA -0.10177479 -0.3323072791
## C150_4      -0.1362937987 -0.1760712808       NA  0.18044070  0.1855819640
## PFTFTUG1_EF -0.0974295289 -0.6121385721       NA -0.01993887 -0.0465087641
## RET_FT4     -0.0806554898 -0.1780995556       NA  0.17561405  0.1771748559
## PCTFLOAN     0.1449600287  0.0212480573       NA  0.34129797  0.2088519335
##                  TUITFTE    INEXPFTE        PFTFAC      PCTPELL
## UNITID       0.054380685 -0.01938255 -1.769490e-01 -0.048612995
## CONTROL               NA          NA            NA           NA
## ADM_RATE    -0.051322977 -0.12830488 -8.006359e-02  0.216345286
## SAT_AVG      0.288944729  0.60526858  4.105594e-01 -0.535133784
## UGDS         0.013804081 -0.03395162 -3.985584e-02 -0.015988268
## UGDS_WHITE   0.010879298  0.05446975  5.553733e-02 -0.248328018
## UGDS_BLACK   0.014765381 -0.02718023 -1.453902e-01  0.220688553
## UGDS_HISP   -0.114227297 -0.10858521  5.485111e-02  0.154652199
## UGDS_ASIAN   0.007033817 -0.00470825 -8.563675e-05 -0.143037686
## UGDS_AIAN   -0.003246465 -0.02129568  7.649870e-02  0.026041206
## UGDS_NHPI    0.047668259  0.06064067 -1.488013e-02 -0.033517211
## UGDS_2MOR    0.076083794  0.05689815  2.592372e-02 -0.023216129
## UGDS_NRA     0.146919382  0.12354459  1.114097e-01 -0.172685703
## UGDS_UNKN    0.094455492  0.08597448 -1.378630e-03 -0.004028267
## PPTUG_EF     0.088948630  0.02007551 -2.582199e-01 -0.082703168
## NPT4_PUB              NA          NA            NA           NA
## NPT4_PRIV    0.457273020  0.18241881 -1.507695e-02 -0.101774790
## COSTT4_A     0.402043024  0.31963997  1.019987e-01 -0.332307279
## TUITFTE      1.000000000  0.65876543  1.394439e-02 -0.117801808
## INEXPFTE     0.658765426  1.00000000  2.956579e-01 -0.113289957
## PFTFAC       0.013944394  0.29565793  1.000000e+00 -0.165838230
## PCTPELL     -0.117801808 -0.11328996 -1.658382e-01  1.000000000
## C150_4       0.082458112  0.18622118  3.429519e-01 -0.092793128
## PFTFTUG1_EF  0.083319651 -0.09867887  1.334678e-02  0.240134007
## RET_FT4      0.149157316  0.12505271  2.309278e-01 -0.140478718
## PCTFLOAN     0.165204223  0.02684142 -8.789651e-02  0.441937946
##                    C150_4  PFTFTUG1_EF     RET_FT4      PCTFLOAN
## UNITID      -0.1125158954 -0.028452245 -0.10421265 -0.0120440416
## CONTROL                NA           NA          NA            NA
## ADM_RATE    -0.0838292784  0.317193726 -0.17356395 -0.0276071746
## SAT_AVG      0.6311847737  0.571846384  0.60742201 -0.3479708025
## UGDS        -0.0637333790 -0.165842451 -0.04628135  0.0041321521
## UGDS_WHITE   0.0551750204  0.042691099  0.12197640  0.1011309617
## UGDS_BLACK  -0.2216000958 -0.015019303 -0.20413370  0.1367613052
## UGDS_HISP    0.2066904051  0.061021468  0.06455256 -0.2523426822
## UGDS_ASIAN   0.2190671611 -0.085841665  0.15481418 -0.2096347747
## UGDS_AIAN   -0.0203723428  0.007382187  0.02326999  0.0141225562
## UGDS_NHPI    0.0565600379 -0.097799395  0.02531659 -0.0164465512
## UGDS_2MOR   -0.0559086519  0.014081728 -0.01335488  0.1134283354
## UGDS_NRA     0.0343832297 -0.005822726  0.11908737 -0.1053983095
## UGDS_UNKN   -0.1362937987 -0.097429529 -0.08065549  0.1449600287
## PPTUG_EF    -0.1760712808 -0.612138572 -0.17809956  0.0212480573
## NPT4_PUB               NA           NA          NA            NA
## NPT4_PRIV    0.1804407008 -0.019938872  0.17561405  0.3412979707
## COSTT4_A     0.1855819640 -0.046508764  0.17717486  0.2088519335
## TUITFTE      0.0824581118  0.083319651  0.14915732  0.1652042233
## INEXPFTE     0.1862211806 -0.098678873  0.12505271  0.0268414181
## PFTFAC       0.3429518514  0.013346778  0.23092780 -0.0878965077
## PCTPELL     -0.0927931281  0.240134007 -0.14047872  0.4419379461
## C150_4       1.0000000000  0.202991152  0.37974183  0.0007217879
## PFTFTUG1_EF  0.2029911517  1.000000000  0.17019919  0.0369836168
## RET_FT4      0.3797418271  0.170199186  1.00000000  0.0034305104
## PCTFLOAN     0.0007217879  0.036983617  0.00343051  1.0000000000
covmatrix1<-cov(public, use = "p")
covmatrix2<-cov(nonprofit, use = "p")
covmatrix3<-cov(forprofit, use = "p")

covmatrix1
##                    UNITID CONTROL      ADM_RATE       SAT_AVG
## UNITID       9.299721e+12       0  5.334552e+02 -2.186320e+05
## CONTROL      0.000000e+00       0  0.000000e+00  0.000000e+00
## ADM_RATE     5.334552e+02       0  3.360117e-02 -3.868647e+00
## SAT_AVG     -2.186320e+05       0 -3.868647e+00  1.246351e+04
## UGDS        -2.063166e+08       0 -2.125850e+02  5.450683e+05
## UGDS_WHITE   2.963131e+03       0  1.240260e-02  7.768440e+00
## UGDS_BLACK  -1.196239e+03       0 -7.653838e-03 -1.128908e+01
## UGDS_HISP   -1.123649e+03       0 -1.708462e-03 -5.753930e-02
## UGDS_ASIAN  -8.506188e+02       0 -3.384347e-03  2.972124e+00
## UGDS_AIAN    1.085392e+03       0  7.446680e-04 -5.342317e-01
## UGDS_NHPI    1.365980e+02       0  6.792911e-04 -3.247896e-02
## UGDS_2MOR   -2.516531e+02       0  2.595622e-04  3.434692e-01
## UGDS_NRA    -3.812806e+02       0 -4.671890e-04  1.260189e+00
## UGDS_UNKN   -3.816534e+02       0 -8.725182e-04 -4.301800e-01
## PPTUG_EF    -2.971123e+03       0  9.543694e-05 -4.229417e+00
## NPT4_PUB     8.555903e+06       0  2.228791e+01  1.546401e+05
## NPT4_PRIV              NA      NA            NA            NA
## COSTT4_A    -7.820823e+06       0 -1.032139e+02  2.261949e+05
## TUITFTE      1.851754e+07       0 -1.018153e+01  2.279867e+05
## INEXPFTE     5.311294e+07       0 -1.510772e+02  2.410387e+05
## PFTFAC       1.567501e+03       0  1.630107e-03  2.444422e+00
## PCTPELL      1.985426e+03       0 -5.362106e-04 -9.470237e+00
## C150_4      -4.738395e+02       0 -5.241809e-03  1.425736e+01
## PFTFTUG1_EF  3.156513e+02       0  1.184064e-03  5.269431e+00
## RET_FT4     -1.979873e+02       0 -4.300130e-03  7.840027e+00
## PCTFLOAN     1.433992e+03       0  1.566870e-03 -6.513858e+00
##                      UGDS    UGDS_WHITE    UGDS_BLACK     UGDS_HISP
## UNITID      -2.063166e+08  2.963131e+03 -1.196239e+03 -1.123649e+03
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -2.125850e+02  1.240260e-02 -7.653838e-03 -1.708462e-03
## SAT_AVG      5.450683e+05  7.768440e+00 -1.128908e+01 -5.753930e-02
## UGDS         5.998626e+07 -4.026432e+02 -7.028814e+01  3.051411e+02
## UGDS_WHITE  -4.026432e+02  6.554591e-02 -2.081700e-02 -2.769155e-02
## UGDS_BLACK  -7.028814e+01 -2.081700e-02  3.093196e-02 -5.093818e-03
## UGDS_HISP    3.051411e+02 -2.769155e-02 -5.093818e-03  3.269396e-02
## UGDS_ASIAN   1.640611e+02 -5.566508e-03 -1.004513e-03  2.241202e-03
## UGDS_AIAN   -1.074524e+02 -6.626126e-03 -2.462275e-03 -1.872419e-03
## UGDS_NHPI   -1.215033e+01 -1.916665e-03 -4.834959e-04 -2.986142e-04
## UGDS_2MOR    3.082565e+01 -9.362987e-04 -5.724160e-04 -7.591289e-05
## UGDS_NRA     7.681463e+01 -9.054697e-04 -3.026625e-04  1.092018e-04
## UGDS_UNKN    1.569799e+01 -1.085878e-03 -1.961427e-04 -1.232269e-05
## PPTUG_EF     8.946758e+01 -1.006654e-02 -3.448588e-04  8.220827e-03
## NPT4_PUB     5.346029e+06  2.601627e+02 -2.465739e+01 -2.043260e+02
## NPT4_PRIV              NA            NA            NA            NA
## COSTT4_A     1.114200e+07  1.699173e+02 -3.620696e+01 -1.694033e+02
## TUITFTE      6.336576e+06  1.879837e+02 -6.069906e+01 -1.354007e+02
## INEXPFTE    -1.806406e+06  5.803787e+01 -4.392371e+01 -8.083123e+01
## PFTFAC      -4.365770e+01  5.844623e-03 -7.702821e-04 -6.623997e-03
## PCTPELL     -2.844552e+02 -6.598399e-03  1.039038e-02 -1.385046e-03
## C150_4       7.574312e+02  1.182786e-02 -1.046351e-02 -2.019975e-03
## PFTFTUG1_EF  1.814096e+02  4.703051e-03 -1.083308e-03 -3.213946e-03
## RET_FT4      4.918125e+02  4.100246e-04 -5.770553e-03  2.552484e-03
## PCTFLOAN     9.105230e+01  1.582585e-02  5.410460e-03 -1.450111e-02
##                UGDS_ASIAN     UGDS_AIAN     UGDS_NHPI     UGDS_2MOR
## UNITID      -8.506188e+02  1.085392e+03  1.365980e+02 -2.516531e+02
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -3.384347e-03  7.446680e-04  6.792911e-04  2.595622e-04
## SAT_AVG      2.972124e+00 -5.342317e-01 -3.247896e-02  3.434692e-01
## UGDS         1.640611e+02 -1.074524e+02 -1.215033e+01  3.082565e+01
## UGDS_WHITE  -5.566508e-03 -6.626126e-03 -1.916665e-03 -9.362987e-04
## UGDS_BLACK  -1.004513e-03 -2.462275e-03 -4.834959e-04 -5.724160e-04
## UGDS_HISP    2.241202e-03 -1.872419e-03 -2.986142e-04 -7.591289e-05
## UGDS_ASIAN   3.378545e-03 -6.222649e-04  3.475660e-04  6.569181e-04
## UGDS_AIAN   -6.222649e-04  1.229328e-02 -7.651158e-05 -1.897741e-04
## UGDS_NHPI    3.475660e-04 -7.651158e-05  2.374568e-03  8.111316e-05
## UGDS_2MOR    6.569181e-04 -1.897741e-04  8.111316e-05  9.008865e-04
## UGDS_NRA     4.981175e-04 -2.098941e-04  2.475399e-05  1.255937e-04
## UGDS_UNKN    7.089872e-05 -2.340234e-04 -5.262125e-05  9.915596e-06
## PPTUG_EF     9.672637e-04  6.569355e-04  9.753696e-05  2.580145e-04
## NPT4_PUB     7.956598e+00 -5.032745e+01 -1.792213e+01  5.157079e+00
## NPT4_PRIV              NA            NA            NA            NA
## COSTT4_A     5.245991e+01 -5.323768e+01 -2.352689e+01  1.339656e+01
## TUITFTE      2.646566e+01 -4.336759e+01 -6.358758e+00  2.775516e+00
## INEXPFTE     5.022575e+01  1.726056e+01 -5.031347e+00 -3.977466e+00
## PFTFAC      -1.241610e-03  1.389657e-03  2.952458e-04  6.410420e-05
## PCTPELL     -1.894008e-03  1.189288e-03  9.818011e-04 -9.317130e-04
## C150_4       3.753202e-03 -3.535197e-03 -7.818610e-04  2.391049e-04
## PFTFTUG1_EF -1.163898e-03  6.136038e-04  7.842150e-04 -5.159151e-04
## RET_FT4      3.028595e-03 -1.130038e-03  2.091550e-04  6.617733e-05
## PCTFLOAN    -1.420587e-03 -5.309695e-03 -9.334880e-04  4.543542e-06
##                  UGDS_NRA     UGDS_UNKN      PPTUG_EF      NPT4_PUB
## UNITID      -3.812806e+02 -3.816534e+02 -2.971123e+03  8.555903e+06
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -4.671890e-04 -8.725182e-04  9.543694e-05  2.228791e+01
## SAT_AVG      1.260189e+00 -4.301800e-01 -4.229417e+00  1.546401e+05
## UGDS         7.681463e+01  1.569799e+01  8.946758e+01  5.346029e+06
## UGDS_WHITE  -9.054697e-04 -1.085878e-03 -1.006654e-02  2.601627e+02
## UGDS_BLACK  -3.026625e-04 -1.961427e-04 -3.448588e-04 -2.465739e+01
## UGDS_HISP    1.092018e-04 -1.232269e-05  8.220827e-03 -2.043260e+02
## UGDS_ASIAN   4.981175e-04  7.089872e-05  9.672637e-04  7.956598e+00
## UGDS_AIAN   -2.098941e-04 -2.340234e-04  6.569355e-04 -5.032745e+01
## UGDS_NHPI    2.475399e-05 -5.262125e-05  9.753696e-05 -1.792213e+01
## UGDS_2MOR    1.255937e-04  9.915596e-06  2.580145e-04  5.157079e+00
## UGDS_NRA     6.214688e-04  3.896061e-05 -1.120198e-03  2.182463e+01
## UGDS_UNKN    3.896061e-05  1.461287e-03  1.331121e-03  2.137406e+00
## PPTUG_EF    -1.120198e-03  1.331121e-03  5.591984e-02 -4.947463e+02
## NPT4_PUB     2.182463e+01  2.137406e+00 -4.947463e+02  2.180583e+07
## NPT4_PRIV              NA            NA            NA            NA
## COSTT4_A     4.396388e+01  2.642081e+00 -6.629519e+02  2.042028e+07
## TUITFTE      2.794397e+01  6.592411e-01 -3.994381e+02  1.121518e+07
## INEXPFTE     1.624281e+01 -8.017755e+00 -4.640903e+02  6.239927e+06
## PFTFAC       1.256147e-03 -2.140569e-04 -2.557631e-02  2.924302e+02
## PCTPELL     -7.846350e-04 -9.678444e-04 -7.516323e-03 -8.278810e+01
## C150_4       1.634943e-03 -6.543867e-04 -1.773768e-02  4.508953e+02
## PFTFTUG1_EF  9.330706e-04 -1.056923e-03 -3.289604e-02  3.593479e+02
## RET_FT4      9.719275e-04 -3.378427e-04 -7.870056e-03  1.611303e+02
## PCTFLOAN     7.577333e-04  1.666833e-04 -2.711538e-02  7.296435e+02
##             NPT4_PRIV      COSTT4_A       TUITFTE      INEXPFTE
## UNITID             NA -7.820823e+06  1.851754e+07  5.311294e+07
## CONTROL            NA  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE           NA -1.032139e+02 -1.018153e+01 -1.510772e+02
## SAT_AVG            NA  2.261949e+05  2.279867e+05  2.410387e+05
## UGDS               NA  1.114200e+07  6.336576e+06 -1.806406e+06
## UGDS_WHITE         NA  1.699173e+02  1.879837e+02  5.803787e+01
## UGDS_BLACK         NA -3.620696e+01 -6.069906e+01 -4.392371e+01
## UGDS_HISP          NA -1.694033e+02 -1.354007e+02 -8.083123e+01
## UGDS_ASIAN         NA  5.245991e+01  2.646566e+01  5.022575e+01
## UGDS_AIAN          NA -5.323768e+01 -4.336759e+01  1.726056e+01
## UGDS_NHPI          NA -2.352689e+01 -6.358758e+00 -5.031347e+00
## UGDS_2MOR          NA  1.339656e+01  2.775516e+00 -3.977466e+00
## UGDS_NRA           NA  4.396388e+01  2.794397e+01  1.624281e+01
## UGDS_UNKN          NA  2.642081e+00  6.592411e-01 -8.017755e+00
## PPTUG_EF           NA -6.629519e+02 -3.994381e+02 -4.640903e+02
## NPT4_PUB           NA  2.042028e+07  1.121518e+07  6.239927e+06
## NPT4_PRIV          NA            NA            NA            NA
## COSTT4_A           NA  2.456897e+07  1.348679e+07  8.950068e+06
## TUITFTE            NA  1.348679e+07  2.911632e+07  2.504544e+07
## INEXPFTE           NA  8.950068e+06  2.504544e+07  1.340642e+08
## PFTFAC             NA  3.681358e+02  2.977349e+02  3.706367e+02
## PCTPELL            NA -1.531094e+02 -9.895271e+01 -1.699340e+02
## C150_4             NA  5.956546e+02  4.226993e+02  3.750481e+02
## PFTFTUG1_EF        NA  4.447050e+02  3.233810e+02  2.118222e+02
## RET_FT4            NA  2.552317e+02  1.971872e+02  2.082404e+02
## PCTFLOAN           NA  7.172317e+02  4.816868e+02  3.850509e+02
##                    PFTFAC       PCTPELL        C150_4   PFTFTUG1_EF
## UNITID       1.567501e+03  1.985426e+03 -4.738395e+02  3.156513e+02
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE     1.630107e-03 -5.362106e-04 -5.241809e-03  1.184064e-03
## SAT_AVG      2.444422e+00 -9.470237e+00  1.425736e+01  5.269431e+00
## UGDS        -4.365770e+01 -2.844552e+02  7.574312e+02  1.814096e+02
## UGDS_WHITE   5.844623e-03 -6.598399e-03  1.182786e-02  4.703051e-03
## UGDS_BLACK  -7.702821e-04  1.039038e-02 -1.046351e-02 -1.083308e-03
## UGDS_HISP   -6.623997e-03 -1.385046e-03 -2.019975e-03 -3.213946e-03
## UGDS_ASIAN  -1.241610e-03 -1.894008e-03  3.753202e-03 -1.163898e-03
## UGDS_AIAN    1.389657e-03  1.189288e-03 -3.535197e-03  6.136038e-04
## UGDS_NHPI    2.952458e-04  9.818011e-04 -7.818610e-04  7.842150e-04
## UGDS_2MOR    6.410420e-05 -9.317130e-04  2.391049e-04 -5.159151e-04
## UGDS_NRA     1.256147e-03 -7.846350e-04  1.634943e-03  9.330706e-04
## UGDS_UNKN   -2.140569e-04 -9.678444e-04 -6.543867e-04 -1.056923e-03
## PPTUG_EF    -2.557631e-02 -7.516323e-03 -1.773768e-02 -3.289604e-02
## NPT4_PUB     2.924302e+02 -8.278810e+01  4.508953e+02  3.593479e+02
## NPT4_PRIV              NA            NA            NA            NA
## COSTT4_A     3.681358e+02 -1.531094e+02  5.956546e+02  4.447050e+02
## TUITFTE      2.977349e+02 -9.895271e+01  4.226993e+02  3.233810e+02
## INEXPFTE     3.706367e+02 -1.699340e+02  3.750481e+02  2.118222e+02
## PFTFAC       7.795924e-02 -9.690150e-05  5.839147e-03  1.643322e-02
## PCTPELL     -9.690150e-05  2.886076e-02 -1.389922e-02  2.801677e-03
## C150_4       5.839147e-03 -1.389922e-02  3.231275e-02  1.513416e-02
## PFTFTUG1_EF  1.643322e-02  2.801677e-03  1.513416e-02  4.096281e-02
## RET_FT4      2.286057e-03 -6.631786e-03  1.640806e-02  7.702755e-03
## PCTFLOAN     1.963037e-02  1.051458e-02  4.159769e-03  1.932124e-02
##                   RET_FT4      PCTFLOAN
## UNITID      -1.979873e+02  1.433992e+03
## CONTROL      0.000000e+00  0.000000e+00
## ADM_RATE    -4.300130e-03  1.566870e-03
## SAT_AVG      7.840027e+00 -6.513858e+00
## UGDS         4.918125e+02  9.105230e+01
## UGDS_WHITE   4.100246e-04  1.582585e-02
## UGDS_BLACK  -5.770553e-03  5.410460e-03
## UGDS_HISP    2.552484e-03 -1.450111e-02
## UGDS_ASIAN   3.028595e-03 -1.420587e-03
## UGDS_AIAN   -1.130038e-03 -5.309695e-03
## UGDS_NHPI    2.091550e-04 -9.334880e-04
## UGDS_2MOR    6.617733e-05  4.543542e-06
## UGDS_NRA     9.719275e-04  7.577333e-04
## UGDS_UNKN   -3.378427e-04  1.666833e-04
## PPTUG_EF    -7.870056e-03 -2.711538e-02
## NPT4_PUB     1.611303e+02  7.296435e+02
## NPT4_PRIV              NA            NA
## COSTT4_A     2.552317e+02  7.172317e+02
## TUITFTE      1.971872e+02  4.816868e+02
## INEXPFTE     2.082404e+02  3.850509e+02
## PFTFAC       2.286057e-03  1.963037e-02
## PCTPELL     -6.631786e-03  1.051458e-02
## C150_4       1.640806e-02  4.159769e-03
## PFTFTUG1_EF  7.702755e-03  1.932124e-02
## RET_FT4      1.367290e-02 -2.793926e-03
## PCTFLOAN    -2.793926e-03  6.593408e-02
covmatrix2
##                    UNITID CONTROL      ADM_RATE       SAT_AVG
## UNITID       1.729389e+13       0  1.389662e+03 -6.024547e+03
## CONTROL      0.000000e+00       0  0.000000e+00  0.000000e+00
## ADM_RATE     1.389662e+03       0  4.536895e-02 -1.190873e+01
## SAT_AVG     -6.024547e+03       0 -1.190873e+01  2.083891e+04
## UGDS        -4.606384e+07       0 -1.107615e+02  1.557286e+05
## UGDS_WHITE  -3.710665e+03       0  1.274632e-02  5.106529e+00
## UGDS_BLACK   1.323914e+03       0 -3.006599e-03 -1.160736e+01
## UGDS_HISP    3.782066e+03       0 -2.319609e-03 -1.266250e-01
## UGDS_ASIAN  -1.053227e+01       0 -3.135088e-03  4.317976e+00
## UGDS_AIAN    2.609302e+02       0 -8.715762e-05 -1.939833e-01
## UGDS_NHPI    1.459451e+02       0 -5.079462e-05 -1.009831e-01
## UGDS_2MOR   -4.300747e+02       0 -9.704476e-04  1.023550e+00
## UGDS_NRA    -7.783334e+02       0 -2.937042e-03  2.752199e+00
## UGDS_UNKN   -5.638965e+02       0 -2.404558e-04 -1.171670e+00
## PPTUG_EF     2.000852e+03       0  1.581536e-03 -6.234855e+00
## NPT4_PUB               NA      NA            NA            NA
## NPT4_PRIV   -2.000964e+08       0 -1.788793e+02  3.203899e+05
## COSTT4_A    -4.371317e+08       0 -8.001455e+02  1.113885e+06
## TUITFTE      1.947793e+07       0 -4.044905e+02  5.173568e+05
## INEXPFTE    -3.382833e+07       0 -8.531035e+02  1.032820e+06
## PFTFAC      -2.147922e+03       0 -3.387767e-03  7.623504e+00
## PCTPELL      6.158432e+03       0  5.326634e-03 -1.630479e+01
## C150_4      -2.347755e+03       0 -1.325186e-02  2.046047e+01
## PFTFTUG1_EF -1.968755e+03       0 -7.776027e-03  1.271935e+01
## RET_FT4     -1.164202e+03       0 -5.604484e-03  1.333383e+01
## PCTFLOAN    -4.799743e+03       0  2.975208e-03 -1.627136e+01
##                      UGDS    UGDS_WHITE    UGDS_BLACK     UGDS_HISP
## UNITID      -4.606384e+07 -3.710665e+03  1.323914e+03  3.782066e+03
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -1.107615e+02  1.274632e-02 -3.006599e-03 -2.319609e-03
## SAT_AVG      1.557286e+05  5.106529e+00 -1.160736e+01 -1.266250e-01
## UGDS         9.331219e+06 -2.059421e+01 -4.018257e+01  1.142529e+01
## UGDS_WHITE  -2.059421e+01  7.755369e-02 -2.965038e-02 -3.265294e-02
## UGDS_BLACK  -4.018257e+01 -2.965038e-02  4.140457e-02 -5.531855e-03
## UGDS_HISP    1.142529e+01 -3.265294e-02 -5.531855e-03  4.294322e-02
## UGDS_ASIAN   2.103326e+01 -4.098247e-03 -1.783743e-03 -1.636133e-04
## UGDS_AIAN   -9.410536e+00 -2.588628e-03 -7.082901e-04 -6.828854e-04
## UGDS_NHPI   -1.799093e+00 -5.698056e-04 -1.927936e-04 -4.221583e-05
## UGDS_2MOR    9.216479e+00 -1.392742e-04 -5.953970e-04 -4.574627e-04
## UGDS_NRA     1.593747e+01 -3.803603e-03 -1.947165e-03 -1.252820e-03
## UGDS_UNKN    1.954116e+01 -2.297023e-03 -5.703675e-04 -1.778657e-03
## PPTUG_EF    -3.963589e+00 -6.997340e-03  6.105967e-03  2.029921e-03
## NPT4_PUB               NA            NA            NA            NA
## NPT4_PRIV    5.167513e+06  2.586921e+02 -1.973060e+02 -4.058424e+02
## COSTT4_A     1.043862e+07  5.887293e+02 -6.333163e+02 -6.044283e+02
## TUITFTE      3.227969e+06 -9.716158e+01  3.764037e+01 -2.030514e+02
## INEXPFTE     3.532012e+06  4.865996e+01 -1.438109e+02 -2.028240e+02
## PFTFAC       2.394198e+01  7.097292e-03 -1.420142e-03 -3.236248e-03
## PCTPELL     -1.228868e+02 -2.380767e-02  1.714417e-02  1.453299e-02
## C150_4       1.312989e+02  9.853973e-03 -1.221938e-02 -4.649648e-03
## PFTFTUG1_EF  7.350802e+01  4.431194e-03 -5.915548e-03 -6.838199e-04
## RET_FT4      9.572951e+01  7.280116e-03 -9.843601e-03 -1.349271e-03
## PCTFLOAN    -1.627088e+01  1.903675e-03  1.392197e-02 -1.018841e-02
##                UGDS_ASIAN     UGDS_AIAN     UGDS_NHPI     UGDS_2MOR
## UNITID      -1.053227e+01  2.609302e+02  1.459451e+02 -4.300747e+02
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -3.135088e-03 -8.715762e-05 -5.079462e-05 -9.704476e-04
## SAT_AVG      4.317976e+00 -1.939833e-01 -1.009831e-01  1.023550e+00
## UGDS         2.103326e+01 -9.410536e+00 -1.799093e+00  9.216479e+00
## UGDS_WHITE  -4.098247e-03 -2.588628e-03 -5.698056e-04 -1.392742e-04
## UGDS_BLACK  -1.783743e-03 -7.082901e-04 -1.927936e-04 -5.953970e-04
## UGDS_HISP   -1.636133e-04 -6.828854e-04 -4.221583e-05 -4.574627e-04
## UGDS_ASIAN   4.632460e-03 -2.390501e-04  1.194368e-04  3.545936e-04
## UGDS_AIAN   -2.390501e-04  4.698595e-03  2.420734e-06 -9.824162e-05
## UGDS_NHPI    1.194368e-04  2.420734e-06  6.966427e-04  5.561508e-05
## UGDS_2MOR    3.545936e-04 -9.824162e-05  5.561508e-05  7.657043e-04
## UGDS_NRA     1.301689e-03 -2.353237e-04 -3.241483e-05  1.630202e-04
## UGDS_UNKN   -9.591836e-06 -1.154609e-04 -2.626496e-05  2.178079e-05
## PPTUG_EF    -1.149184e-03  3.236805e-04  8.230183e-05 -4.914570e-04
## NPT4_PUB               NA            NA            NA            NA
## NPT4_PRIV    1.125215e+02 -6.563269e+01 -3.867938e+00  6.443584e+01
## COSTT4_A     2.663787e+02 -1.372005e+02 -2.207545e+01  1.342530e+02
## TUITFTE      9.646182e+01 -6.679439e+01 -1.023563e+01  8.164403e+01
## INEXPFTE     1.735125e+02 -1.572635e+01 -7.209269e+00  6.211886e+01
## PFTFAC      -4.979777e-04  1.543920e-04 -4.781543e-05 -8.385646e-05
## PCTPELL     -2.603472e-03  1.850532e-03  3.678032e-04 -1.218142e-03
## C150_4       4.144713e-03 -1.140529e-03  2.905697e-04  1.400528e-03
## PFTFTUG1_EF  1.388544e-03 -5.606137e-04 -3.039270e-04  8.282901e-04
## RET_FT4      2.794559e-03 -1.143036e-03 -2.770611e-04  6.279306e-04
## PCTFLOAN    -2.502309e-03 -1.655861e-03 -3.314764e-04  8.719972e-04
##                  UGDS_NRA     UGDS_UNKN      PPTUG_EF NPT4_PUB
## UNITID      -7.783334e+02 -5.638965e+02  2.000852e+03       NA
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00       NA
## ADM_RATE    -2.937042e-03 -2.404558e-04  1.581536e-03       NA
## SAT_AVG      2.752199e+00 -1.171670e+00 -6.234855e+00       NA
## UGDS         1.593747e+01  1.954116e+01 -3.963589e+00       NA
## UGDS_WHITE  -3.803603e-03 -2.297023e-03 -6.997340e-03       NA
## UGDS_BLACK  -1.947165e-03 -5.703675e-04  6.105967e-03       NA
## UGDS_HISP   -1.252820e-03 -1.778657e-03  2.029921e-03       NA
## UGDS_ASIAN   1.301689e-03 -9.591836e-06 -1.149184e-03       NA
## UGDS_AIAN   -2.353237e-04 -1.154609e-04  3.236805e-04       NA
## UGDS_NHPI   -3.241483e-05 -2.626496e-05  8.230183e-05       NA
## UGDS_2MOR    1.630202e-04  2.178079e-05 -4.914570e-04       NA
## UGDS_NRA     5.919008e-03  7.906814e-06 -1.997066e-03       NA
## UGDS_UNKN    7.906814e-06  4.908971e-03  2.093184e-03       NA
## PPTUG_EF    -1.997066e-03  2.093184e-03  4.632924e-02       NA
## NPT4_PUB               NA            NA            NA       NA
## NPT4_PRIV    1.272409e+02  1.112608e+02 -2.350124e+02       NA
## COSTT4_A     2.602727e+02  1.501018e+02 -9.195262e+02       NA
## TUITFTE      8.786793e+01  7.008077e+01  5.113895e+02       NA
## INEXPFTE     1.171903e+02 -2.900858e+01  7.483286e+01       NA
## PFTFAC      -7.298864e-04 -1.491022e-03 -9.203744e-03       NA
## PCTPELL     -4.989582e-03 -1.530720e-03  3.912476e-03       NA
## C150_4       2.895213e-03 -7.973277e-04 -1.208337e-02       NA
## PFTFTUG1_EF  2.382618e-03 -1.567152e-03 -3.038821e-02       NA
## RET_FT4      2.456673e-03 -5.466105e-04 -7.911504e-03       NA
## PCTFLOAN    -3.886695e-03  2.487782e-03  2.890825e-03       NA
##                 NPT4_PRIV      COSTT4_A       TUITFTE      INEXPFTE
## UNITID      -2.000964e+08 -4.371317e+08  1.947793e+07 -3.382833e+07
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -1.788793e+02 -8.001455e+02 -4.044905e+02 -8.531035e+02
## SAT_AVG      3.203899e+05  1.113885e+06  5.173568e+05  1.032820e+06
## UGDS         5.167513e+06  1.043862e+07  3.227969e+06  3.532012e+06
## UGDS_WHITE   2.586921e+02  5.887293e+02 -9.716158e+01  4.865996e+01
## UGDS_BLACK  -1.973060e+02 -6.333163e+02  3.764037e+01 -1.438109e+02
## UGDS_HISP   -4.058424e+02 -6.044283e+02 -2.030514e+02 -2.028240e+02
## UGDS_ASIAN   1.125215e+02  2.663787e+02  9.646182e+01  1.735125e+02
## UGDS_AIAN   -6.563269e+01 -1.372005e+02 -6.679439e+01 -1.572635e+01
## UGDS_NHPI   -3.867938e+00 -2.207545e+01 -1.023563e+01 -7.209269e+00
## UGDS_2MOR    6.443584e+01  1.342530e+02  8.164403e+01  6.211886e+01
## UGDS_NRA     1.272409e+02  2.602727e+02  8.786793e+01  1.171903e+02
## UGDS_UNKN    1.112608e+02  1.501018e+02  7.008077e+01 -2.900858e+01
## PPTUG_EF    -2.350124e+02 -9.195262e+02  5.113895e+02  7.483286e+01
## NPT4_PUB               NA            NA            NA            NA
## NPT4_PRIV    5.873135e+07  7.961180e+07  3.802106e+07  1.986666e+07
## COSTT4_A     7.961180e+07  1.844518e+08  7.140962e+07  6.515278e+07
## TUITFTE      3.802106e+07  7.140962e+07  9.531392e+08  5.429300e+08
## INEXPFTE     1.986666e+07  6.515278e+07  5.429300e+08  4.131702e+08
## PFTFAC      -7.520620e+01  3.165501e+02  2.949318e+02  5.895843e+02
## PCTPELL     -8.397928e+02 -1.882063e+03 -8.968566e+02 -8.973091e+02
## C150_4       7.086510e+02  1.800918e+03  7.315198e+02  9.611969e+02
## PFTFTUG1_EF  4.240169e+02  1.497041e+03  5.190187e+02  6.817941e+02
## RET_FT4      3.445869e+02  1.051291e+03  4.255470e+02  5.632499e+02
## PCTFLOAN     5.262233e+02  4.206266e+02 -2.434516e+02 -6.885527e+02
##                    PFTFAC       PCTPELL        C150_4   PFTFTUG1_EF
## UNITID      -2.147922e+03  6.158432e+03 -2.347755e+03 -1.968755e+03
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -3.387767e-03  5.326634e-03 -1.325186e-02 -7.776027e-03
## SAT_AVG      7.623504e+00 -1.630479e+01  2.046047e+01  1.271935e+01
## UGDS         2.394198e+01 -1.228868e+02  1.312989e+02  7.350802e+01
## UGDS_WHITE   7.097292e-03 -2.380767e-02  9.853973e-03  4.431194e-03
## UGDS_BLACK  -1.420142e-03  1.714417e-02 -1.221938e-02 -5.915548e-03
## UGDS_HISP   -3.236248e-03  1.453299e-02 -4.649648e-03 -6.838199e-04
## UGDS_ASIAN  -4.979777e-04 -2.603472e-03  4.144713e-03  1.388544e-03
## UGDS_AIAN    1.543920e-04  1.850532e-03 -1.140529e-03 -5.606137e-04
## UGDS_NHPI   -4.781543e-05  3.678032e-04  2.905697e-04 -3.039270e-04
## UGDS_2MOR   -8.385646e-05 -1.218142e-03  1.400528e-03  8.282901e-04
## UGDS_NRA    -7.298864e-04 -4.989582e-03  2.895213e-03  2.382618e-03
## UGDS_UNKN   -1.491022e-03 -1.530720e-03 -7.973277e-04 -1.567152e-03
## PPTUG_EF    -9.203744e-03  3.912476e-03 -1.208337e-02 -3.038821e-02
## NPT4_PUB               NA            NA            NA            NA
## NPT4_PRIV   -7.520620e+01 -8.397928e+02  7.086510e+02  4.240169e+02
## COSTT4_A     3.165501e+02 -1.882063e+03  1.800918e+03  1.497041e+03
## TUITFTE      2.949318e+02 -8.968566e+02  7.315198e+02  5.190187e+02
## INEXPFTE     5.895843e+02 -8.973091e+02  9.611969e+02  6.817941e+02
## PFTFAC       8.264291e-02 -7.665825e-03  1.046738e-02  1.391281e-02
## PCTPELL     -7.665825e-03  4.616285e-02 -2.442826e-02 -1.257610e-02
## C150_4       1.046738e-02 -2.442826e-02  4.577030e-02  2.076359e-02
## PFTFTUG1_EF  1.391281e-02 -1.257610e-02  2.076359e-02  6.132454e-02
## RET_FT4      6.734007e-03 -1.615475e-02  1.968018e-02  1.508620e-02
## PCTFLOAN    -4.350305e-03  9.849093e-03 -5.069604e-03 -4.878319e-03
##                   RET_FT4      PCTFLOAN
## UNITID      -1.164202e+03 -4.799743e+03
## CONTROL      0.000000e+00  0.000000e+00
## ADM_RATE    -5.604484e-03  2.975208e-03
## SAT_AVG      1.333383e+01 -1.627136e+01
## UGDS         9.572951e+01 -1.627088e+01
## UGDS_WHITE   7.280116e-03  1.903675e-03
## UGDS_BLACK  -9.843601e-03  1.392197e-02
## UGDS_HISP   -1.349271e-03 -1.018841e-02
## UGDS_ASIAN   2.794559e-03 -2.502309e-03
## UGDS_AIAN   -1.143036e-03 -1.655861e-03
## UGDS_NHPI   -2.770611e-04 -3.314764e-04
## UGDS_2MOR    6.279306e-04  8.719972e-04
## UGDS_NRA     2.456673e-03 -3.886695e-03
## UGDS_UNKN   -5.466105e-04  2.487782e-03
## PPTUG_EF    -7.911504e-03  2.890825e-03
## NPT4_PUB               NA            NA
## NPT4_PRIV    3.445869e+02  5.262233e+02
## COSTT4_A     1.051291e+03  4.206266e+02
## TUITFTE      4.255470e+02 -2.434516e+02
## INEXPFTE     5.632499e+02 -6.885527e+02
## PFTFAC       6.734007e-03 -4.350305e-03
## PCTPELL     -1.615475e-02  9.849093e-03
## C150_4       1.968018e-02 -5.069604e-03
## PFTFTUG1_EF  1.508620e-02 -4.878319e-03
## RET_FT4      2.820645e-02 -1.052766e-02
## PCTFLOAN    -1.052766e-02  6.508525e-02
covmatrix3
##                    UNITID CONTROL      ADM_RATE       SAT_AVG
## UNITID       7.395282e+13       0 -1.831698e+02  1.350623e+07
## CONTROL      0.000000e+00       0  0.000000e+00  0.000000e+00
## ADM_RATE    -1.831698e+02       0  3.018528e-02 -5.813080e+00
## SAT_AVG      1.350623e+07       0 -5.813080e+00  1.678867e+04
## UGDS        -6.040104e+06       0 -4.787506e+01 -1.404658e+05
## UGDS_WHITE  -5.015770e+03       0 -1.894686e-03 -1.058373e+00
## UGDS_BLACK   3.061125e+03       0 -5.916370e-04 -1.020131e+01
## UGDS_HISP    6.054119e+02       0  2.906497e-03 -2.564013e+00
## UGDS_ASIAN   3.899984e+02       0 -1.526879e-03  2.280160e+00
## UGDS_AIAN   -1.766549e+02       0  2.675216e-04 -1.828133e-01
## UGDS_NHPI   -7.365140e+01       0  1.754811e-04 -5.924667e-02
## UGDS_2MOR    2.288033e+02       0  3.023800e-04  1.649580e+00
## UGDS_NRA     2.123741e+02       0 -4.605336e-04  7.616167e+00
## UGDS_UNKN    8.060504e+02       0  8.215073e-04  2.514260e+00
## PPTUG_EF     1.427122e+03       0 -3.562037e-03 -1.481329e+01
## NPT4_PUB               NA      NA            NA            NA
## NPT4_PRIV    5.881774e+07       0 -2.635406e+02  7.930320e+04
## COSTT4_A    -3.305798e+07       0 -2.823340e+02  1.013990e+05
## TUITFTE      5.972800e+07       0 -5.482883e+01  3.643763e+05
## INEXPFTE    -1.238892e+07       0 -7.029751e+01  3.671487e+05
## PFTFAC      -6.454437e+03       0 -3.889060e-03  1.503040e+01
## PCTPELL     -1.270223e+03       0  6.797696e-03 -8.236240e+00
## C150_4      -3.097190e+03       0 -2.131956e-03  1.437395e+01
## PFTFTUG1_EF -1.142483e+03       0  1.694741e-02  1.570487e+01
## RET_FT4     -3.959028e+03       0 -8.682872e-03  1.130607e+01
## PCTFLOAN    -3.952153e+02       0 -9.220602e-04 -7.846287e+00
##                      UGDS    UGDS_WHITE    UGDS_BLACK     UGDS_HISP
## UNITID      -6.040104e+06 -5.015770e+03  3.061125e+03  6.054119e+02
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -4.787506e+01 -1.894686e-03 -5.916370e-04  2.906497e-03
## SAT_AVG     -1.404658e+05 -1.058373e+00 -1.020131e+01 -2.564013e+00
## UGDS         1.011364e+07 -3.493332e+01  1.742072e-02  1.141777e+00
## UGDS_WHITE  -3.493332e+01  8.337791e-02 -3.344426e-02 -3.631938e-02
## UGDS_BLACK   1.742072e-02 -3.344426e-02  6.089201e-02 -1.902799e-02
## UGDS_HISP    1.141777e+00 -3.631938e-02 -1.902799e-02  6.032735e-02
## UGDS_ASIAN  -2.534462e+00 -4.689344e-03 -2.840582e-03  6.762256e-05
## UGDS_AIAN   -1.088131e-01  4.826809e-04 -7.049658e-04 -1.546391e-04
## UGDS_NHPI    4.945693e-01 -4.181693e-04 -4.023105e-04 -5.576631e-05
## UGDS_2MOR    5.106683e+00 -3.071243e-06 -6.730626e-04 -9.452677e-04
## UGDS_NRA     1.872580e+00 -1.104809e-03 -6.023167e-04 -1.486824e-05
## UGDS_UNKN    2.923280e+01 -7.626129e-03 -3.052765e-03 -3.761066e-03
## PPTUG_EF     3.320511e+01 -1.022675e-03  4.049642e-03 -4.541317e-03
## NPT4_PUB               NA            NA            NA            NA
## NPT4_PRIV    9.374831e+05 -1.240066e+02  1.146384e+02 -2.180677e+02
## COSTT4_A    -1.054564e+06  1.366213e+02  1.071934e+02 -3.908326e+02
## TUITFTE      3.612887e+05  2.582911e+01  2.993496e+01 -2.307021e+02
## INEXPFTE    -5.252836e+05  7.644524e+01 -3.257419e+01 -1.296399e+02
## PFTFAC      -6.668619e+01  3.705677e-03 -8.937824e-03  3.498506e-03
## PCTPELL     -1.015440e+01 -1.429713e-02  1.086400e-02  7.576123e-03
## C150_4      -1.009311e+02  2.664676e-03 -9.138176e-03  8.380106e-03
## PFTFTUG1_EF -1.321671e+02  3.386934e-03 -1.067939e-03  3.722735e-03
## RET_FT4     -1.158528e+02  8.031208e-03 -1.197112e-02  3.612188e-03
## PCTFLOAN     3.295771e+00  7.311984e-03  8.454763e-03 -1.552422e-02
##                UGDS_ASIAN     UGDS_AIAN     UGDS_NHPI     UGDS_2MOR
## UNITID       3.899984e+02 -1.766549e+02 -7.365140e+01  2.288033e+02
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -1.526879e-03  2.675216e-04  1.754811e-04  3.023800e-04
## SAT_AVG      2.280160e+00 -1.828133e-01 -5.924667e-02  1.649580e+00
## UGDS        -2.534462e+00 -1.088131e-01  4.945693e-01  5.106683e+00
## UGDS_WHITE  -4.689344e-03  4.826809e-04 -4.181693e-04 -3.071243e-06
## UGDS_BLACK  -2.840582e-03 -7.049658e-04 -4.023105e-04 -6.730626e-04
## UGDS_HISP    6.762256e-05 -1.546391e-04 -5.576631e-05 -9.452677e-04
## UGDS_ASIAN   7.464686e-03 -6.426224e-05  2.750342e-04 -3.839737e-05
## UGDS_AIAN   -6.426224e-05  4.743664e-04  1.114916e-05  5.467154e-05
## UGDS_NHPI    2.750342e-04  1.114916e-05  5.126742e-04  6.369530e-05
## UGDS_2MOR   -3.839737e-05  5.467154e-05  6.369530e-05  1.109162e-03
## UGDS_NRA     2.793003e-04 -2.517022e-05 -6.670523e-06 -5.444729e-05
## UGDS_UNKN   -4.353933e-04 -6.910826e-05  2.305510e-05  5.001657e-04
## PPTUG_EF     1.412896e-03 -3.013514e-04  2.529098e-06  2.556290e-04
## NPT4_PUB               NA            NA            NA            NA
## NPT4_PRIV    6.730717e+00 -1.599170e+00  2.583758e+00  3.388250e+01
## COSTT4_A     6.871751e+01  5.013602e+00 -5.355119e-02  1.402869e+01
## TUITFTE      4.957734e+00 -5.818548e-01  8.882462e+00  2.083927e+01
## INEXPFTE    -1.961725e+00 -2.256223e+00  6.679664e+00  9.212449e+00
## PFTFAC      -1.258733e-06  4.505304e-04 -1.125309e-04  2.065476e-04
## PCTPELL     -2.458619e-03  1.131439e-04 -1.515557e-04 -1.542680e-04
## C150_4       2.282545e-03 -7.231991e-05  3.514270e-04 -2.985267e-04
## PFTFTUG1_EF -1.301617e-03  3.528656e-05 -8.173915e-04  1.067049e-04
## RET_FT4      1.901256e-03  8.727148e-05  2.451845e-04 -9.552644e-05
## PCTFLOAN    -4.525142e-03  7.705691e-05 -9.339149e-05  9.465330e-04
##                  UGDS_NRA     UGDS_UNKN      PPTUG_EF NPT4_PUB
## UNITID       2.123741e+02  8.060504e+02  1.427122e+03       NA
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00       NA
## ADM_RATE    -4.605336e-04  8.215073e-04 -3.562037e-03       NA
## SAT_AVG      7.616167e+00  2.514260e+00 -1.481329e+01       NA
## UGDS         1.872580e+00  2.923280e+01  3.320511e+01       NA
## UGDS_WHITE  -1.104809e-03 -7.626129e-03 -1.022675e-03       NA
## UGDS_BLACK  -6.023167e-04 -3.052765e-03  4.049642e-03       NA
## UGDS_HISP   -1.486824e-05 -3.761066e-03 -4.541317e-03       NA
## UGDS_ASIAN   2.793003e-04 -4.353933e-04  1.412896e-03       NA
## UGDS_AIAN   -2.517022e-05 -6.910826e-05 -3.013514e-04       NA
## UGDS_NHPI   -6.670523e-06  2.305510e-05  2.529098e-06       NA
## UGDS_2MOR   -5.444729e-05  5.001657e-04  2.556290e-04       NA
## UGDS_NRA     1.551995e-03 -1.969338e-05  8.796026e-05       NA
## UGDS_UNKN   -1.969338e-05  1.447376e-02  5.664905e-05       NA
## PPTUG_EF     8.796026e-05  5.664905e-05  5.709555e-02       NA
## NPT4_PUB               NA            NA            NA       NA
## NPT4_PRIV    4.199023e+01  1.438584e+02  9.444090e+01       NA
## COSTT4_A     5.864873e+01  6.722633e-01  7.811069e+01       NA
## TUITFTE      4.763389e+01  9.350436e+01  1.735878e+02       NA
## INEXPFTE     2.367812e+01  5.031074e+01  2.332564e+01       NA
## PFTFAC       1.134849e-03 -4.440726e-05 -1.706967e-02       NA
## PCTPELL     -1.215527e-03 -9.672852e-05 -3.937273e-03       NA
## C150_4       2.738086e-04 -4.443238e-03 -8.996381e-03       NA
## PFTFTUG1_EF -7.699709e-05 -3.988181e-03 -4.286071e-02       NA
## RET_FT4      1.845032e-03 -3.655752e-03 -1.335981e-02       NA
## PCTFLOAN    -9.316870e-04  4.371320e-03  1.270867e-03       NA
##                 NPT4_PRIV      COSTT4_A       TUITFTE      INEXPFTE
## UNITID       5.881774e+07 -3.305798e+07  5.972800e+07 -1.238892e+07
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -2.635406e+02 -2.823340e+02 -5.482883e+01 -7.029751e+01
## SAT_AVG      7.930320e+04  1.013990e+05  3.643763e+05  3.671487e+05
## UGDS         9.374831e+05 -1.054564e+06  3.612887e+05 -5.252836e+05
## UGDS_WHITE  -1.240066e+02  1.366213e+02  2.582911e+01  7.644524e+01
## UGDS_BLACK   1.146384e+02  1.071934e+02  2.993496e+01 -3.257419e+01
## UGDS_HISP   -2.180677e+02 -3.908326e+02 -2.307021e+02 -1.296399e+02
## UGDS_ASIAN   6.730717e+00  6.871751e+01  4.957734e+00 -1.961725e+00
## UGDS_AIAN   -1.599170e+00  5.013602e+00 -5.818548e-01 -2.256223e+00
## UGDS_NHPI    2.583758e+00 -5.355119e-02  8.882462e+00  6.679664e+00
## UGDS_2MOR    3.388250e+01  1.402869e+01  2.083927e+01  9.212449e+00
## UGDS_NRA     4.199023e+01  5.864873e+01  4.763389e+01  2.367812e+01
## UGDS_UNKN    1.438584e+02  6.722633e-01  9.350436e+01  5.031074e+01
## PPTUG_EF     9.444090e+01  7.811069e+01  1.735878e+02  2.332564e+01
## NPT4_PUB               NA            NA            NA            NA
## NPT4_PRIV    4.742631e+07  3.652982e+07  2.180722e+07  4.297221e+06
## COSTT4_A     3.652982e+07  3.643841e+07  1.813643e+07  5.311617e+06
## TUITFTE      2.180722e+07  1.813643e+07  7.022704e+07  2.692307e+07
## INEXPFTE     4.297221e+06  5.311617e+06  2.692307e+07  2.378391e+07
## PFTFAC      -2.505588e+01  1.523769e+02  2.607751e+01  2.548895e+02
## PCTPELL     -1.326173e+02 -3.559557e+02 -1.916434e+02 -1.097408e+02
## C150_4       1.999895e+02  1.954150e+02  8.835031e+01  1.082532e+02
## PFTFTUG1_EF -3.757500e+01 -8.427464e+01  2.007595e+02 -8.561791e+01
## RET_FT4      2.950110e+02  2.920637e+02  2.260812e+02  8.775900e+01
## PCTFLOAN     5.772991e+02  2.539930e+02  3.373045e+02  3.263181e+01
##                    PFTFAC       PCTPELL        C150_4   PFTFTUG1_EF
## UNITID      -6.454437e+03 -1.270223e+03 -3.097190e+03 -1.142483e+03
## CONTROL      0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
## ADM_RATE    -3.889060e-03  6.797696e-03 -2.131956e-03  1.694741e-02
## SAT_AVG      1.503040e+01 -8.236240e+00  1.437395e+01  1.570487e+01
## UGDS        -6.668619e+01 -1.015440e+01 -1.009311e+02 -1.321671e+02
## UGDS_WHITE   3.705677e-03 -1.429713e-02  2.664676e-03  3.386934e-03
## UGDS_BLACK  -8.937824e-03  1.086400e-02 -9.138176e-03 -1.067939e-03
## UGDS_HISP    3.498506e-03  7.576123e-03  8.380106e-03  3.722735e-03
## UGDS_ASIAN  -1.258733e-06 -2.458619e-03  2.282545e-03 -1.301617e-03
## UGDS_AIAN    4.505304e-04  1.131439e-04 -7.231991e-05  3.528656e-05
## UGDS_NHPI   -1.125309e-04 -1.515557e-04  3.514270e-04 -8.173915e-04
## UGDS_2MOR    2.065476e-04 -1.542680e-04 -2.985267e-04  1.067049e-04
## UGDS_NRA     1.134849e-03 -1.215527e-03  2.738086e-04 -7.699709e-05
## UGDS_UNKN   -4.440726e-05 -9.672852e-05 -4.443238e-03 -3.988181e-03
## PPTUG_EF    -1.706967e-02 -3.937273e-03 -8.996381e-03 -4.286071e-02
## NPT4_PUB               NA            NA            NA            NA
## NPT4_PRIV   -2.505588e+01 -1.326173e+02  1.999895e+02 -3.757500e+01
## COSTT4_A     1.523769e+02 -3.559557e+02  1.954150e+02 -8.427464e+01
## TUITFTE      2.607751e+01 -1.916434e+02  8.835031e+01  2.007595e+02
## INEXPFTE     2.548895e+02 -1.097408e+02  1.082532e+02 -8.561791e+01
## PFTFAC       7.681149e-02 -7.948022e-03  1.605758e-02  9.990057e-04
## PCTPELL     -7.948022e-03  3.975721e-02 -2.823815e-03  1.193181e-02
## C150_4       1.605758e-02 -2.823815e-03  4.177170e-02  1.157788e-02
## PFTFTUG1_EF  9.990057e-04  1.193181e-02  1.157788e-02  9.410520e-02
## RET_FT4      1.481703e-02 -6.302667e-03  2.106522e-02  1.291551e-02
## PCTFLOAN    -4.795995e-03  2.206536e-02  2.240202e-05  1.934220e-03
##                   RET_FT4      PCTFLOAN
## UNITID      -3.959028e+03 -3.952153e+02
## CONTROL      0.000000e+00  0.000000e+00
## ADM_RATE    -8.682872e-03 -9.220602e-04
## SAT_AVG      1.130607e+01 -7.846287e+00
## UGDS        -1.158528e+02  3.295771e+00
## UGDS_WHITE   8.031208e-03  7.311984e-03
## UGDS_BLACK  -1.197112e-02  8.454763e-03
## UGDS_HISP    3.612188e-03 -1.552422e-02
## UGDS_ASIAN   1.901256e-03 -4.525142e-03
## UGDS_AIAN    8.727148e-05  7.705691e-05
## UGDS_NHPI    2.451845e-04 -9.339149e-05
## UGDS_2MOR   -9.552644e-05  9.465330e-04
## UGDS_NRA     1.845032e-03 -9.316870e-04
## UGDS_UNKN   -3.655752e-03  4.371320e-03
## PPTUG_EF    -1.335981e-02  1.270867e-03
## NPT4_PUB               NA            NA
## NPT4_PRIV    2.950110e+02  5.772991e+02
## COSTT4_A     2.920637e+02  2.539930e+02
## TUITFTE      2.260812e+02  3.373045e+02
## INEXPFTE     8.775900e+01  3.263181e+01
## PFTFAC       1.481703e-02 -4.795995e-03
## PCTPELL     -6.302667e-03  2.206536e-02
## C150_4       2.106522e-02  2.240202e-05
## PFTFTUG1_EF  1.291551e-02  1.934220e-03
## RET_FT4      7.748550e-02  1.649988e-04
## PCTFLOAN     1.649988e-04  6.270230e-02
library(ggplot2)
## 
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
## 
##     %+%, alpha
library(lm.beta)
library(psych)
library(QuantPsyc)
## Loading required package: boot
## 
## Attaching package: 'boot'
## The following object is masked from 'package:psych':
## 
##     logit
## Loading required package: MASS
## 
## Attaching package: 'QuantPsyc'
## The following object is masked from 'package:lm.beta':
## 
##     lm.beta
## The following object is masked from 'package:base':
## 
##     norm
reg1 <- lm(COSTT4_A ~ SAT_AVG, data=data2)
summary(reg1)
## 
## Call:
## lm(formula = COSTT4_A ~ SAT_AVG, data = data2)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -32053 -10000    942   9354  25867 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -22454.499   2520.612  -8.908   <2e-16 ***
## SAT_AVG         51.901      2.361  21.984   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11350 on 1296 degrees of freedom
##   (6405 observations deleted due to missingness)
## Multiple R-squared:  0.2716, Adjusted R-squared:  0.2711 
## F-statistic: 483.3 on 1 and 1296 DF,  p-value: < 2.2e-16
coefficients(reg1)
##  (Intercept)      SAT_AVG 
## -22454.49939     51.90104
confint(reg1, level=0.95)
##                   2.5 %       97.5 %
## (Intercept) -27399.4268 -17509.57199
## SAT_AVG         47.2695     56.53259
lm.beta(reg1)
##   SAT_AVG 
## 0.5211713
fitted(reg1)
##        1        2        4        5        6        9       10       11 
## 20467.66 34999.96 40812.87 21713.29 39048.24 29913.65 40605.27 38840.63 
##       13       24       27       33       35       37       38       40 
## 26436.28 30795.97 31574.49 28927.53 32301.10 30173.16 33079.62 30951.67 
##       42       47       51       52       53       54       57       58 
## 25709.67 38010.22 31937.79 35467.07 25813.47 19637.25 32041.60 28304.72 
##       65       83      116      123      129      135      138      139 
## 32249.20 36972.20 33235.32 28823.73 31937.79 35103.76 37491.21 23529.83 
##      141      142      145      147      148      157      158      159 
## 34013.84 29965.55 28927.53 31989.70 28668.03 36245.58 28875.63 42110.40 
##      172      175      176      187      189      211      216      224 
## 35259.46 32612.51 25813.47 28564.23 28875.63 31366.88 35778.47 28200.92 
##      227      228      229      233      234      235      237      238 
## 57732.61 35103.76 41591.39 23426.02 33287.22 29238.94 24775.45 30536.47 
##      240      241      242      243      244      245      246      247 
## 32249.20 22751.31 24983.05 26176.78 49272.74 41176.18 38165.92 46573.89 
##      248      249      251      252      275      277      278      284 
## 36089.88 45691.57 42577.51 37179.80 40345.76 31418.78 29031.34 51193.08 
##      308      331      344      351      353      367      369      378 
## 31885.89 29965.55 55397.07 23477.92 28719.93 24412.14 30173.16 26021.08 
##      387      393      408      411      423      441      442      446 
## 34792.35 40760.97 29187.04 37335.50 24360.24 25917.27 45016.86 29965.55 
##      448      455      456      461      464      465      472      489 
## 24048.84 30328.86 39048.24 41591.39 36453.19 53009.62 35155.66 35415.16 
##      490      493      495      499      501      507      511      520 
## 42058.50 28927.53 37335.50 29913.65 31418.78 45483.97 48130.92 30692.17 
##      525      527      531      536      537      541      559      560 
## 35103.76 28616.13 27889.51 37283.60 49168.94 42992.72 38529.23 32612.51 
##      568      573      574      576      583      585      596      598 
## 27111.00 32301.10 34065.74 40190.06 46729.59 36089.88 41435.69 30484.57 
##      605      606      613      620      623      629      636      637 
## 27889.51 28045.22 31159.28 35051.86 27941.41 28927.53 24204.54 30225.06 
##      643      653      664      671      673      675      678      684 
## 42214.20 29446.54 32716.31 21920.89 34844.25 27837.61 25917.27 28460.42 
##      686      692      693      696      698      699      702      703 
## 55033.76 23945.03 39515.35 21817.09 42525.61 36193.68 21609.49 44861.15 
##      704      705      714      715      717      718      726      727 
## 50933.58 34896.15 27474.30 26228.68 19222.04 28408.52 26332.48 39048.24 
##      730      734      736      738      739      741      742      746 
## 28097.12 37387.40 20363.86 26747.69 32456.80 32456.80 32716.31 25709.67 
##      747      749      754      755      758      796      805      806 
## 38581.13 34065.74 37076.00 41279.98 43615.53 46573.89 36349.38 25242.56 
##      807      811      835      836      839      846      849      853 
## 36868.39 33131.52 37854.51 25242.56 27630.01 34325.24 24204.54 22336.10 
##      855      857      862      868      869      870      874      878 
## 26851.49 32820.11 25657.77 22958.91 18962.53 29757.95 25138.76 22180.40 
##      883      885      888      891      894      896      901      902 
## 38944.44 28668.03 25294.46 25813.47 28200.92 38529.23 27370.50 48442.33 
##      904      906      907      908      909      910      911      912 
## 22855.11 50206.96 27889.51 36297.48 34584.75 32301.10 42318.00 22128.50 
##      918      919      924      925      929      930      931      933 
## 33391.02 31263.08 40086.26 29654.15 36660.79 16990.29 27785.71 28149.02 
##      935      936      937      940      941      944      945      947 
## 33650.53 21505.68 26903.39 29706.05 36401.28 27889.51 27941.41 30380.76 
##      949      950      952      953      954      968      969      972 
## 26851.49 28927.53 27266.70 26124.88 33079.62 29238.94 31626.39 32404.90 
##      973      974      979      981      987      989      994      997 
## 33391.02 25450.16 32145.40 31574.49 32820.11 29965.55 28875.63 37854.51 
##     1011     1013     1022     1031     1033     1034     1041     1046 
## 22699.41 55656.57 31055.48 29965.55 34065.74 32197.30 32353.00 31003.58 
##     1049     1050     1052     1053     1057     1059     1067     1080 
## 35934.17 31003.58 46366.28 42369.90 43252.22 35155.66 33598.63 33079.62 
##     1081     1082     1085     1091     1094     1096     1098     1099 
## 29757.95 35934.17 40449.57 27889.51 31937.79 25813.47 31833.99 31159.28 
##     1108     1109     1111     1113     1114     1117     1122     1130 
## 35934.17 30744.07 31003.58 53372.93 23737.43 34896.15 30692.17 29913.65 
##     1131     1132     1135     1137     1138     1150     1151     1156 
## 32041.60 30951.67 32768.21 29861.75 33650.53 32301.10 33079.62 33598.63 
##     1157     1160     1163     1164     1167     1169     1170     1171 
## 32664.41 35103.76 27889.51 45587.77 31937.79 32872.01 31522.59 40086.26 
##     1177     1181     1182     1183     1184     1187     1189     1191 
## 40501.47 36920.29 31055.48 35103.76 35155.66 34688.55 27837.61 31211.18 
##     1193     1194     1196     1197     1198     1199     1200     1201 
## 29550.35 29965.55 30380.76 27630.01 29498.45 24931.15 26021.08 26436.28 
##     1202     1203     1204     1205     1218     1219     1220     1228 
## 39722.95 25086.86 27318.60 26488.18 29446.54 31314.98 33650.53 52802.01 
##     1229     1231     1232     1235     1237     1238     1239     1240 
## 27370.50 27630.01 27318.60 45432.07 28460.42 29238.94 26488.18 36920.29 
##     1243     1244     1245     1246     1249     1252     1253     1257 
## 26488.18 38996.34 33494.83 37491.21 36089.88 29706.05 31885.89 34688.55 
##     1258     1259     1260     1264     1265     1266     1268     1270 
## 30951.67 37024.10 39826.75 34636.65 41850.89 26384.38 30380.76 29654.15 
##     1272     1273     1274     1286     1287     1289     1295     1296 
## 26228.68 27733.81 50103.16 36972.20 28927.53 37958.32 34013.84 37595.01 
##     1300     1301     1304     1305     1312     1316     1322     1323 
## 32820.11 31003.58 32041.60 34792.35 32041.60 35934.17 26851.49 24931.15 
##     1324     1330     1332     1333     1334     1340     1348     1352 
## 34636.65 32508.71 35674.67 27837.61 29446.54 27681.91 29913.65 30951.67 
##     1355     1365     1366     1369     1374     1375     1376     1382 
## 21713.29 36972.20 33391.02 32508.71 31003.58 29706.05 29965.55 29965.55 
##     1384     1388     1389     1390     1395     1396     1400     1401 
## 29550.35 29809.85 28304.72 31366.88 29861.75 36453.19 35674.67 35934.17 
##     1404     1405     1407     1412     1413     1416     1427     1428 
## 31470.68 27578.11 43096.52 31418.78 29861.75 34740.45 29965.55 23374.12 
##     1429     1430     1431     1435     1440     1441     1443     1448 
## 30536.47 36816.49 27681.91 36920.29 30951.67 32768.21 31833.99 27681.91 
##     1459     1462     1463     1465     1466     1476     1484     1486 
## 27733.81 28512.33 41383.78 27889.51 31885.89 35103.76 23529.83 22595.61 
##     1492     1493     1495     1499     1501     1502     1503     1504 
## 28771.83 37802.61 32041.60 28927.53 34844.25 36453.19 31003.58 33702.43 
##     1505     1506     1509     1511     1524     1525     1526     1528 
## 31055.48 31003.58 30847.87 29965.55 31003.58 24775.45 19377.74 33079.62 
##     1530     1531     1538     1540     1542     1547     1549     1550 
## 47196.70 31470.68 29446.54 46729.59 26903.39 24204.54 33494.83 30692.17 
##     1552     1556     1559     1571     1572     1573     1577     1578 
## 33235.32 27630.01 29342.74 25294.46 22543.71 33339.12 21868.99 23218.42 
##     1582     1591     1598     1599     1600     1601     1605     1606 
## 27733.81 52231.10 40501.47 45795.37 38010.22 21246.18 22907.01 31937.79 
##     1609     1615     1617     1619     1622     1624     1628     1629 
## 31937.79 39203.94 46210.58 33702.43 28927.53 34325.24 23581.73 52231.10 
##     1634     1636     1637     1640     1641     1647     1649     1650 
## 43563.63 22958.91 26903.39 30225.06 42266.10 49168.94 45016.86 48598.03 
##     1651     1661     1663     1666     1667     1668     1673     1674 
## 28979.43 26747.69 22024.69 25190.66 42110.40 34273.34 29654.15 30017.46 
##     1676     1681     1690     1692     1694     1698     1699     1701 
## 37802.61 55448.97 28097.12 33910.03 36972.20 40709.07 32041.60 33287.22 
##     1702     1703     1704     1714     1727     1731     1733     1734 
## 33442.92 55397.07 34896.15 23529.83 28252.82 51244.98 26643.89 18028.31 
##     1741     1743     1747     1749     1751     1753     1754     1755 
## 28616.13 38269.72 30744.07 30744.07 31989.70 51400.69 49687.95 35467.07 
##     1756     1757     1759     1760     1762     1763     1764     1767 
## 33442.92 29290.84 27526.21 52905.82 29290.84 29913.65 35934.17 34688.55 
##     1769     1770     1776     1780     1783     1785     1792     1795 
## 33650.53 34117.64 38892.53 32041.60 28927.53 29965.55 35155.66 30899.77 
##     1796     1799     1802     1805     1808     1812     1818     1820 
## 29965.55 41020.48 32093.50 34065.74 39048.24 41850.89 30899.77 36037.98 
##     1823     1824     1825     1826     1828     1829     1830     1831 
## 31989.70 19066.34 27993.31 49168.94 37646.91 42110.40 34896.15 29083.24 
##     1841     1844     1846     1847     1849     1854     1856     1860 
## 29965.55 29654.15 33079.62 25138.76 31003.58 31003.58 30744.07 31263.08 
##     1862     1868     1871     1879     1882     1883     1884     1887 
## 24775.45 33079.62 31003.58 33287.22 29965.55 33079.62 37024.10 50622.17 
##     1888     1891     1899     1909     1911     1918     1919     1921 
## 38062.12 35934.17 34688.55 47819.51 29965.55 43511.73 29757.95 34013.84 
##     1926     1927     1930     1935     1937     1939     1944     1947 
## 35155.66 37127.90 31989.70 32664.41 35155.66 27578.11 38736.83 29965.55 
##     1948     1949     1950     1951     1952     1953     1955     1958 
## 37491.21 32923.91 44601.65 30276.96 34948.05 26799.59 31107.38 28927.53 
##     1965     1968     1970     1977     1985     1988     1990     1991 
## 32041.60 22803.21 31003.58 27785.71 24827.35 38684.93 34532.85 28823.73 
##     1992     1993     1996     2000     2003     2005     2007     2010 
## 20363.86 35674.67 35986.08 16990.29 30951.67 22388.00 33598.63 31418.78 
##     2015     2018     2019     2025     2027     2030     2031     2036 
## 30173.16 32041.60 29965.55 34896.15 30432.66 28719.93 39048.24 32301.10 
##     2037     2049     2055     2060     2064     2067     2071     2075 
## 32145.40 33910.03 31418.78 36556.99 27889.51 28616.13 28927.53 38062.12 
##     2076     2077     2078     2084     2085     2087     2093     2096 
## 36141.78 44134.54 34896.15 41176.18 32093.50 33287.22 37958.32 41850.89 
##     2101     2102     2105     2110     2111     2112     2117     2118 
## 28927.53 39203.94 33079.62 32768.21 32041.60 34117.64 54255.24 34896.15 
##     2120     2121     2122     2128     2141     2142     2143     2144 
## 35363.26 36764.59 31626.39 36349.38 35934.17 36089.88 33339.12 25138.76 
##     2145     2150     2151     2155     2156     2157     2158     2159 
## 31055.48 28927.53 32041.60 32923.91 39826.75 32560.61 32768.21 33546.73 
##     2162     2164     2167     2169     2173     2174     2179     2185 
## 31989.70 34117.64 29965.55 32041.60 35882.27 37024.10 31003.58 27889.51 
##     2192     2193     2196     2202     2205     2215     2216     2217 
## 29446.54 33650.53 29965.55 52490.61 26799.59 34844.25 27630.01 29965.55 
##     2227     2238     2241     2243     2254     2259     2260     2261 
## 27474.30 19585.35 26851.49 25605.87 35570.87 26540.09 22699.41 31055.48 
##     2263     2264     2271     2273     2279     2280     2287     2294 
## 26591.99 34792.35 23737.43 24619.75 32301.10 28149.02 38165.92 54929.96 
##     2296     2298     2300     2301     2302     2305     2307     2309 
## 33702.43 30795.97 30744.07 40605.27 31263.08 24204.54 36349.38 21298.08 
##     2311     2312     2316     2319     2326     2331     2333     2335 
## 47404.31 33494.83 40501.47 28408.52 26072.98 26591.99 39463.45 32560.61 
##     2339     2353     2357     2360     2373     2393     2403     2407 
## 28616.13 34221.44 38010.22 32768.21 47248.60 33858.13 39567.25 48598.03 
##     2409     2412     2416     2417     2422     2425     2426     2427 
## 53840.03 22803.21 49584.15 51348.78 41643.29 33858.13 29706.05 36193.68 
##     2430     2431     2434     2437     2440     2442     2445     2450 
## 37750.71 27889.51 29187.04 34117.64 24256.44 31263.08 22803.21 33235.32 
##     2455     2462     2468     2469     2474     2481     2486     2487 
## 42629.41 49843.65 37076.00 35726.57 30588.37 46573.89 24983.05 33131.52 
##     2489     2496     2503     2504     2517     2520     2521     2526 
## 26851.49 34480.95 32820.11 21142.38 33183.42 30017.46 25865.37 27266.70 
##     2527     2535     2537     2541     2542     2543     2548     2552 
## 35518.97 47300.50 31522.59 33027.72 26332.48 24723.55 32249.20 27059.10 
##     2553     2561     2563     2565     2571     2572     2576     2581 
## 36764.59 48753.73 32508.71 41902.79 32872.01 26072.98 27266.70 36037.98 
##     2582     2583     2587     2590     2594     2597     2598     2599 
## 41954.70 31055.48 34169.54 34999.96 28512.33 23062.72 28512.33 23996.93 
##     2600     2601     2602     2603     2604     2605     2606     2607 
## 34532.85 44342.14 38010.22 42629.41 39463.45 34584.75 32353.00 26280.58 
##     2609     2610     2611     2612     2613     2615     2617     2618 
## 32353.00 40916.67 35778.47 33910.03 34948.05 34377.14 29187.04 31055.48 
##     2621     2624     2642     2644     2646     2647     2658     2664 
## 34948.05 38996.34 50362.66 30951.67 51244.98 32197.30 40916.67 37127.90 
##     2666     2668     2675     2677     2686     2691     2692     2694 
## 27474.30 29446.54 27889.51 30744.07 17665.01 46937.20 53009.62 31314.98 
##     2696     2697     2700     2702     2704     2710     2714     2720 
## 22491.80 41124.28 23841.23 30484.57 23010.81 34429.04 19481.54 14914.25 
##     2721     2722     2728     2734     2735     2738     2739     2740 
## 17768.81 25502.06 27474.30 30276.96 24360.24 24775.45 39359.64 46470.09 
##     2741     2742     2743     2744     2745     2746     2747     2749 
## 33546.73 31678.29 23529.83 35467.07 42577.51 25450.16 36972.20 23737.43 
##     2750     2751     2752     2755     2758     2763     2764     2770 
## 25813.47 26747.69 26176.78 32093.50 28564.23 15952.27 34740.45 26332.48 
##     2782     2788     2791     2792     2795     2799     2803     2805 
## 36401.28 29498.45 22128.50 31263.08 27214.80 38684.93 32041.60 31263.08 
##     2807     2810     2814     2817     2822     2828     2830     2833 
## 34117.64 34221.44 26643.89 30484.57 32041.60 27422.40 31937.79 33858.13 
##     2836     2839     2844     2848     2849     2852     2855     2856 
## 30951.67 30069.36 34636.65 48909.44 39152.04 19273.94 26695.79 27837.61 
##     2858     2862     2865     2868     2871     2876     2877     2884 
## 38010.22 25813.47 31937.79 30173.16 31730.19 39515.35 28149.02 31263.08 
##     2888     2893     2894     2902     2911     2913     2915     2922 
## 24775.45 30847.87 29654.15 35467.07 32041.60 46677.69 27681.91 26851.49 
##     2923     2924     2931     2935     2936     2937     2938     2940 
## 31782.09 34896.15 41902.79 31003.58 32404.90 31833.99 29706.05 29913.65 
##     2948     2951     2954     2956     2966     2971     2976     2981 
## 26176.78 47560.01 29706.05 38788.73 44601.65 34948.05 34325.24 43978.84 
##     3000     3005     3016     3019     3022     3023     3026     3029 
## 38944.44 31055.48 30173.16 31678.29 15692.77 27889.51 41331.88 35311.36 
##     3031     3033     3034     3041     3044     3049     3054     3058 
## 28668.03 21401.88 29394.64 28927.53 29706.05 26332.48 29913.65 25813.47 
##     3060     3062     3063     3065     3067     3068     3071     3074 
## 36037.98 24775.45 36556.99 38321.62 38010.22 39255.84 29965.55 21661.39 
##     3078     3081     3082     3083     3086     3104     3107     3110 
## 31470.68 27889.51 28460.42 29965.55 44809.25 31366.88 26747.69 33650.53 
##     3115     3123     3126     3128     3130     3131     3133     3140 
## 33754.33 31885.89 28771.83 31730.19 35259.46 35467.07 34117.64 31003.58 
##     3141     3142     3147     3152     3156     3157     3162     3167 
## 39567.25 49324.64 30951.67 30276.96 40293.86 29498.45 24256.44 38269.72 
##     3169     3171     3179     3181     3184     3186     3187     3192 
## 31159.28 27889.51 29654.15 34896.15 27889.51 45691.57 45899.17 24100.74 
##     3193     3195     3196     3197     3200     3204     3210     3214 
## 26021.08 26384.38 52075.40 29706.05 27785.71 25709.67 28927.53 39100.14 
##     3217     3218     3219     3220     3221     3240     3241     3247 
## 36920.29 27059.10 31418.78 25709.67 36349.38 31366.88 33183.42 27422.40 
##     3250     3252     3255     3256     3262     3265     3266     3267 
## 51348.78 25553.97 27474.30 27266.70 25346.36 27370.50 25605.87 29135.14 
##     3269     3270     3278     3282     3283     3284     3288     3289 
## 45016.86 29238.94 46366.28 22284.20 26695.79 29861.75 31678.29 16886.49 
##     3290     3291     3295     3297     3298     3301     3302     3305 
## 26851.49 31003.58 35934.17 30069.36 33287.22 30588.37 24931.15 21817.09 
##     3313     3316     3317     3318     3319     3320     3321     3322 
## 32249.20 28097.12 23477.92 27578.11 27318.60 29602.25 29498.45 27059.10 
##     3323     3324     3325     3326     3327     3328     3329     3330 
## 28045.22 30692.17 27785.71 25553.97 24983.05 26643.89 39619.15 27733.81 
##     3331     3332     3333     3334     3344     3345     3346     3347 
## 26747.69 26903.39 24204.54 30536.47 52905.82 33287.22 29757.95 29083.24 
##     3349     3351     3352     3353     3354     3355     3362     3366 
## 38217.82 28668.03 30017.46 30173.16 43719.33 23270.32 29187.04 25813.47 
##     3371     3373     3374     3376     3379     3384     3385     3392 
## 32093.50 29083.24 31159.28 31211.18 35934.17 28460.42 29394.64 51919.70 
##     3395     3396     3405     3406     3408     3412     3414     3417 
## 35934.17 27889.51 26384.38 19066.34 45691.57 29861.75 33546.73 32301.10 
##     3420     3421     3422     3424     3428     3435     3437     3438 
## 30640.27 31782.09 28200.92 32041.60 52023.50 25190.66 33442.92 42629.41 
##     3446     3447     3450     3453     3456     3457     3458     3460 
## 31418.78 29290.84 32145.40 36556.99 33235.32 19377.74 42992.72 29031.34 
##     3461     3462     3463     3465     3468     3474     3475     3480 
## 31263.08 31159.28 31782.09 30276.96 25969.17 26124.88 30484.57 26591.99 
##     3481     3484     3485     3486     3487     3488     3489     3490 
## 37335.50 34117.64 27889.51 25969.17 40709.07 22958.91 19170.14 25138.76 
##     3491     3492     3493     3494     3496     3504     3505     3507 
## 17716.91 29238.94 19585.35 26695.79 22699.41 32197.30 39515.35 37854.51 
##     3509     3511     3512     3517     3521     3523     3525     3526 
## 26903.39 30795.97 31730.19 28927.53 30744.07 28408.52 38840.63 32975.82 
##     3528     3533     3536     3539     3540     3541     3542     3543 
## 30899.77 31730.19 35830.37 29965.55 35155.66 38581.13 25813.47 32820.11 
##     3544     3546     3548     3552     3553     3557     3562     3564 
## 33754.33 34896.15 24775.45 31730.19 38529.23 31003.58 26643.89 35518.97 
##     3567     3572     3574     3577     3578     3579     3580     3583 
## 21298.08 31211.18 31626.39 17094.10 15692.77 33391.02 32301.10 31989.70 
##     3587     3589     3591     3593     3601     3605     3607     3621 
## 30744.07 30951.67 31107.38 34480.95 32041.60 44809.25 24775.45 29550.35 
##     3622     3623     3624     3628     3629     3630     3632     3633 
## 34013.84 39722.95 32041.60 34896.15 27474.30 32872.01 28927.53 38269.72 
##     3635     3641     3645     3649     3656     3668     3671     3674 
## 54410.95 34169.54 28200.92 37698.81 41228.08 30536.47 27889.51 33339.12 
##     3675     3678     3681     3682     3683     3696     3699     3702 
## 29238.94 40397.66 26955.29 24100.74 24723.55 31366.88 32249.20 23945.03 
##     3704     3706     3707     3708     3717     3722     3724     3727 
## 36660.79 28200.92 19792.95 27526.21 27526.21 24567.85 38633.03 29965.55 
##     3729     3731     3735     3746     3754     3755     3759     3760 
## 32768.21 24308.34 29187.04 34429.04 26384.38 27007.20 33079.62 21661.39 
##     3763     3766     3768     3769     3772     3774     3780     3784 
## 53321.02 35467.07 35207.56 29446.54 29290.84 31159.28 45847.27 37698.81 
##     3785     3786     3787     3789     3790     3798     3799     3800 
## 29342.74 31107.38 24515.95 23737.43 27422.40 25398.26 40138.16 32197.30 
##     3801     3802     3804     3806     3809     3810     3811     3813 
## 44809.25 42888.91 32093.50 40190.06 30484.57 27526.21 31366.88 19689.15 
##     3814     3816     3817     3818     3830     3832     3838     3839 
## 35155.66 28616.13 27007.20 44030.74 26643.89 27889.51 44497.85 35155.66 
##     3855     3859     3862     3864     3867     3868     3872     3873 
## 32716.31 32923.91 36245.58 35778.47 27733.81 37231.70 26384.38 26176.78 
##     3875     3877     3882     3886     3889     3891     3892     3893 
## 49117.04 32197.30 21609.49 39359.64 25450.16 24619.75 32353.00 48805.63 
##     3894     3897     3906     3907     3909     3910     3912     3913 
## 32872.01 37335.50 29187.04 29602.25 21765.19 37335.50 34532.85 29394.64 
##     3914     3916     3919     3920     3922     3924     3925     3926 
## 33702.43 37387.40 31522.59 29706.05 29342.74 28356.62 35363.26 29498.45 
##     3933     3935     3941     3943     3944     3949     3951     3953 
## 22491.80 29809.85 27785.71 33910.03 33910.03 46937.20 33961.93 29135.14 
##     3954     3960     3964     3966     3968     3969     3970     3973 
## 32353.00 32353.00 26643.89 40605.27 34896.15 47975.22 37854.51 20986.67 
##     3974     3975     3977     3990     3999     4003     4006     4025 
## 17820.71 28979.43 49947.46 28304.72 27266.70 31678.29 40190.06 30380.76 
##     4028     4030     4032     4036     4037     4046     4047     4048 
## 35415.16 41383.78 32404.90 36712.69 38944.44 33339.12 31003.58 41902.79 
##     4051     4053     4056     4058     4061     4062     4065     4067 
## 35155.66 46210.58 28927.53 29809.85 24567.85 25657.77 28823.73 29394.64 
##     4068     4069     4070     4074     4082     4087     4091     4093 
## 28719.93 27630.01 24256.44 30536.47 26540.09 29394.64 26436.28 27630.01 
##     4094     4095     4101     4102     4106     4108     4111     4112 
## 28564.23 29706.05 33027.72 31107.38 25813.47 32041.60 29602.25 34117.64 
##     4113     4115     4116     4122     4126     4127     4132     4134 
## 34844.25 34065.74 31937.79 26799.59 26851.49 40864.77 42058.50 25813.47 
##     4140     4141     4143     4144     4148     4149     4153     4157 
## 33858.13 35051.86 35934.17 20104.36 27889.51 34065.74 32041.60 35155.66 
##     4158     4159     4160     4161     4162     4164     4165     4166 
## 32041.60 36972.20 33546.73 31003.58 28927.53 32041.60 29965.55 44290.24 
##     4167     4168     4169     4170     4180     4239     4242     4243 
## 29965.55 34117.64 32041.60 32041.60 35570.87 32249.20 30121.26 37076.00 
##     4249     4260     4261     4262     4386     4473     4628     4629 
## 39203.94 18858.73 53580.53 40501.47 43667.43 26747.69 29913.65 28356.62 
##     4739     4754     4811     5056     5165     5195     5201     5263 
## 29446.54 41020.48 34377.14 36608.89 38633.03 30121.26 32508.71 29654.15 
##     5264     5265     5339     5458     5528     5632     5685     5856 
## 32041.60 29498.45 30276.96 54099.54 40397.66 31055.48 33858.13 37854.51 
##     5858     5912     6051     6104     6301     6700     6948     7082 
## 33754.33 31055.48 34896.15 36037.98 35259.46 33910.03 31522.59 31003.58 
##     7129     7252 
## 30276.96 23581.73
reg2 <- lm(COSTT4_A ~ ADM_RATE, data=data2)
summary(reg2)
## 
## Call:
## lm(formula = COSTT4_A ~ ADM_RATE, data = data2)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -31765  -9986  -1323   9705  36241 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  43930.1      981.5   44.76   <2e-16 ***
## ADM_RATE    -17799.4     1380.0  -12.90   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12620 on 1994 degrees of freedom
##   (5707 observations deleted due to missingness)
## Multiple R-squared:  0.07701,    Adjusted R-squared:  0.07654 
## F-statistic: 166.4 on 1 and 1994 DF,  p-value: < 2.2e-16
coefficients(reg2)
## (Intercept)    ADM_RATE 
##    43930.13   -17799.40
confint(reg2, level=0.95)
##                 2.5 %    97.5 %
## (Intercept)  42005.31  45854.95
## ADM_RATE    -20505.77 -15093.03
lm.beta(reg2)
##   ADM_RATE 
## -0.2775023
fitted(reg2)
##        1        2        4        5        6        9       10       11 
## 34574.76 28677.82 29329.28 34450.17 34843.54 29660.35 29072.97 34427.03 
##       13       23       24       25       27       31       33       35 
## 34446.61 26130.73 33537.06 26130.73 29110.35 32316.02 31116.34 33003.08 
##       37       38       40       42       47       51       52       53 
## 33522.82 30705.17 31847.90 35409.56 33332.37 29094.33 34715.38 26130.73 
##       54       57       58       65       83       85       96       99 
## 33426.70 36073.47 35169.26 36441.92 28919.89 30648.22 29662.13 33683.01 
##      103      104      108      116      123      129      135      138 
## 27273.45 27570.70 29514.39 31696.60 33832.53 33378.64 32997.74 32887.38 
##      139      141      142      145      147      148      157      158 
## 37045.32 31045.14 28576.37 32976.38 27152.41 33789.81 26287.36 32755.67 
##      159      162      172      175      176      187      189      192 
## 29188.67 31509.71 31361.97 28102.90 32928.32 31383.33 31217.80 33910.85 
##      194      200      208      211      215      216      217      224 
## 28624.42 40341.77 29530.41 29364.88 32029.45 30509.38 26287.36 29749.35 
##      225      227      228      229      230      231      232      233 
## 32593.69 42358.44 33077.83 38431.90 37068.46 31363.75 30986.40 28898.53 
##      234      235      236      237      238      239      240      241 
## 34697.58 31299.67 36393.86 33357.29 36014.74 31415.37 37618.46 33060.04 
##      242      243      244      245      246      247      248      249 
## 34521.37 30998.86 41078.67 36744.51 37269.59 40626.56 33554.86 38004.71 
##      251      252      258      259      275      276      277      278 
## 37461.83 34012.30 39583.52 32057.93 35557.29 26130.73 28608.40 34051.46 
##      284      288      293      308      319      320      321      331 
## 42013.14 36133.99 29959.38 29526.85 34713.60 34339.81 32175.41 32072.17 
##      344      351      353      360      361      362      365      367 
## 41393.72 33773.79 30304.69 27113.25 27230.73 27946.27 36550.50 32123.79 
##      369      370      378      387      393      408      411      423 
## 35642.73 33522.82 36696.45 30423.94 34548.07 35909.72 30377.67 29993.20 
##      426      435      441      442      446      448      455      456 
## 27109.69 26486.72 30098.21 36447.26 32097.09 38412.32 35486.09 34158.26 
##      461      462      464      465      472      489      490      491 
## 37618.46 41612.65 31554.21 41760.38 30920.55 37792.90 35697.91 27006.46 
##      492      493      495      499      501      507      511      514 
## 37296.29 32187.86 33241.59 30436.40 33277.19 35146.13 38875.10 26130.73 
##      520      525      527      531      536      537      541      559 
## 33720.39 30411.48 29687.05 33606.48 29549.99 40722.68 29210.02 29804.52 
##      560      565      568      571      573      574      576      577 
## 32915.86 30941.91 32308.90 29439.64 30938.35 27483.48 28950.15 27141.73 
##      578      583      585      596      598      605      606      608 
## 40744.04 37438.69 29605.17 30315.37 27764.71 29286.56 32340.94 31459.87 
##      613      620      623      629      636      637      640      643 
## 31313.91 26835.58 27415.84 26591.73 33122.33 33172.17 37237.56 35037.55 
##      646      647      653      660      664      671      673      674 
## 32698.71 31198.22 31091.42 31463.43 29537.53 28432.19 32198.54 33757.77 
##      675      677      678      681      683      684      686      692 
## 29695.95 37084.48 31196.44 38049.21 39674.29 36805.03 42808.77 36144.67 
##      693      694      696      698      699      702      703      704 
## 31856.80 34861.34 33837.87 35770.88 30774.59 32303.56 36135.77 40841.93 
##      705      708      709      714      715      717      718      724 
## 35313.44 26130.73 27759.37 34040.78 35722.83 32590.13 30603.72 37648.72 
##      726      727      730      734      736      737      738      739 
## 37641.60 35099.85 32908.74 30982.85 34505.35 30925.89 35217.32 32177.19 
##      741      742      746      747      749      751      754      755 
## 35407.78 30297.57 26130.73 32971.04 34535.61 40274.13 35954.22 34071.04 
##      758      774      775      777      787      796      799      805 
## 35811.82 29948.70 33950.01 35265.38 35247.58 37134.32 31048.70 33149.03 
##      806      807      811      820      822      824      832      835 
## 36847.75 35242.24 26972.64 28761.48 33732.85 31086.08 26130.73 34467.97 
##      836      838      839      846      849      853      855      857 
## 28818.44 33029.78 36109.07 34695.80 32595.47 39302.29 34930.75 36513.12 
##      862      863      868      869      870      874      878      883 
## 30178.31 31876.38 35512.79 35687.23 31821.20 34694.02 28859.38 33102.75 
##      885      887      888      891      894      896      901      902 
## 30436.40 29690.61 27492.38 36374.28 34101.30 26728.79 35187.06 39156.33 
##      904      906      907      908      909      910      911      912 
## 39624.46 37988.69 31534.63 30359.87 32698.71 33350.17 34012.30 35317.00 
##      918      919      921      923      924      925      929      930 
## 34416.35 34095.96 33766.67 26130.73 32054.37 28973.29 30005.66 40048.08 
##      931      932      933      935      936      937      940      941 
## 33686.57 37997.59 27907.11 32084.63 30112.45 31609.38 34318.45 29857.92 
##      943      944      945      947      949      950      952      953 
## 33202.43 37335.45 26783.97 34293.53 35277.84 34978.81 28690.28 31232.04 
##      954      956      965      968      969      972      973      974 
## 29900.64 32924.76 31310.35 27421.18 30224.59 31919.09 27394.49 26301.60 
##      975      979      981      987      988      989      994      997 
## 30507.60 32348.06 26198.37 31621.84 34387.87 29494.81 32342.72 32485.11 
##     1011     1013     1021     1022     1027     1031     1033     1034 
## 38597.43 42370.90 28172.32 34345.15 31491.91 35073.15 31878.16 32453.08 
##     1036     1041     1046     1049     1050     1052     1053     1055 
## 32063.27 34019.42 27405.17 30673.14 30194.33 33421.36 33173.95 34295.31 
##     1057     1059     1067     1070     1072     1075     1080     1081 
## 34923.63 30779.93 30915.21 29065.85 31783.82 34104.86 32910.52 35461.17 
##     1082     1085     1091     1094     1096     1097     1098     1099 
## 33919.75 32655.99 29980.74 33045.80 36123.31 28266.66 32764.57 31637.86 
##     1100     1105     1108     1109     1111     1112     1113     1114 
## 31102.10 26586.39 33278.97 34209.88 34872.01 27282.35 41596.63 33675.89 
##     1117     1122     1127     1130     1131     1132     1135     1137 
## 30671.36 28101.12 39599.54 34176.06 30110.67 33131.23 34930.75 35094.51 
##     1138     1141     1150     1151     1152     1153     1156     1157 
## 32969.26 37289.17 29418.28 28451.77 26130.73 26130.73 27871.51 26130.73 
##     1160     1163     1164     1167     1169     1170     1171     1172 
## 30386.57 31534.63 31621.84 34156.48 33271.85 31376.21 31744.66 37917.49 
##     1177     1180     1181     1182     1183     1184     1187     1189 
## 33855.67 32445.96 29165.53 31609.38 34318.45 29669.25 32454.86 27348.21 
##     1191     1193     1194     1195     1196     1197     1198     1199 
## 26645.13 27755.81 31383.33 26130.73 32097.09 31369.09 31232.04 29238.50 
##     1200     1201     1202     1203     1204     1205     1206     1207 
## 31958.25 30877.83 30386.57 30263.75 29633.65 32581.23 29977.18 34895.15 
##     1208     1209     1210     1211     1218     1219     1220     1228 
## 29822.32 30342.07 27221.83 36810.37 30708.73 33884.15 27011.80 40167.34 
##     1229     1231     1232     1235     1237     1238     1239     1240 
## 34133.34 33307.45 31023.78 33465.86 26689.63 32109.55 26130.73 29096.11 
##     1243     1244     1245     1246     1249     1250     1251     1252 
## 32412.14 28261.32 30404.36 29270.54 31474.11 43930.13 33389.32 32949.68 
##     1253     1257     1258     1259     1260     1263     1264     1265 
## 31846.12 31666.34 31383.33 34087.06 30824.43 27748.69 30938.35 31602.26 
##     1266     1268     1270     1272     1273     1274     1286     1287 
## 30067.96 36853.09 31945.79 35058.91 26362.12 38944.52 28460.67 36619.92 
##     1289     1295     1296     1297     1299     1300     1301     1304 
## 29521.51 26997.56 31264.08 37148.56 26723.45 33816.51 33814.73 30096.43 
##     1305     1310     1312     1313     1316     1322     1323     1324 
## 30076.86 26130.73 26830.24 39658.27 28720.54 31481.23 31675.24 29898.86 
##     1328     1330     1332     1333     1334     1339     1340     1348 
## 33323.47 31554.21 26525.87 26584.61 35190.62 26130.73 35096.29 30315.37 
##     1350     1351     1352     1355     1365     1366     1368     1369 
## 28286.24 34394.99 33004.86 33588.68 27657.92 34530.27 27033.16 32988.84 
##     1370     1374     1375     1376     1380     1382     1384     1388 
## 35551.95 33412.46 26258.88 31650.32 26225.06 29834.78 35475.41 28279.12 
##     1389     1390     1393     1395     1396     1400     1401     1404 
## 36032.54 28679.60 26926.36 37492.09 31701.94 29085.43 37938.85 35160.37 
##     1405     1407     1412     1413     1416     1427     1428     1429 
## 30986.40 31191.10 32132.69 30781.71 28133.16 34318.45 35441.60 33122.33 
##     1430     1431     1434     1435     1439     1440     1441     1443 
## 31077.18 35432.70 28037.04 30783.49 33567.32 28902.09 29697.73 27782.51 
##     1448     1459     1462     1463     1465     1466     1476     1484 
## 26130.73 35794.02 27326.85 29224.26 30539.64 27319.73 32241.26 36705.35 
##     1486     1492     1493     1495     1499     1501     1502     1503 
## 36107.29 34220.56 30290.45 30283.33 33061.82 32355.18 27866.17 30532.52 
##     1504     1505     1506     1509     1510     1511     1521     1524 
## 36174.93 28200.80 30185.43 30940.13 33930.43 31007.76 30730.09 29026.69 
##     1525     1526     1528     1530     1531     1534     1535     1537 
## 34380.75 40245.65 33998.06 38955.20 32184.30 31274.76 39405.52 41276.24 
##     1538     1540     1542     1546     1547     1549     1550     1552 
## 37997.59 38937.40 31123.46 28880.74 30650.00 29233.16 29934.46 28679.60 
##     1555     1556     1559     1560     1561     1571     1572     1573 
## 26605.97 29952.26 28987.53 30708.73 27358.89 32887.38 34129.78 31381.55 
##     1577     1578     1582     1584     1588     1591     1594     1598 
## 35934.64 36255.03 33515.70 30457.76 29567.79 41067.99 33316.35 33319.91 
##     1599     1600     1601     1605     1606     1607     1609     1614 
## 35398.88 34289.97 33024.44 32316.02 32027.67 30057.28 35126.55 34195.64 
##     1615     1617     1619     1622     1623     1624     1628     1629 
## 29891.74 28451.77 33391.10 32839.32 34022.98 30379.45 31903.07 41466.69 
##     1631     1633     1634     1636     1637     1638     1640     1641 
## 30123.13 29459.22 39247.11 30774.59 32707.61 34957.45 32810.84 35722.83 
##     1642     1647     1648     1649     1650     1651     1658     1659 
## 36742.73 37894.35 36981.24 37787.56 37661.18 29813.42 27825.23 34313.11 
##     1661     1663     1666     1667     1668     1669     1672     1673 
## 28466.01 31709.06 34519.59 35176.38 31595.14 30909.87 32259.06 31059.38 
##     1674     1676     1680     1681     1685     1690     1692     1694 
## 32848.22 28200.80 32068.61 42869.29 36215.87 30345.63 31205.34 32892.72 
##     1698     1699     1701     1702     1703     1704     1709     1713 
## 33003.08 31333.49 28976.85 30947.25 42527.54 32965.70 30087.54 34193.86 
##     1714     1717     1720     1724     1725     1726     1727     1731 
## 31739.32 27848.37 38743.38 27189.79 31424.27 30352.75 31066.50 38195.16 
##     1733     1734     1738     1741     1743     1744     1745     1747 
## 29873.94 31855.02 30418.60 31369.09 34645.96 28019.24 36417.00 31315.69 
##     1749     1750     1751     1753     1754     1755     1756     1757 
## 30256.63 30231.71 28994.65 40861.51 38570.73 29220.70 29663.91 30658.90 
##     1758     1759     1760     1761     1762     1763     1764     1767 
## 31536.41 28352.09 40491.29 36137.55 33019.10 32914.08 33109.87 31118.12 
##     1769     1770     1776     1780     1783     1785     1786     1791 
## 37365.71 32344.50 30911.65 31600.48 29816.98 35811.82 27309.05 26216.16 
##     1792     1795     1796     1799     1801     1802     1805     1808 
## 31637.86 31671.68 29971.84 31178.64 31216.02 31677.02 29614.07 30151.61 
##     1809     1812     1818     1820     1823     1824     1825     1826 
## 27383.81 31532.85 27716.65 33709.71 33501.46 35311.66 36705.35 38191.60 
##     1828     1829     1830     1831     1841     1844     1846     1847 
## 32166.51 30491.58 32775.24 29932.68 31098.54 31564.89 32004.53 32995.96 
##     1849     1854     1856     1860     1862     1868     1871     1879 
## 31354.85 29697.73 30715.85 32068.61 35840.30 30165.85 28967.95 31822.98 
##     1882     1883     1884     1887     1888     1889     1891     1898 
## 27282.35 30103.55 26944.16 39877.21 32488.67 34453.73 26607.75 33060.04 
##     1899     1909     1911     1917     1918     1919     1921     1923 
## 31543.53 37460.05 32079.29 26130.73 35858.10 31121.68 32465.54 26130.73 
##     1925     1926     1927     1930     1935     1937     1939     1944 
## 27853.71 30263.75 32611.49 28944.81 27697.08 31552.43 32063.27 29302.58 
##     1947     1948     1949     1950     1951     1952     1953     1955 
## 29300.80 29911.32 30715.85 34802.60 38875.10 32150.49 28512.29 31967.15 
##     1958     1962     1965     1968     1969     1970     1977     1985 
## 32015.21 31043.36 32709.39 29968.28 31169.74 34135.12 27494.16 31386.89 
##     1988     1990     1991     1992     1993     1996     2000     2003 
## 33752.43 29473.46 27268.11 41023.49 32709.39 31288.99 37015.06 32050.81 
##     2005     2007     2010     2011     2014     2015     2017     2018 
## 36756.97 34955.67 34678.00 32901.62 34220.56 26130.73 36383.18 33156.15 
##     2019     2025     2027     2030     2031     2036     2037     2041 
## 30055.50 26130.73 31358.41 33656.32 30685.60 32444.18 27802.09 33040.46 
##     2049     2050     2055     2059     2060     2064     2067     2071 
## 33255.83 26130.73 34517.81 26130.73 31105.66 30338.51 33209.55 26842.70 
##     2072     2073     2075     2076     2077     2078     2084     2085 
## 26130.73 36137.55 30105.33 32492.23 28649.34 30441.74 30673.14 30299.35 
##     2087     2088     2089     2093     2096     2101     2105     2110 
## 42451.00 32070.39 26130.73 30235.27 33058.26 27317.95 32921.20 34389.65 
##     2111     2112     2117     2118     2120     2121     2122     2128 
## 28839.80 28795.30 40881.09 31103.88 32122.01 32746.77 30349.19 33690.13 
##     2136     2141     2142     2143     2144     2145     2150     2151 
## 32234.14 27777.17 29005.33 27426.52 26130.73 32607.93 33011.98 33731.07 
##     2155     2156     2157     2158     2159     2162     2164     2167 
## 30294.01 30995.30 29806.30 35988.04 31532.85 28959.05 29226.04 33218.45 
##     2169     2173     2174     2177     2179     2185     2192     2193 
## 29957.60 30021.68 31490.13 34523.15 34649.52 36675.09 28464.23 28999.99 
##     2196     2199     2201     2202     2205     2211     2213     2215 
## 32228.80 27810.99 32736.09 41883.20 28925.23 26890.76 28941.25 29687.05 
##     2216     2217     2218     2227     2228     2229     2231     2232 
## 29941.58 31456.31 30544.98 32794.82 30386.57 37997.59 30402.58 39017.50 
##     2238     2241     2243     2254     2255     2259     2260     2261 
## 32645.31 32550.97 29350.64 31440.29 28108.24 29671.03 28950.15 29557.11 
##     2263     2264     2268     2269     2271     2272     2273     2279 
## 31815.86 36174.93 38406.98 43930.13 30297.57 26883.64 31406.47 30724.75 
##     2280     2282     2283     2287     2294     2295     2296     2298 
## 32034.79 32063.27 35717.49 32647.09 42605.86 28734.78 34439.49 31308.57 
##     2300     2301     2302     2305     2307     2309     2311     2312 
## 33182.85 33161.49 32761.01 33802.27 30484.46 33679.45 36137.55 32405.02 
##     2313     2316     2319     2326     2328     2331     2333     2335 
## 26130.73 35213.76 30655.34 32705.83 26130.73 36829.95 37452.93 35852.76 
##     2339     2344     2352     2353     2357     2360     2362     2363 
## 31541.75 26130.73 30619.74 31039.80 31933.33 31570.23 34437.71 32643.53 
##     2365     2366     2369     2372     2373     2376     2377     2378 
## 31500.81 39822.03 26586.39 35989.82 39699.21 26130.73 26130.73 40694.20 
##     2393     2397     2398     2402     2403     2407     2408     2409 
## 29649.67 30366.99 26130.73 28403.71 32869.58 39259.57 34569.42 42693.07 
##     2412     2416     2417     2420     2421     2422     2425     2426 
## 30621.52 41249.54 41404.40 39405.52 32593.69 38964.10 37641.60 27150.63 
##     2427     2430     2431     2434     2435     2436     2437     2440 
## 37155.68 37759.08 37289.17 38784.32 27565.36 30975.73 36842.41 37321.21 
##     2442     2443     2444     2445     2446     2448     2450     2452 
## 31685.92 34158.26 26130.73 32750.33 29982.52 36513.12 29297.24 36048.56 
##     2454     2455     2462     2463     2466     2467     2468     2469 
## 33941.11 35365.06 39239.99 27988.99 29578.47 35470.07 32963.92 27232.51 
##     2474     2477     2479     2481     2482     2485     2486     2487 
## 28498.05 33408.90 27243.19 32919.42 42429.64 29181.55 30721.19 32191.42 
##     2488     2489     2494     2496     2497     2498     2499     2500 
## 28563.91 29153.07 26130.73 32086.41 35952.44 30783.49 37700.34 26130.73 
##     2501     2503     2504     2505     2507     2508     2510     2514 
## 37075.58 30847.57 32912.30 26130.73 31134.14 31470.55 27358.89 26921.02 
##     2517     2518     2520     2521     2524     2525     2526     2527 
## 30509.38 36762.31 28156.30 26983.32 31383.33 32486.89 37072.02 32200.32 
##     2535     2537     2541     2542     2543     2548     2549     2551 
## 37620.24 32207.44 32533.17 35829.62 26244.64 28802.42 26410.18 38556.49 
##     2552     2553     2555     2557     2558     2560     2561     2563 
## 35423.80 34498.23 26130.73 31365.53 26130.73 27020.70 37255.35 31693.04 
##     2565     2566     2569     2571     2572     2573     2574     2575 
## 33700.81 37449.37 34174.28 31394.01 30217.47 31470.55 35450.50 30350.97 
##     2576     2577     2578     2580     2581     2582     2583     2586 
## 29544.65 26130.73 34471.53 28503.39 32207.44 37283.83 31340.61 32882.04 
##     2587     2590     2594     2595     2596     2597     2598     2599 
## 31842.56 32801.94 34275.73 29571.35 31792.72 30876.05 35626.71 33928.65 
##     2600     2601     2602     2603     2604     2605     2606     2607 
## 33990.94 36087.71 33640.30 36571.86 34829.30 33944.67 35217.32 32974.60 
##     2608     2609     2610     2611     2612     2613     2614     2615 
## 35215.54 34457.29 33405.34 36466.84 35051.79 35320.56 31901.29 36664.41 
##     2617     2618     2620     2621     2624     2625     2626     2630 
## 32832.20 35411.34 29491.26 34558.75 34455.51 26130.73 26130.73 26130.73 
##     2631     2632     2636     2640     2642     2643     2644     2645 
## 38629.47 33615.38 36611.02 29418.28 39740.15 29719.09 30265.53 31082.52 
##     2646     2647     2648     2651     2653     2655     2658     2659 
## 38058.11 33857.45 29806.30 27597.40 26130.73 26130.73 29370.22 26130.73 
##     2660     2664     2666     2668     2669     2672     2675     2677 
## 26130.73 32777.02 37084.48 31607.60 27592.06 36239.01 28065.52 31815.86 
##     2681     2686     2691     2692     2694     2696     2697     2700 
## 37540.15 33284.31 40073.00 41899.22 30174.75 35208.42 34330.91 34973.47 
##     2702     2704     2705     2710     2713     2714     2716     2718 
## 31983.17 30916.99 32862.46 29656.79 29142.39 36409.88 32901.62 32218.12 
##     2720     2721     2722     2727     2728     2734     2735     2738 
## 32494.01 36436.58 32878.48 33024.44 33973.14 35731.73 35591.11 33784.47 
##     2739     2740     2741     2742     2743     2744     2745     2746 
## 30911.65 38857.30 32522.49 33120.55 36237.23 36240.79 34745.64 34450.17 
##     2747     2749     2750     2751     2752     2755     2758     2763 
## 33508.58 32732.53 30890.29 35523.47 35729.95 29966.50 37185.94 30753.23 
##     2764     2767     2770     2780     2782     2788     2791     2792 
## 33277.19 33366.19 33761.33 37805.36 31155.50 30569.90 33222.01 36256.81 
##     2795     2799     2803     2805     2807     2810     2814     2817 
## 33067.16 32474.44 29930.90 33663.44 28622.64 29202.90 37442.25 27862.61 
##     2819     2821     2822     2828     2830     2833     2834     2836 
## 30774.59 26130.73 26894.32 39597.76 31013.10 30580.58 32543.85 33957.13 
##     2839     2844     2848     2849     2852     2855     2856     2858 
## 34430.59 30982.85 37111.18 30671.36 37216.20 30459.54 33515.70 30441.74 
##     2862     2865     2867     2868     2871     2876     2877     2878 
## 32289.32 32006.31 36117.97 28941.25 28152.74 33426.70 32415.70 34046.12 
##     2884     2887     2888     2893     2894     2900     2902     2903 
## 31119.90 26130.73 29895.30 30569.90 32880.26 30112.45 29172.65 28042.38 
##     2911     2913     2914     2915     2922     2923     2924     2927 
## 28910.99 39469.60 26431.54 31584.46 32440.62 31160.84 31566.67 33777.35 
##     2931     2935     2936     2937     2938     2940     2948     2951 
## 32211.00 30778.15 30838.67 30406.14 28334.29 30324.27 27999.67 38106.17 
##     2954     2956     2966     2971     2974     2975     2976     2981 
## 35640.95 31721.52 34503.57 30710.51 26130.73 30705.17 30525.40 27177.33 
##     2982     2984     2988     3000     3004     3005     3016     3018 
## 29640.77 29690.61 32241.26 30060.84 34250.82 27068.76 32269.74 26130.73 
##     3019     3022     3023     3025     3026     3029     3030     3031 
## 29569.57 37248.24 26954.84 27665.04 33412.46 30909.87 30886.73 29103.23 
##     3033     3034     3041     3044     3049     3053     3054     3058 
## 36283.51 32769.91 27853.71 26630.89 34473.31 30247.73 30578.80 32141.59 
##     3060     3062     3063     3065     3067     3068     3071     3074 
## 32536.73 33339.49 30589.48 33165.05 31867.48 29453.88 29733.33 30222.81 
##     3076     3078     3081     3082     3083     3086     3104     3107 
## 34544.51 31906.63 29927.34 29533.97 28754.36 36764.09 34564.09 32506.47 
##     3109     3110     3112     3114     3115     3118     3123     3126 
## 31935.11 30089.32 28724.10 32072.17 27239.63 26130.73 33843.21 31130.58 
##     3128     3129     3130     3131     3132     3133     3140     3141 
## 33278.97 34934.31 30089.32 30598.38 29272.32 29610.51 31589.80 32728.97 
##     3142     3147     3151     3152     3156     3157     3162     3164 
## 37036.42 30158.73 34542.73 37276.71 29457.44 28134.94 33602.92 35017.97 
##     3167     3169     3171     3179     3181     3184     3185     3186 
## 31155.50 29752.91 30617.96 28535.43 33464.08 28300.48 28211.48 36726.71 
##     3187     3192     3193     3195     3196     3197     3199     3200 
## 38462.15 30530.74 27969.41 27786.07 39551.48 34615.70 34619.26 30632.20 
##     3204     3207     3210     3211     3214     3217     3218     3219 
## 27428.30 43031.26 30448.86 35370.40 30400.80 30925.89 29430.74 32862.46 
##     3220     3221     3237     3238     3239     3240     3241     3242 
## 26255.32 31324.59 33759.55 29690.61 37000.82 30105.33 31281.88 35843.86 
##     3247     3248     3250     3252     3253     3255     3256     3260 
## 30334.95 27243.19 39535.46 30890.29 32321.36 30413.26 27068.76 36231.89 
##     3261     3262     3263     3265     3266     3267     3269     3270 
## 30728.31 27545.78 31956.47 29749.35 27209.37 30005.66 38634.81 33346.61 
##     3275     3278     3282     3283     3284     3288     3289     3290 
## 31372.65 37830.28 39095.81 27307.27 28779.28 31075.40 34361.17 27786.07 
##     3291     3294     3295     3296     3297     3298     3300     3301 
## 30726.53 29630.09 29694.17 33412.46 31700.16 31210.68 33496.12 28587.05 
##     3302     3303     3305     3313     3316     3317     3318     3319 
## 30762.13 34532.05 27191.57 28498.05 29471.68 31976.05 29014.23 30383.01 
##     3320     3321     3322     3323     3324     3325     3326     3327 
## 28779.28 28204.36 29500.15 28149.18 29320.38 28841.58 28156.30 29051.61 
##     3328     3329     3330     3331     3332     3333     3334     3336 
## 28626.20 34978.81 30431.06 30043.04 29808.08 30619.74 29094.33 28149.18 
##     3339     3343     3344     3345     3346     3347     3349     3351 
## 26467.14 36402.76 42084.33 32549.19 31552.43 26522.31 33627.84 32285.76 
##     3352     3353     3354     3355     3359     3362     3366     3369 
## 30666.02 29658.57 34475.09 30212.13 28743.68 31338.83 39558.60 28362.77 
##     3371     3373     3374     3375     3376     3379     3380     3381 
## 30366.99 33627.84 31698.38 28862.94 31128.80 30178.31 31625.40 28426.85 
##     3383     3384     3385     3386     3388     3391     3392     3393 
## 29398.70 29133.49 32187.86 26130.73 27631.22 30011.00 40900.67 39688.53 
##     3394     3395     3396     3404     3405     3406     3408     3411 
## 30580.58 32942.56 31561.33 29128.15 27369.57 26712.77 35149.69 36516.68 
##     3412     3414     3415     3417     3420     3421     3422     3424 
## 29056.95 34411.01 36965.22 27259.21 32358.74 29934.46 38362.48 35833.18 
##     3428     3429     3430     3434     3435     3437     3438     3439 
## 42374.46 30566.34 29485.92 32705.83 32280.42 30258.41 38129.31 30057.28 
##     3440     3446     3447     3450     3451     3453     3456     3457 
## 31294.33 31200.00 33489.00 29510.83 32691.59 30043.04 30484.46 36139.33 
##     3458     3460     3461     3462     3463     3465     3468     3469 
## 34759.88 34870.23 38017.17 29859.70 34411.01 33149.03 33408.90 31700.16 
##     3474     3475     3480     3481     3484     3485     3486     3487 
## 33645.64 34674.44 33828.97 33346.61 34368.29 32278.64 33741.75 32324.92 
##     3488     3489     3490     3491     3492     3493     3494     3496 
## 32622.17 34427.03 33679.45 31264.08 32609.71 28882.52 35596.45 32248.38 
##     3502     3504     3505     3507     3509     3511     3512     3517 
## 35023.31 31260.52 30155.17 33020.88 27180.89 28943.03 30860.03 31050.48 
##     3521     3523     3525     3526     3528     3533     3536     3539 
## 29176.21 33793.37 28263.10 27552.90 26621.99 28120.70 33065.38 28040.60 
##     3540     3541     3542     3543     3544     3546     3548     3552 
## 34366.51 29206.46 33709.71 35311.66 32823.30 35082.05 26130.73 35667.65 
##     3553     3557     3562     3564     3567     3572     3574     3577 
## 34037.22 27600.96 29076.53 27307.27 35786.90 33896.61 33841.43 36228.33 
##     3578     3579     3580     3583     3587     3589     3591     3593 
## 34647.74 28079.76 30692.71 31322.81 37155.68 35493.21 31103.88 32821.52 
##     3601     3605     3607     3609     3611     3621     3622     3623 
## 34613.92 33252.27 26356.78 26130.73 32413.92 32063.27 30174.75 30610.84 
##     3624     3628     3629     3630     3632     3633     3635     3641 
## 30876.05 27125.71 33576.22 30922.33 31125.24 31723.30 41600.19 34946.77 
##     3645     3649     3656     3659     3660     3668     3671     3674 
## 29256.30 34250.82 34076.38 32077.51 36349.37 28749.02 28868.28 35705.03 
##     3675     3678     3681     3682     3683     3696     3699     3702 
## 37173.48 28777.50 33964.25 35466.51 35414.90 33820.07 37570.40 28948.37 
##     3703     3704     3706     3707     3708     3711     3712     3715 
## 34005.18 32718.29 29313.26 33303.89 27339.31 27218.27 27342.87 28419.73 
##     3717     3722     3724     3727     3729     3731     3735     3746 
## 29902.42 35617.81 35137.23 27141.73 29706.63 33001.30 32958.58 32292.88 
##     3748     3754     3755     3759     3760     3763     3766     3768 
## 31653.88 35115.87 32752.11 27916.01 36965.22 41242.42 29982.52 29870.38 
##     3769     3772     3774     3780     3783     3784     3785     3786 
## 30817.31 27282.35 33346.61 34603.24 37979.79 35293.86 33515.70 30954.37 
##     3787     3789     3790     3798     3799     3800     3801     3802 
## 35092.73 27305.49 34578.32 29055.17 31287.21 33001.30 36870.89 32905.18 
##     3803     3804     3806     3809     3810     3811     3813     3814 
## 26150.31 29053.39 35231.56 33985.60 28444.65 30418.60 34688.68 32159.39 
##     3816     3817     3818     3830     3832     3838     3839     3850 
## 37155.68 28745.46 35311.66 26532.99 31929.77 35564.41 37725.26 27691.74 
##     3855     3859     3862     3864     3865     3866     3867     3868 
## 33067.16 26516.97 29437.86 26885.42 31967.15 29977.18 27618.76 32508.25 
##     3870     3871     3872     3873     3874     3875     3877     3879 
## 26130.73 31764.24 26938.82 26283.80 29405.82 40873.97 32228.80 29608.73 
##     3881     3882     3883     3885     3886     3888     3889     3891 
## 32257.28 27246.75 26392.38 29122.81 30858.25 27830.57 33314.57 26488.50 
##     3892     3893     3894     3897     3906     3907     3909     3910 
## 35418.46 38052.77 29722.65 33983.82 31164.40 33172.17 30881.39 32066.83 
##     3912     3913     3914     3916     3919     3920     3922     3924 
## 35516.35 38757.62 33878.81 32230.58 39957.30 30950.81 32049.03 26940.60 
##     3925     3926     3933     3935     3941     3943     3944     3947 
## 30274.43 28985.75 32241.26 29354.20 29884.62 33189.97 29510.83 34517.81 
##     3949     3951     3953     3954     3960     3964     3966     3968 
## 38269.92 31591.58 29229.60 35551.95 27280.57 31680.58 31002.42 30518.28 
##     3969     3970     3973     3974     3975     3977     3990     3997 
## 38768.30 36027.20 29679.93 39677.85 28081.54 40466.37 28540.77 28708.08 
##     3999     4003     4006     4013     4014     4020     4025     4028 
## 30689.15 26326.52 31913.75 27606.30 27351.77 30616.18 26821.34 30578.80 
##     4030     4032     4036     4037     4046     4047     4048     4051 
## 29816.98 28120.70 29085.43 30874.27 33643.86 29320.38 34103.08 28877.18 
##     4053     4054     4056     4058     4061     4062     4065     4067 
## 36630.60 30623.30 36351.15 31623.62 32885.60 37105.84 33113.43 37209.08 
##     4068     4069     4070     4074     4082     4087     4091     4093 
## 33567.32 32091.75 35642.73 30308.25 38172.02 26435.10 36554.06 31050.48 
##     4094     4095     4101     4102     4106     4108     4109     4111 
## 32908.74 30119.57 28660.02 32782.36 32326.70 35270.72 31593.36 29160.19 
##     4112     4113     4115     4116     4121     4122     4124     4125 
## 29541.09 31176.86 30507.60 30363.43 27125.71 34193.86 30945.47 30413.26 
##     4126     4127     4131     4132     4134     4140     4141     4143 
## 30270.87 32056.15 33414.24 31710.84 37652.28 32639.97 31924.43 29386.24 
##     4144     4148     4149     4153     4157     4158     4159     4160 
## 35493.21 26173.45 31623.62 29372.00 29033.81 28382.35 30350.97 32481.55 
##     4161     4162     4163     4164     4165     4166     4167     4168 
## 29630.09 28619.08 26130.73 27768.27 28165.20 33795.15 27990.77 27127.49 
##     4169     4170     4180     4191     4193     4198     4199     4202 
## 27992.55 28015.68 26547.23 28969.73 34955.67 36301.31 30836.89 27577.82 
##     4204     4208     4209     4217     4218     4219     4220     4221 
## 31607.60 27424.74 28734.78 28490.93 26442.22 26874.74 30699.83 32625.73 
##     4222     4223     4224     4225     4226     4227     4228     4235 
## 34361.17 35804.70 39927.05 32136.25 30628.64 30756.79 33024.44 27944.49 
##     4236     4239     4240     4241     4242     4243     4244     4245 
## 30302.91 27827.01 29904.20 39318.31 29950.48 29224.26 35292.08 36831.73 
##     4246     4248     4249     4252     4254     4256     4258     4260 
## 30397.24 30820.87 38916.04 38930.28 36020.08 33907.29 27237.85 26652.25 
##     4261     4262     4265     4267     4268     4272     4284     4319 
## 43024.14 33376.86 30342.07 26602.41 26698.53 34791.92 29423.62 28588.83 
##     4321     4335     4338     4343     4352     4363     4370     4371 
## 29097.89 33487.22 29781.39 27214.71 32842.88 35030.43 27129.27 28118.92 
##     4376     4382     4385     4386     4412     4462     4466     4470 
## 29822.32 31826.54 30906.31 33273.63 29076.53 29578.47 27597.40 27056.30 
##     4471     4472     4473     4485     4494     4505     4507     4516 
## 26525.87 27552.90 32930.10 32390.78 30706.95 35224.44 27430.08 30324.27 
##     4552     4556     4584     4606     4613     4616     4617     4627 
## 31187.54 32616.83 30997.08 29727.99 28218.60 27424.74 30459.54 30292.23 
##     4628     4629     4636     4645     4672     4680     4707     4712 
## 29841.90 28886.08 28647.56 31623.62 27063.42 26563.25 33426.70 26130.73 
##     4717     4718     4719     4739     4754     4757     4792     4795 
## 28644.00 32869.58 26130.73 39238.21 36194.51 30085.76 26130.73 29690.61 
##     4811     4813     4819     4820     4847     4851     4860     4877 
## 30082.20 29446.76 29799.18 26130.73 27933.81 30851.13 31584.46 29080.09 
##     4888     4889     4890     4891     4892     4902     4905     4906 
## 27453.22 27834.13 29870.38 27935.59 26381.70 28126.04 30194.33 33428.48 
##     4909     4910     4912     4953     4954     4960     4972     5009 
## 31463.43 27668.60 32063.27 29436.08 26440.44 26130.73 26130.73 28674.26 
##     5043     5047     5056     5072     5086     5090     5102     5114 
## 38695.33 26798.21 30272.65 30845.79 31691.26 26718.11 32995.96 27458.56 
##     5126     5129     5130     5131     5132     5135     5139     5165 
## 31166.18 29530.41 28282.68 30886.73 29665.69 30283.33 26130.73 28108.24 
##     5176     5186     5188     5195     5199     5201     5204     5215 
## 26130.73 35300.98 26130.73 40870.41 26130.73 33449.84 31913.75 30383.01 
##     5223     5224     5225     5226     5256     5263     5264     5265 
## 26821.34 28930.57 26728.79 27232.51 30318.93 32212.78 32552.75 33811.17 
##     5266     5267     5271     5308     5315     5318     5327     5339 
## 27816.33 27545.78 26500.96 31573.79 27389.15 29297.24 30639.32 26130.73 
##     5348     5364     5369     5381     5434     5451     5454     5455 
## 32805.50 27243.19 30254.85 29564.23 43930.13 34213.44 31041.58 29053.39 
##     5456     5458     5466     5472     5473     5474     5495     5508 
## 29112.13 41794.20 33250.49 33610.04 28094.00 36402.76 26130.73 37739.50 
##     5520     5524     5528     5532     5533     5537     5558     5585 
## 33569.10 34394.99 32381.88 29774.27 32460.20 27132.83 26429.76 34578.32 
##     5627     5632     5634     5638     5663     5664     5685     5700 
## 27720.21 31972.49 30580.58 30833.33 29037.37 31689.48 34727.84 32486.89 
##     5734     5735     5736     5737     5755     5823     5829     5830 
## 27613.42 28288.02 26397.72 31742.88 34183.18 36020.08 26967.30 26983.32 
##     5831     5832     5833     5834     5835     5836     5856     5858 
## 26915.68 26413.74 29599.83 28191.90 31778.48 31568.45 37639.82 29893.52 
##     5903     5904     5912     5945     5946     5947     5948     5949 
## 26130.73 35300.98 39661.83 27102.58 27006.46 30737.21 28229.28 28953.71 
##     5950     5951     5998     6028     6029     6030     6051     6061 
## 27074.10 32716.51 27285.91 26130.73 26130.73 26883.64 37890.79 29434.30 
##     6062     6067     6068     6069     6070     6071     6072     6073 
## 29884.62 26643.35 31009.54 27337.53 30030.58 29165.53 26554.35 31856.80 
##     6104     6105     6106     6107     6186     6195     6220     6266 
## 31401.13 33250.49 28426.85 35030.43 26130.73 29181.55 36000.50 26727.01 
##     6267     6268     6269     6270     6271     6301     6305     6311 
## 27867.95 26490.28 28259.54 32063.27 26986.88 37239.34 26130.73 36301.31 
##     6336     6375     6384     6391     6400     6401     6419     6421 
## 28674.26 27700.64 38134.65 33759.55 40962.97 38985.46 26130.73 27472.80 
##     6491     6507     6508     6509     6510     6512     6513     6514 
## 30190.77 30468.44 32317.80 32428.16 30658.90 27093.68 26130.73 26532.99 
##     6515     6516     6518     6519     6520     6521     6526     6527 
## 26534.77 27414.06 28400.15 26605.97 26650.47 37905.03 26130.73 26130.73 
##     6579     6583     6671     6682     6700     6701     6702     6711 
## 27921.35 33376.86 26130.73 27748.69 28355.65 28391.25 28843.36 33759.55 
##     6713     6748     6750     6783     6784     6786     6787     6834 
## 29444.98 26130.73 28941.25 26799.99 28044.16 27031.38 27770.05 26130.73 
##     6837     6845     6846     6848     6881     6887     6889     6918 
## 26130.73 34220.56 32063.27 28674.26 26842.70 26130.73 26130.73 41952.62 
##     6936     6937     6940     6941     6943     6944     6945     6946 
## 28951.93 26675.39 31751.78 26782.19 27440.76 29475.24 29347.08 26460.02 
##     6948     7002     7040     7042     7057     7058     7082     7083 
## 33592.24 32602.59 26130.73 26130.73 26819.56 26905.00 30306.47 33182.85 
##     7086     7104     7105     7106     7107     7108     7109     7110 
## 30489.80 30690.93 28519.41 29327.50 31632.52 30507.60 30509.38 31070.06 
##     7111     7112     7113     7114     7115     7116     7117     7118 
## 27278.79 26130.73 31470.55 30085.76 30402.58 31216.02 28166.98 31365.53 
##     7119     7120     7122     7123     7124     7126     7127     7128 
## 28729.44 31470.55 28553.23 31653.88 29355.98 28827.34 28585.27 32063.27 
##     7129     7140     7195     7252 
## 31563.11 33088.51 32063.27 29316.82
reg3 <- lm(UGDS ~ SAT_AVG, data=data2)
summary(reg3)
## 
## Call:
## lm(formula = UGDS ~ SAT_AVG, data = data2)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -11197  -3981  -2485   1077  45035 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -8999.262   1573.214  -5.720 1.32e-08 ***
## SAT_AVG        13.708      1.474   9.301  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7095 on 1302 degrees of freedom
##   (6399 observations deleted due to missingness)
## Multiple R-squared:  0.06231,    Adjusted R-squared:  0.06159 
## F-statistic: 86.51 on 1 and 1302 DF,  p-value: < 2.2e-16
coefficients(reg3)
## (Intercept)     SAT_AVG 
## -8999.26201    13.70842
confint(reg3, level=0.95)
##                    2.5 %      97.5 %
## (Intercept) -12085.57297 -5912.95105
## SAT_AVG         10.81707    16.59977
lm.beta(reg3)
##   SAT_AVG 
## 0.2496111
fitted(reg3)
##          1          2          4          5          6          9 
##  2337.6046  6175.9632  7711.3067  2666.6067  7245.2203  4832.5377 
##         10         11         13         24         27         33 
##  7656.4730  7190.3866  3914.0733  5065.5809  5271.2073  4572.0777 
##         35         37         38         40         42         47 
##  5463.1252  4901.0798  5668.7516  5106.7062  3722.1554  6971.0518 
##         51         52         53         54         57         58 
##  5367.1662  6299.3391  3749.5722  2118.2698  5394.5831  4407.5766 
##         65         83        116        123        129        135 
##  5449.4168  6696.8834  5709.8768  4544.6608  5367.1662  6203.3801 
##        138        139        141        142        145        147 
##  6833.9676  3146.4016  5915.5032  4846.2461  4572.0777  5380.8747 
##        148        157        158        159        172        175 
##  4503.5355  6504.9654  4558.3692  8054.0173  6244.5054  5545.3757 
##        176        187        189        211        216        224 
##  3749.5722  4476.1187  4558.3692  5216.3736  6381.5896  4380.1597 
##        227        228        229        233        234        235 
## 12180.2529  6203.3801  7916.9331  3118.9847  5723.5853  4654.3282 
##        237        238        240        241        242        243 
##  3475.4037  4997.0388  5449.4168  2940.7752  3530.2374  3845.5312 
##        244        245        246        247        248        249 
##  9945.7798  7807.2657  7012.1771  9232.9418  6463.8402  8999.8986 
##        251        252        275        277        278        284 
##  8177.3931  6751.7171  7587.9309  5230.0820  4599.4945 10452.9915 
##        308        331        344        351        353        367 
##  5353.4578  4846.2461 11563.3738  3132.6931  4517.2440  3379.4448 
##        369        378        387        393        408        411 
##  4901.0798  3804.4059  6121.1296  7697.5983  4640.6198  6792.8423 
##        423        441        442        446        448        455 
##  3365.7363  3776.9891  8821.6891  4846.2461  3283.4858  4942.2051 
##        456        461        464        465        472        489 
##  7245.2203  7916.9331  6559.7991 10932.7863  6217.0885  6285.6306 
##        490        493        495        499        501        507 
##  8040.3089  4572.0777  6792.8423  4832.5377  5230.0820  8945.0649 
##        511        520        525        527        531        536 
##  9644.1945  5038.1641  6203.3801  4489.8271  4297.9092  6779.1339 
##        537        541        559        560        568        573 
##  9918.3630  8287.0605  7108.1361  5545.3757  4092.2828  5463.1252 
##        574        576        583        585        596        598 
##  5929.2116  7546.8056  9274.0671  6463.8402  7875.8078  4983.3304 
##        605        606        613        620        623        629 
##  4297.9092  4339.0344  5161.5399  6189.6717  4311.6176  4572.0777 
##        636        637        643        653        664        671 
##  3324.6111  4914.7883  8081.4342  4709.1619  5572.7926  2721.4404 
##        673        675        678        684        686        692 
##  6134.8380  4284.2008  3776.9891  4448.7018 11467.4149  3256.0690 
##        693        696        698        699        702        703 
##  7368.5961  2694.0236  8163.6847  6491.2570  2639.1899  8780.5638 
##        704        705        714        715        717        718 
## 10384.4494  6148.5464  4188.2418  3859.2396  2008.6024  4434.9934 
##        726        727        730        734        736        738 
##  3886.6565  7245.2203  4352.7429  6806.5507  2310.1877  3996.3238 
##        739        741        742        746        747        749 
##  5504.2505  5504.2505  5572.7926  3722.1554  7121.8445  5929.2116 
##        754        755        758        796        805        806 
##  6724.3002  7834.6825  8451.5616  9232.9418  6532.3823  3598.7796 
##        807        811        835        836        839        846 
##  6669.4665  5682.4600  6929.9266  3598.7796  4229.3671  5997.7537 
##        849        853        855        857        862        868 
##  3324.6111  2831.1078  4023.7407  5600.2094  3708.4469  2995.6089 
##        869        870        874        878        883        885 
##  1940.0603  4791.4124  3571.3627  2789.9825  7217.8035  4503.5355 
##        888        891        894        896        901        902 
##  3612.4880  3749.5722  4380.1597  7108.1361  4160.8249  9726.4450 
##        904        906        907        908        909        910 
##  2968.1921 10192.5315  4297.9092  6518.6738  6066.2959  5463.1252 
##        911        912        918        919        924        925 
##  8108.8510  2776.2741  5751.0021  5188.9567  7519.3888  4763.9956 
##        929        930        931        933        935        936 
##  6614.6328  1419.1402  4270.4923  4366.4513  5819.5442  2611.7730 
##        937        940        941        944        945        947 
##  4037.4491  4777.7040  6546.0907  4297.9092  4311.6176  4955.9135 
##        949        950        952        953        954        968 
##  4023.7407  4572.0777  4133.4081  3831.8228  5668.7516  4654.3282 
##        969        972        973        974        979        981 
##  5284.9157  5490.5421  5751.0021  3653.6133  5421.9999  5271.2073 
##        987        989        994        997       1011       1013 
##  5600.2094  4846.2461  4558.3692  6929.9266  2927.0668 11631.9160 
##       1022       1031       1033       1034       1039       1040 
##  5134.1230  4846.2461  5929.2116  5435.7084  3461.6953  3749.5722 
##       1041       1046       1049       1050       1052       1053 
##  5476.8336  5120.4146  6422.7149  5120.4146  9178.1081  8122.5594 
##       1057       1059       1067       1080       1081       1082 
##  8355.6026  6217.0885  5805.8358  5668.7516  4791.4124  6422.7149 
##       1085       1091       1094       1096       1098       1099 
##  7615.3478  4297.9092  5367.1662  3749.5722  5339.7494  5161.5399 
##       1108       1109       1111       1113       1114       1117 
##  6422.7149  5051.8725  5120.4146 11028.7453  3201.2353  6148.5464 
##       1122       1130       1131       1132       1135       1137 
##  5038.1641  4832.5377  5394.5831  5106.7062  5586.5010  4818.8293 
##       1138       1150       1151       1156       1157       1160 
##  5819.5442  5463.1252  5668.7516  5805.8358  5559.0842  6203.3801 
##       1163       1164       1167       1169       1170       1171 
##  4297.9092  8972.4817  5367.1662  5613.9179  5257.4988  7519.3888 
##       1177       1181       1182       1183       1184       1187 
##  7629.0562  6683.1749  5134.1230  6203.3801  6217.0885  6093.7127 
##       1189       1191       1193       1194       1196       1197 
##  4284.2008  5175.2483  4736.5787  4846.2461  4955.9135  4229.3671 
##       1198       1199       1200       1201       1202       1203 
##  4722.8703  3516.5290  3804.4059  3914.0733  7423.4298  3557.6543 
##       1204       1205       1218       1219       1220       1228 
##  4147.1165  3927.7817  4709.1619  5202.6652  5819.5442 10877.9526 
##       1229       1231       1232       1235       1237       1238 
##  4160.8249  4229.3671  4147.1165  8931.3565  4448.7018  4654.3282 
##       1239       1240       1243       1244       1245       1246 
##  3927.7817  6683.1749  3927.7817  7231.5119  5778.4190  6833.9676 
##       1249       1252       1253       1257       1258       1259 
##  6463.8402  4777.7040  5353.4578  6093.7127  5106.7062  6710.5918 
##       1260       1264       1265       1266       1268       1270 
##  7450.8467  6080.0043  7985.4752  3900.3649  4955.9135  4763.9956 
##       1272       1273       1274       1286       1287       1289 
##  3859.2396  4256.7839 10165.1146  6696.8834  4572.0777  6957.3434 
##       1295       1296       1300       1301       1304       1305 
##  5915.5032  6861.3844  5600.2094  5120.4146  5394.5831  6121.1296 
##       1312       1316       1322       1323       1324       1330 
##  5394.5831  6422.7149  4023.7407  3516.5290  6080.0043  5517.9589 
##       1332       1333       1334       1340       1348       1352 
##  6354.1728  4284.2008  4709.1619  4243.0755  4832.5377  5106.7062 
##       1355       1365       1366       1369       1374       1375 
##  2666.6067  6696.8834  5751.0021  5517.9589  5120.4146  4777.7040 
##       1376       1382       1384       1388       1389       1390 
##  4846.2461  4846.2461  4736.5787  4805.1209  4407.5766  5216.3736 
##       1395       1396       1400       1401       1404       1405 
##  4818.8293  6559.7991  6354.1728  6422.7149  5243.7904  4215.6586 
##       1407       1412       1413       1416       1427       1428 
##  8314.4774  5230.0820  4818.8293  6107.4211  4846.2461  3105.2763 
##       1429       1430       1431       1435       1440       1441 
##  4997.0388  6655.7581  4243.0755  6683.1749  5106.7062  5586.5010 
##       1443       1448       1459       1462       1463       1465 
##  5339.7494  4243.0755  4256.7839  4462.4103  7862.0994  4297.9092 
##       1466       1476       1484       1486       1492       1493 
##  5353.4578  6203.3801  3146.4016  2899.6499  4530.9524  6916.2181 
##       1495       1499       1501       1502       1503       1504 
##  5394.5831  4572.0777  6134.8380  6559.7991  5120.4146  5833.2527 
##       1505       1506       1509       1511       1524       1525 
##  5134.1230  5120.4146  5079.2893  4846.2461  5120.4146  3475.4037 
##       1526       1528       1530       1531       1538       1540 
##  2049.7277  5668.7516  9397.4429  5243.7904  4709.1619  9274.0671 
##       1542       1547       1549       1550       1552       1556 
##  4037.4491  3324.6111  5778.4190  5038.1641  5709.8768  4229.3671 
##       1559       1571       1572       1573       1577       1578 
##  4681.7450  3612.4880  2885.9415  5737.2937  2707.7320  3064.1510 
##       1582       1591       1598       1599       1600       1601 
##  4256.7839 10727.1600  7629.0562  9027.3154  6971.0518  2543.2309 
##       1605       1606       1609       1615       1617       1619 
##  2981.9005  5367.1662  5367.1662  7286.3456  9136.9828  5833.2527 
##       1622       1624       1628       1629       1634       1636 
##  4572.0777  5997.7537  3160.1100 10727.1600  8437.8532  2995.6089 
##       1637       1640       1641       1647       1649       1650 
##  4037.4491  4914.7883  8095.1426  9918.3630  8821.6891  9767.5703 
##       1651       1661       1663       1666       1667       1668 
##  4585.7861  3996.3238  2748.8573  3585.0711  8054.0173  5984.0453 
##       1673       1674       1676       1681       1690       1692 
##  4763.9956  4859.9546  6916.2181 11577.0823  4352.7429  5888.0863 
##       1694       1698       1699       1701       1702       1703 
##  6696.8834  7683.8899  5394.5831  5723.5853  5764.7105 11563.3738 
##       1704       1714       1727       1731       1733       1734 
##  6148.5464  3146.4016  4393.8681 10466.6999  3968.9070  1693.3086 
##       1741       1743       1747       1749       1751       1753 
##  4489.8271  7039.5940  5051.8725  5051.8725  5380.8747 10507.8252 
##       1754       1755       1756       1757       1759       1760 
## 10055.4472  6299.3391  5764.7105  4668.0366  4201.9502 10905.3695 
##       1762       1763       1764       1767       1769       1770 
##  4668.0366  4832.5377  6422.7149  6093.7127  5819.5442  5942.9200 
##       1776       1780       1783       1785       1792       1795 
##  7204.0950  5394.5831  4572.0777  4846.2461  6217.0885  5092.9978 
##       1796       1799       1802       1805       1808       1812 
##  4846.2461  7766.1404  5408.2915  5929.2116  7245.2203  7985.4752 
##       1818       1820       1823       1824       1825       1826 
##  5092.9978  6450.1317  5380.8747  1967.4771  4325.3260  9918.3630 
##       1828       1829       1830       1831       1841       1844 
##  6875.0929  8054.0173  6148.5464  4613.2029  4846.2461  4763.9956 
##       1846       1847       1849       1854       1856       1860 
##  5668.7516  3571.3627  5120.4146  5120.4146  5051.8725  5188.9567 
##       1862       1868       1871       1879       1882       1883 
##  3475.4037  5668.7516  5120.4146  5723.5853  4846.2461  5668.7516 
##       1884       1887       1888       1891       1899       1909 
##  6710.5918 10302.1988  6984.7603  6422.7149  6093.7127  9561.9440 
##       1911       1918       1919       1921       1926       1927 
##  4846.2461  8424.1448  4791.4124  5915.5032  6217.0885  6738.0086 
##       1930       1935       1937       1939       1944       1947 
##  5380.8747  5559.0842  6217.0885  4215.6586  7162.9698  4846.2461 
##       1948       1949       1950       1951       1952       1953 
##  6833.9676  5627.6263  8712.0217  4928.4967  6162.2548  4010.0323 
##       1955       1958       1965       1968       1970       1977 
##  5147.8315  4572.0777  5394.5831  2954.4836  5120.4146  4270.4923 
##       1985       1988       1990       1991       1992       1993 
##  3489.1122  7149.2613  6052.5874  4544.6608  2310.1877  6354.1728 
##       1996       2000       2003       2005       2007       2010 
##  6436.4233  1419.1402  5106.7062  2844.8162  5805.8358  5230.0820 
##       2015       2018       2019       2022       2025       2027 
##  4901.0798  5394.5831  4846.2461  5394.5831  6148.5464  4969.6219 
##       2030       2031       2036       2037       2049       2055 
##  4517.2440  7245.2203  5463.1252  5421.9999  5888.0863  5230.0820 
##       2060       2064       2067       2071       2075       2076 
##  6587.2160  4297.9092  4489.8271  4572.0777  6984.7603  6477.5486 
##       2077       2078       2084       2085       2087       2093 
##  8588.6459  6148.5464  7807.2657  5408.2915  5723.5853  6957.3434 
##       2096       2101       2102       2105       2110       2111 
##  7985.4752  4572.0777  7286.3456  5668.7516  5586.5010  5394.5831 
##       2112       2117       2118       2120       2121       2122 
##  5942.9200 11261.7885  6148.5464  6271.9222  6642.0497  5284.9157 
##       2128       2141       2142       2143       2144       2145 
##  6532.3823  6422.7149  6463.8402  5737.2937  3571.3627  5134.1230 
##       2150       2151       2155       2156       2157       2158 
##  4572.0777  5394.5831  5627.6263  7450.8467  5531.6673  5586.5010 
##       2159       2162       2164       2167       2169       2173 
##  5792.1274  5380.8747  5942.9200  4846.2461  5394.5831  6409.0065 
##       2174       2179       2185       2192       2193       2196 
##  6710.5918  5120.4146  4297.9092  4709.1619  5819.5442  4846.2461 
##       2202       2205       2215       2216       2217       2227 
## 10795.7021  4010.0323  6134.8380  4229.3671  4846.2461  4188.2418 
##       2238       2241       2243       2254       2259       2260 
##  2104.5614  4023.7407  3694.7385  6326.7559  3941.4902  2927.0668 
##       2261       2263       2264       2271       2273       2279 
##  5134.1230  3955.1986  6121.1296  3201.2353  3434.2785  5463.1252 
##       2280       2287       2294       2296       2298       2300 
##  4366.4513  7012.1771 11439.9980  5833.2527  5065.5809  5051.8725 
##       2301       2302       2305       2307       2309       2311 
##  7656.4730  5188.9567  3324.6111  6532.3823  2556.9393  9452.2766 
##       2312       2316       2319       2326       2331       2333 
##  5778.4190  7629.0562  4434.9934  3818.1143  3955.1986  7354.8877 
##       2335       2339       2353       2357       2360       2373 
##  5531.6673  4489.8271  5970.3369  6971.0518  5586.5010  9411.1513 
##       2393       2403       2407       2409       2412       2416 
##  5874.3779  7382.3046  9767.5703 11152.1211  2954.4836 10028.0304 
##       2417       2422       2425       2426       2427       2430 
## 10494.1168  7930.6415  5874.3779  4777.7040  6491.2570  6902.5097 
##       2431       2434       2437       2440       2442       2445 
##  4297.9092  4640.6198  5942.9200  3338.3195  5188.9567  2954.4836 
##       2450       2455       2462       2468       2469       2474 
##  5709.8768  8191.1016 10096.5725  6724.3002  6367.8812  5010.7472 
##       2481       2486       2487       2489       2496       2503 
##  9232.9418  3530.2374  5682.4600  4023.7407  6038.8790  5600.2094 
##       2504       2517       2520       2521       2526       2527 
##  2515.8141  5696.1684  4859.9546  3763.2806  4133.4081  6313.0475 
##       2535       2537       2541       2542       2543       2548 
##  9424.8597  5257.4988  5655.0431  3886.6565  3461.6953  5449.4168 
##       2552       2553       2561       2563       2565       2571 
##  4078.5744  6642.0497  9808.6956  5517.9589  7999.1836  5613.9179 
##       2572       2576       2581       2582       2583       2587 
##  3818.1143  4133.4081  6450.1317  8012.8921  5134.1230  5956.6285 
##       2590       2594       2597       2598       2599       2600 
##  6175.9632  4462.4103  3023.0258  4462.4103  3269.7774  6052.5874 
##       2601       2602       2603       2604       2605       2606 
##  8643.4796  6971.0518  8191.1016  7354.8877  6066.2959  5476.8336 
##       2607       2609       2610       2611       2612       2613 
##  3872.9480  5476.8336  7738.7236  6381.5896  5888.0863  6162.2548 
##       2615       2617       2618       2621       2624       2642 
##  6011.4622  4640.6198  5134.1230  6162.2548  7231.5119 10233.6567 
##       2644       2646       2647       2658       2664       2666 
##  5106.7062 10466.6999  5435.7084  7738.7236  6738.0086  4188.2418 
##       2668       2675       2677       2686       2691       2692 
##  4709.1619  4297.9092  5051.8725  1597.3497  9328.9007 10932.7863 
##       2694       2696       2697       2700       2702       2704 
##  5202.6652  2872.2331  7793.5573  3228.6521  4983.3304  3009.3173 
##       2710       2714       2720       2721       2722       2726 
##  6025.1706  2077.1445   870.8032  1624.7665  3667.3217  4503.5355 
##       2728       2734       2735       2738       2739       2740 
##  4188.2418  4928.4967  3365.7363  3475.4037  7327.4709  9205.5249 
##       2741       2742       2743       2744       2745       2746 
##  5792.1274  5298.6241  3146.4016  6299.3391  8177.3931  3653.6133 
##       2747       2749       2750       2751       2752       2755 
##  6696.8834  3201.2353  3749.5722  3996.3238  3845.5312  5408.2915 
##       2758       2763       2764       2770       2782       2788 
##  4476.1187  1144.9717  6107.4211  3886.6565  6546.0907  4722.8703 
##       2791       2792       2795       2799       2803       2805 
##  2776.2741  5188.9567  4119.6997  7149.2613  5394.5831  5188.9567 
##       2807       2810       2814       2817       2822       2828 
##  5942.9200  5970.3369  3968.9070  4983.3304  5394.5831  4174.5334 
##       2830       2833       2836       2839       2844       2848 
##  5367.1662  5874.3779  5106.7062  4873.6630  6080.0043  9849.8209 
##       2849       2852       2855       2856       2858       2862 
##  7272.6372  2022.3108  3982.6154  4284.2008  6971.0518  3749.5722 
##       2865       2868       2871       2876       2877       2884 
##  5367.1662  4901.0798  5312.3325  7368.5961  4366.4513  5188.9567 
##       2888       2893       2894       2902       2911       2913 
##  3475.4037  5079.2893  4763.9956  6299.3391  5394.5831  9260.3586 
##       2915       2922       2923       2924       2931       2935 
##  4243.0755  4023.7407  5326.0410  6148.5464  7999.1836  5120.4146 
##       2936       2937       2938       2940       2948       2951 
##  5490.5421  5339.7494  4777.7040  4832.5377  3845.5312  9493.4018 
##       2954       2956       2966       2971       2976       2981 
##  4777.7040  7176.6782  8712.0217  6162.2548  5997.7537  8547.5206 
##       3000       3005       3016       3019       3022       3023 
##  7217.8035  5134.1230  4901.0798  5298.6241  1076.4296  4297.9092 
##       3026       3029       3031       3033       3034       3041 
##  7848.3910  6258.2138  4503.5355  2584.3562  4695.4535  4572.0777 
##       3044       3049       3054       3058       3060       3062 
##  4777.7040  3886.6565  4832.5377  3749.5722  6450.1317  3475.4037 
##       3063       3065       3067       3068       3071       3074 
##  6587.2160  7053.3024  6971.0518  7300.0540  4846.2461  2652.8983 
##       3078       3081       3082       3083       3086       3104 
##  5243.7904  4297.9092  4448.7018  4846.2461  8766.8554  5216.3736 
##       3107       3110       3115       3123       3126       3128 
##  3996.3238  5819.5442  5846.9611  5353.4578  4530.9524  5312.3325 
##       3130       3131       3133       3140       3141       3142 
##  6244.5054  6299.3391  5942.9200  5120.4146  7382.3046  9959.4882 
##       3147       3152       3156       3157       3162       3167 
##  5106.7062  4928.4967  7574.2225  4722.8703  3338.3195  7039.5940 
##       3169       3171       3179       3181       3184       3186 
##  5161.5399  4297.9092  4763.9956  6148.5464  4297.9092  8999.8986 
##       3187       3192       3193       3195       3196       3197 
##  9054.7323  3297.1942  3804.4059  3900.3649 10686.0347  4777.7040 
##       3200       3204       3210       3214       3217       3218 
##  4270.4923  3722.1554  4572.0777  7258.9287  6683.1749  4078.5744 
##       3219       3220       3221       3240       3241       3247 
##  5230.0820  3722.1554  6532.3823  5216.3736  5696.1684  4174.5334 
##       3250       3252       3255       3256       3262       3265 
## 10494.1168  3681.0301  4188.2418  4133.4081  3626.1964  4160.8249 
##       3266       3267       3269       3270       3278       3282 
##  3694.7385  4626.9113  8821.6891  4654.3282  9178.1081  2817.3994 
##       3283       3284       3288       3289       3290       3291 
##  3982.6154  4818.8293  5298.6241  1391.7233  4023.7407  5120.4146 
##       3295       3297       3298       3301       3302       3305 
##  6422.7149  4873.6630  5723.5853  5010.7472  3516.5290  2694.0236 
##       3313       3316       3317       3318       3319       3320 
##  5449.4168  4352.7429  3132.6931  4215.6586  4147.1165  4750.2872 
##       3321       3322       3323       3324       3325       3326 
##  4722.8703  4078.5744  4339.0344  5038.1641  4270.4923  3681.0301 
##       3327       3328       3329       3330       3331       3332 
##  3530.2374  3968.9070  7396.0130  4256.7839  3996.3238  4037.4491 
##       3333       3334       3344       3345       3346       3347 
##  3324.6111  4997.0388 10905.3695  5723.5853  4791.4124  4613.2029 
##       3349       3351       3352       3353       3354       3355 
##  7025.8855  4503.5355  4859.9546  4901.0798  8478.9785  3077.8594 
##       3362       3366       3371       3373       3374       3376 
##  4640.6198  3749.5722  5408.2915  4613.2029  5161.5399  5175.2483 
##       3379       3384       3385       3392       3395       3396 
##  6422.7149  4448.7018  4695.4535 10644.9094  6422.7149  4297.9092 
##       3405       3406       3408       3412       3414       3417 
##  3900.3649  1967.4771  8999.8986  4818.8293  5792.1274  5463.1252 
##       3420       3421       3422       3424       3428       3435 
##  5024.4556  5326.0410  4380.1597  5394.5831 10672.3263  3585.0711 
##       3437       3438       3446       3447       3450       3453 
##  5764.7105  8191.1016  5230.0820  4668.0366  5421.9999  6587.2160 
##       3456       3457       3458       3460       3461       3462 
##  5709.8768  2049.7277  8287.0605  4599.4945  5188.9567  5161.5399 
##       3463       3465       3468       3474       3475       3480 
##  5326.0410  4928.4967  3790.6975  3831.8228  4983.3304  3955.1986 
##       3481       3484       3485       3486       3487       3488 
##  6792.8423  5942.9200  4297.9092  3790.6975  7683.8899  2995.6089 
##       3489       3490       3491       3492       3493       3494 
##  1994.8940  3571.3627  1611.0581  4654.3282  2104.5614  3982.6154 
##       3496       3504       3505       3507       3509       3511 
##  2927.0668  5435.7084  7368.5961  6929.9266  4037.4491  5065.5809 
##       3512       3517       3521       3523       3525       3526 
##  5312.3325  4572.0777  5051.8725  4434.9934  7190.3866  5641.3347 
##       3528       3533       3536       3539       3540       3541 
##  5092.9978  5312.3325  6395.2980  4846.2461  6217.0885  7121.8445 
##       3542       3543       3544       3546       3548       3552 
##  3749.5722  5600.2094  5846.9611  6148.5464  3475.4037  5312.3325 
##       3553       3557       3562       3564       3567       3572 
##  7108.1361  5120.4146  3968.9070  6313.0475  2556.9393  5175.2483 
##       3574       3577       3578       3579       3580       3583 
##  5284.9157  1446.5570  1076.4296  5751.0021  5463.1252  5380.8747 
##       3587       3589       3591       3593       3601       3605 
##  5051.8725  5106.7062  5147.8315  6038.8790  5394.5831  8766.8554 
##       3607       3621       3622       3623       3624       3628 
##  3475.4037  4736.5787  5915.5032  7423.4298  5394.5831  6148.5464 
##       3629       3630       3632       3633       3635       3641 
##  4188.2418  5613.9179  4572.0777  7039.5940 11302.9138  5956.6285 
##       3645       3649       3656       3668       3671       3674 
##  4380.1597  6888.8013  7820.9741  4997.0388  4297.9092  5737.2937 
##       3675       3678       3681       3682       3683       3696 
##  4654.3282  7601.6393  4051.1575  3297.1942  3461.6953  5216.3736 
##       3699       3700       3702       3704       3706       3707 
##  5449.4168  5312.3325  3256.0690  6614.6328  4380.1597  2159.3950 
##       3708       3717       3722       3724       3727       3729 
##  4201.9502  4201.9502  3420.5700  7135.5529  4846.2461  5586.5010 
##       3731       3735       3746       3754       3755       3759 
##  3352.0279  4640.6198  6025.1706  3900.3649  4064.8660  5668.7516 
##       3760       3763       3766       3768       3769       3772 
##  2652.8983 11015.0369  6299.3391  6230.7969  4709.1619  4668.0366 
##       3774       3780       3784       3785       3786       3787 
##  5161.5399  9041.0238  6888.8013  4681.7450  5147.8315  3406.8616 
##       3789       3790       3798       3799       3800       3801 
##  3201.2353  4174.5334  3639.9048  7533.0972  5435.7084  8766.8554 
##       3802       3804       3806       3809       3810       3811 
##  8259.6437  5408.2915  7546.8056  4983.3304  4201.9502  5216.3736 
##       3813       3814       3816       3817       3818       3830 
##  2131.9782  6217.0885  4489.8271  4064.8660  8561.2290  3968.9070 
##       3832       3838       3839       3855       3859       3862 
##  4297.9092  8684.6048  6217.0885  5572.7926  5627.6263  6504.9654 
##       3864       3867       3868       3872       3873       3875 
##  6381.5896  4256.7839  6765.4255  3900.3649  3845.5312  9904.6546 
##       3877       3882       3886       3889       3891       3892 
##  5435.7084  2639.1899  7327.4709  3653.6133  3434.2785  5476.8336 
##       3893       3894       3897       3906       3907       3909 
##  9822.4040  5613.9179  6792.8423  4640.6198  4750.2872  2680.3152 
##       3910       3912       3913       3914       3916       3919 
##  6792.8423  6052.5874  4695.4535  5833.2527  6806.5507  5257.4988 
##       3920       3922       3924       3925       3926       3933 
##  4777.7040  4681.7450  4421.2850  6271.9222  4722.8703  2872.2331 
##       3935       3941       3943       3944       3949       3951 
##  4805.1209  4270.4923  5888.0863  5888.0863  9328.9007  5901.7948 
##       3953       3954       3960       3964       3966       3968 
##  4626.9113  5476.8336  5476.8336  3968.9070  7656.4730  6148.5464 
##       3969       3970       3973       3974       3975       3977 
##  9603.0692  6929.9266  2474.6888  1638.4749  4585.7861 10123.9893 
##       3990       3999       4003       4006       4025       4028 
##  4407.5766  4133.4081  5298.6241  7546.8056  4955.9135  6285.6306 
##       4030       4032       4036       4037       4046       4047 
##  7862.0994  5490.5421  6628.3412  7217.8035  5737.2937  5120.4146 
##       4048       4051       4053       4056       4058       4061 
##  7999.1836  6217.0885  9136.9828  4572.0777  4805.1209  3420.5700 
##       4062       4065       4067       4068       4069       4070 
##  3708.4469  4544.6608  4695.4535  4517.2440  4229.3671  3338.3195 
##       4074       4082       4087       4091       4093       4094 
##  4997.0388  3941.4902  4695.4535  3914.0733  4229.3671  4476.1187 
##       4095       4101       4102       4106       4108       4111 
##  4777.7040  5655.0431  5147.8315  3749.5722  5394.5831  4750.2872 
##       4112       4113       4115       4116       4122       4126 
##  5942.9200  6134.8380  5929.2116  5367.1662  4010.0323  4023.7407 
##       4127       4132       4134       4140       4141       4143 
##  7725.0152  8040.3089  3749.5722  5874.3779  6189.6717  6422.7149 
##       4144       4148       4149       4153       4157       4158 
##  2241.6456  4297.9092  5929.2116  5394.5831  6217.0885  5394.5831 
##       4159       4160       4161       4162       4164       4165 
##  6696.8834  5792.1274  5120.4146  4572.0777  5394.5831  4846.2461 
##       4166       4167       4168       4169       4170       4180 
##  8629.7711  4846.2461  5942.9200  5394.5831  5394.5831  6326.7559 
##       4239       4242       4243       4249       4260       4261 
##  5449.4168  4887.3714  6724.3002  7286.3456  1912.6434 11083.5790 
##       4262       4386       4473       4628       4629       4739 
##  7629.0562  8465.2700  3996.3238  4832.5377  4421.2850  4709.1619 
##       4754       4811       5056       5165       5195       5201 
##  7766.1404  6011.4622  6600.9244  7135.5529  4887.3714  5517.9589 
##       5263       5264       5265       5339       5458       5528 
##  4763.9956  5394.5831  4722.8703  4928.4967 11220.6632  7601.6393 
##       5632       5685       5856       5858       5912       6051 
##  5134.1230  5874.3779  6929.9266  5846.9611  5134.1230  6148.5464 
##       6104       6301       6700       6948       7082       7129 
##  6450.1317  6244.5054  5888.0863  5257.4988  5120.4146  4928.4967 
##       7228       7252 
##  6847.6760  3160.1100
reg4 <- lm(UGDS ~ ADM_RATE, data=data2)
summary(reg4)
## 
## Call:
## lm(formula = UGDS ~ ADM_RATE, data = data2)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##  -6377  -3081  -2259     81  47716 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   6474.7      462.7  13.994  < 2e-16 ***
## ADM_RATE     -3852.2      640.6  -6.013 2.12e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6273 on 2196 degrees of freedom
##   (5505 observations deleted due to missingness)
## Multiple R-squared:  0.0162, Adjusted R-squared:  0.01575 
## F-statistic: 36.16 on 1 and 2196 DF,  p-value: 2.122e-09
coefficients(reg4)
## (Intercept)    ADM_RATE 
##    6474.726   -3852.210
confint(reg4, level=0.95)
##                 2.5 %    97.5 %
## (Intercept)  5567.423  7382.029
## ADM_RATE    -5108.459 -2595.960
lm.beta(reg4)
##   ADM_RATE 
## -0.1272796
fitted(reg4)
##        1        2        4        5        6        9       10       11 
## 4450.005 3173.768 3314.759 4423.039 4508.173 3386.410 3259.287 4418.031 
##       13       23       24       25       27       31       33       35 
## 4422.269 2622.517 4225.421 2622.517 3267.376 3961.159 3701.520 4109.855 
##       37       38       40       42       47       51       52       53 
## 4222.339 3612.534 3859.846 4630.673 4181.121 3263.909 4480.437 2622.517 
##       54       57       58       65       76       77       78       83 
## 4201.537 4774.361 4578.669 4854.102 2659.498 2622.517 2622.517 3226.158 
##       85       96       99      103      104      108      116      123 
## 3600.207 3386.795 4257.009 2869.828 2934.160 3354.822 3827.103 4289.368 
##      129      135      138      139      141      142      145      147 
## 4191.136 4108.699 4084.815 4984.692 3686.112 3151.810 4104.076 2843.633 
##      148      157      158      159      162      172      175      176 
## 4280.122 2656.416 4056.309 3284.326 3786.654 3754.681 3049.341 4093.675 
##      187      189      192      194      200      208      211      215 
## 3759.304 3723.478 4306.317 3162.211 5698.121 3358.289 3322.463 3899.139 
##      216      217      224      225      227      228      229      230 
## 3570.160 2656.416 3405.671 4021.254 6134.576 4126.034 5284.779 4989.699 
##      231      232      233      234      235      236      237      238 
## 3755.066 3673.399 3221.535 4476.585 3741.198 4843.701 4186.514 4761.649 
##      239      240      241      242      243      244      245      246 
## 3766.238 5108.733 4122.182 4438.448 3676.096 5857.602 4919.589 5033.229 
##      247      248      249      251      252      258      259      264 
## 5759.756 4229.273 5192.326 5074.833 4328.275 5534.017 3905.302 3104.043 
##      275      276      277      278      284      288      293      308 
## 4662.647 2622.517 3158.744 4336.750 6059.843 4787.458 3451.127 3357.518 
##      319      320      321      331      337      344      351      353 
## 4480.052 4399.156 3930.727 3908.384 2622.517 5925.786 4276.655 3525.860 
##      360      361      362      365      367      369      370      378 
## 2835.159 2860.583 3015.442 4877.600 3919.556 4681.137 4222.339 4909.188 
##      387      393      400      408      411      423      426      435 
## 3551.670 4444.227 3105.969 4738.921 3541.654 3458.446 2834.388 2699.561 
##      438      439      440      441      442      446      448      449 
## 2622.517 2622.517 2622.517 3481.174 4855.257 3913.777 5280.541 2622.517 
##      455      456      461      462      464      465      472      489 
## 4647.238 4359.863 5108.733 5973.169 3796.285 6005.142 3659.146 5146.484 
##      490      491      492      493      495      499      501      507 
## 4693.079 2812.045 5039.008 3933.424 4161.474 3554.366 4169.179 4573.661 
##      511      514      520      525      527      531      532      536 
## 5380.699 2622.517 4265.099 3548.973 3392.188 4240.445 2622.517 3362.526 
##      537      541      545      547      557      559      560      565 
## 5780.558 3288.949 2622.517 2622.517 2790.088 3417.613 4090.979 3663.769 
##      568      571      573      574      576      577      578      579 
## 3959.619 3338.642 3662.998 2915.285 3232.707 2841.322 5785.181 4271.262 
##      583      585      596      598      605      606      608      613 
## 5069.825 3374.468 3528.171 2976.149 3305.513 3966.553 3775.868 3744.280 
##      620      622      623      629      636      637      640      643 
## 2775.064 2622.517 2900.646 2722.289 4135.665 4146.451 5026.295 4550.162 
##      646      647      653      660      664      671      673      674 
## 4043.982 3719.241 3696.127 3776.639 3359.829 3120.607 3935.735 4273.188 
##      675      677      678      681      683      684      686      692 
## 3394.114 4993.166 3718.855 5201.956 5553.663 4932.687 6232.037 4789.770 
##      693      694      696      698      699      702      703      704 
## 3861.772 4512.025 4290.523 4708.873 3627.558 3958.463 4787.844 5806.368 
##      705      708      709      714      715      717      718      724 
## 4609.872 2622.517 2974.994 4334.439 4698.472 4020.483 3590.577 5115.281 
##      726      727      730      734      736      737      738      739 
## 5113.741 4563.645 4089.438 3672.629 4434.981 3660.302 4589.070 3931.112 
##      741      742      743      744      745      746      747      749 
## 4630.288 3524.319 2622.517 2622.517 2622.517 2622.517 4102.921 4441.530 
##      751      754      755      758      774      775      777      787 
## 5683.482 4748.551 4340.987 4717.733 3448.816 4314.792 4599.471 4595.618 
##      796      799      805      806      807      811      820      822 
## 5003.953 3686.882 4141.443 4941.932 4594.463 2804.726 3191.873 4267.795 
##      824      832      835      836      838      839      846      849 
## 3694.972 2622.517 4426.892 3204.200 4115.633 4782.065 4476.200 4021.639 
##      853      855      857      862      863      868      869      870 
## 5473.152 4527.049 4869.510 3498.509 3866.010 4653.016 4690.768 3854.068 
##      874      878      883      885      887      888      891      894 
## 4475.815 3213.060 4131.427 3554.366 3392.959 2917.211 4839.463 4347.536 
##      896      901      902      904      906      907      908      909 
## 2751.951 4582.521 5441.564 5542.877 5188.859 3792.047 3537.802 4043.982 
##      910      911      912      918      919      921      923      924 
## 4184.973 4328.275 4610.642 4415.720 4346.380 4275.115 2622.517 3904.532 
##      925      929      930      931      932      933      935      936 
## 3237.714 3461.143 5634.559 4257.780 5190.785 3006.967 3911.081 3484.256 
##      937      940      941      943      944      945      947      949 
## 3808.227 4394.533 3429.169 4152.999 5047.483 2763.893 4389.140 4602.167 
##      950      952      953      954      956      962      965      967 
## 4537.450 3176.464 3726.560 3438.415 4092.905 2998.492 3743.510 4548.621 
##      968      969      972      973      974      975      979      981 
## 2901.802 3508.525 3875.255 2896.023 2659.498 3569.775 3968.093 2637.155 
##      987      988      989      994      997     1011     1013     1021 
## 3810.923 4409.557 3350.584 3966.938 3997.755 5320.604 6137.273 3064.365 
##     1022     1027     1031     1033     1034     1036     1039     1040 
## 4400.311 3782.802 4557.867 3866.395 3990.821 3906.458 2850.182 2622.517 
##     1041     1046     1049     1050     1052     1053     1055     1057 
## 4329.816 2898.335 3605.600 3501.976 4200.382 4146.836 4389.525 4525.508 
##     1059     1067     1070     1072     1075     1080     1081     1082 
## 3628.714 3657.991 3257.746 3845.978 4348.306 4089.823 4641.845 4308.244 
##     1085     1087     1091     1094     1096     1097     1098     1099 
## 4034.737 4273.574 3455.750 4119.100 4785.147 3084.782 4058.235 3814.390 
##     1100     1105     1108     1109     1111     1112     1113     1114 
## 3698.439 2721.133 4169.564 4371.035 4514.337 2871.755 5969.702 4255.468 
##     1117     1122     1127     1130     1131     1132     1135     1137 
## 3605.215 3048.956 5537.484 4363.715 3483.871 4137.591 4527.049 4562.489 
##     1138     1141     1145     1150     1151     1152     1153     1156 
## 4102.536 5037.467 3855.224 3334.020 3124.845 2622.517 2622.517 2999.263 
##     1157     1160     1163     1164     1167     1169     1170     1171 
## 2622.517 3543.580 3792.047 3810.923 4359.478 4168.023 3757.763 3837.503 
##     1172     1177     1180     1181     1182     1183     1184     1187 
## 5173.450 4294.376 3989.281 3279.318 3808.227 4394.533 3388.336 3991.207 
##     1189     1191     1193     1194     1195     1196     1197     1198 
## 2886.008 2733.845 2974.223 3759.304 2622.517 3913.777 3756.222 3726.560 
##     1199     1200     1201     1202     1203     1204     1205     1206 
## 3295.112 3883.730 3649.901 3543.580 3517.000 3380.631 4018.557 3454.979 
##     1207     1208     1209     1210     1211     1218     1219     1220 
## 4519.345 3421.465 3533.949 2858.657 4933.842 3613.305 4300.539 2813.201 
##     1228     1229     1231     1232     1235     1237     1238     1239 
## 5660.369 4354.470 4175.727 3681.489 4210.012 2743.476 3916.474 2622.517 
##     1240     1243     1244     1245     1246     1249     1250     1251 
## 3264.295 3981.961 3083.626 3547.432 3302.046 3778.950 6474.726 4193.448 
##     1252     1253     1257     1258     1259     1260     1263     1264 
## 4098.298 3859.461 3820.554 3759.304 4344.454 3638.344 2972.682 3662.998 
##     1265     1266     1268     1270     1272     1273     1274     1286 
## 3806.686 3474.625 4943.088 3881.033 4554.785 2672.595 5395.722 3126.771 
##     1287     1289     1295     1296     1297     1299     1300     1301 
## 4892.624 3356.363 2810.119 3733.494 5007.034 2750.795 4285.901 4285.515 
##     1304     1305     1310     1312     1313     1316     1322     1323 
## 3480.789 3476.551 2622.517 2773.908 5550.196 3183.013 3780.491 3822.480 
##     1324     1328     1330     1332     1333     1334     1339     1340 
## 3438.029 4179.194 3796.285 2708.036 2720.748 4583.291 2622.517 4562.875 
##     1348     1350     1351     1352     1355     1362     1365     1366 
## 3528.171 3089.019 4411.098 4110.240 4236.592 2622.517 2953.036 4440.374 
##     1368     1369     1370     1374     1375     1376     1380     1382 
## 2817.824 4106.773 4661.491 4198.456 2650.252 3817.087 2642.933 3424.161 
##     1384     1388     1389     1390     1393     1395     1396     1400 
## 4644.927 3087.478 4765.501 3174.153 2794.710 5081.382 3828.258 3261.983 
##     1401     1404     1405     1407     1412     1413     1416     1427 
## 5178.072 4576.743 3673.399 3717.700 3921.482 3629.099 3055.890 4394.533 
##     1428     1429     1430     1431     1434     1435     1439     1440 
## 4637.607 4135.665 3693.046 4635.681 3035.088 3629.484 4231.970 3222.306 
##     1441     1443     1448     1459     1462     1463     1465     1466 
## 3394.499 2980.002 2622.517 4713.881 2881.385 3292.031 3576.709 2879.844 
##     1476     1484     1486     1492     1493     1495     1499     1501 
## 3944.980 4911.114 4781.680 4373.346 3522.778 3521.237 4122.567 3969.634 
##     1502     1503     1504     1505     1506     1509     1510     1511 
## 2998.107 3575.168 4796.318 3070.529 3500.050 3663.384 4310.555 3678.022 
##     1521     1524     1525     1526     1528     1530     1531     1534 
## 3617.928 3249.271 4408.016 5677.319 4325.193 5398.034 3932.653 3735.805 
##     1535     1537     1538     1540     1542     1546     1547     1549 
## 5495.495 5900.362 5190.785 5394.181 3703.061 3217.683 3600.593 3293.957 
##     1550     1552     1555     1556     1559     1560     1561     1571 
## 3445.734 3174.153 2725.371 3449.586 3240.796 3613.305 2888.319 4084.815 
##     1572     1573     1577     1578     1582     1584     1588     1591 
## 4353.700 3758.918 4744.314 4813.653 4220.798 3558.989 3366.378 5855.291 
##     1592     1594     1598     1599     1600     1601     1605     1606 
## 3028.154 4177.654 4178.424 4628.362 4388.369 4114.477 3961.159 3898.754 
##     1607     1609     1614     1615     1617     1619     1622     1623 
## 3472.314 4569.423 4367.953 3436.488 3124.845 4193.833 4074.414 4330.586 
##     1624     1628     1629     1631     1632     1633     1634     1636 
## 3542.039 3871.788 5941.580 3486.567 3214.986 3342.880 5461.210 3627.558 
##     1637     1638     1640     1641     1642     1647     1648     1649 
## 4045.908 4532.827 4068.251 4698.472 4919.204 5168.442 4970.824 5145.329 
##     1650     1651     1653     1658     1659     1661     1663     1664 
## 5117.978 3419.539 4649.935 2989.247 4393.377 3127.926 3829.799 5377.617 
##     1666     1667     1668     1669     1672     1673     1674     1676 
## 4438.063 4580.210 3805.145 3656.835 3948.832 3689.193 4076.340 3070.529 
##     1680     1681     1685     1690     1692     1694     1698     1699 
## 3907.614 6245.135 4805.179 3534.720 3720.782 4085.971 4109.855 3748.517 
##     1701     1702     1703     1704     1709     1713     1714     1717 
## 3238.485 3664.925 6171.172 4101.765 3478.863 4367.568 3836.348 2994.255 
##     1720     1724     1725     1726     1727     1731     1733     1734 
## 5352.192 2851.723 3768.164 3536.261 3690.734 5233.544 3432.636 3861.387 
##     1738     1741     1743     1744     1745     1746     1747     1749 
## 3550.514 3756.222 4465.414 3031.236 4848.709 3730.027 3744.665 3515.459 
##     1750     1751     1753     1754     1755     1756     1757     1758 
## 3510.066 3242.337 5810.605 5314.826 3291.260 3387.180 3602.519 3792.433 
##     1759     1760     1761     1762     1763     1764     1767     1769 
## 3103.272 5730.479 4788.229 4113.322 4090.594 4132.968 3701.906 5054.031 
##     1770     1776     1780     1783     1785     1786     1791     1792 
## 3967.323 3657.220 3806.301 3420.309 4717.733 2877.533 2641.007 3814.390 
##     1795     1796     1797     1799     1801     1802     1805     1808 
## 3821.709 3453.823 3723.093 3715.003 3723.093 3822.865 3376.394 3492.731 
##     1809     1812     1818     1820     1823     1824     1825     1826 
## 2893.712 3791.662 2965.748 4262.787 4217.717 4609.486 4911.114 5232.774 
##     1828     1829     1830     1831     1841     1844     1846     1847 
## 3928.801 3566.308 4060.546 3445.349 3697.668 3798.596 3893.746 4108.314 
##     1849     1853     1854     1856     1860     1862     1868     1871 
## 3753.140 4273.574 3394.499 3614.846 3907.614 4723.897 3495.812 3236.559 
##     1879     1882     1883     1884     1887     1888     1889     1891 
## 3854.453 2871.755 3482.330 2798.563 5597.578 3998.526 4423.810 2725.756 
##     1898     1899     1909     1911     1917     1918     1919     1921 
## 4122.182 3793.974 5074.448 3909.925 2622.517 4727.749 3702.676 3993.518 
##     1923     1925     1926     1927     1930     1935     1937     1939 
## 2622.517 2995.410 3517.000 4025.106 3231.551 2961.511 3795.900 3906.458 
##     1944     1947     1948     1949     1950     1951     1952     1953 
## 3308.980 3308.595 3440.726 3614.846 4499.313 5380.699 3925.334 3137.942 
##     1955     1958     1962     1965     1968     1969     1970     1977 
## 3885.656 3896.057 3685.726 4046.293 3453.053 3713.077 4354.855 2917.596 
##     1985     1988     1990     1991     1992     1993     1996     2000 
## 3760.074 4272.033 3345.962 2868.673 5845.660 4046.293 3738.887 4978.143 
##     2003     2005     2007     2010     2011     2014     2015     2017 
## 3903.761 4922.286 4532.442 4472.348 4087.897 4373.346 2622.517 4841.389 
##     2018     2019     2020     2022     2023     2025     2027     2030 
## 4142.984 3471.929 3523.163 2622.517 2825.143 2622.517 3753.911 4251.231 
##     2031     2036     2037     2041     2049     2050     2053     2055 
## 3608.297 3988.895 2984.239 4117.944 4164.556 2622.517 2622.517 4437.678 
##     2059     2060     2064     2067     2071     2072     2073     2075 
## 2622.517 3699.209 3533.179 4154.540 2776.605 2622.517 4788.229 3482.715 
##     2076     2077     2078     2084     2085     2087     2088     2089 
## 3999.296 3167.604 3555.522 3605.600 3524.704 6154.608 3907.999 2622.517 
##     2093     2094     2096     2101     2105     2110     2111     2112 
## 3510.836 3958.078 4121.797 2879.459 4092.135 4409.942 3208.823 3199.192 
##     2117     2118     2120     2121     2122     2128     2136     2141 
## 5814.843 3698.824 3919.170 4054.383 3535.490 4258.550 3943.439 2978.846 
##     2142     2143     2144     2145     2150     2151     2155     2156 
## 3244.648 2902.957 2622.517 4024.336 4111.781 4267.410 3523.548 3675.325 
##     2157     2158     2159     2162     2164     2167     2169     2173 
## 3417.998 4755.870 3791.662 3234.633 3292.416 4156.466 3450.742 3464.610 
##     2174     2177     2179     2185     2192     2193     2196     2199 
## 3782.417 4438.833 4466.184 4904.566 3127.541 3243.493 3942.284 2986.165 
##     2201     2202     2205     2209     2211     2213     2215     2216 
## 4052.072 6031.722 3227.313 2622.517 2787.006 3230.780 3392.188 3447.275 
##     2217     2218     2227     2228     2229     2231     2232     2238 
## 3775.098 3577.865 4064.784 3543.580 5190.785 3547.047 5411.516 4032.425 
##     2241     2243     2254     2255     2259     2260     2261     2263 
## 4012.009 3319.381 3771.631 3050.497 3388.721 3232.707 3364.067 3852.912 
##     2264     2268     2269     2271     2272     2273     2279     2280 
## 4796.318 5279.386 6474.726 3524.319 2785.465 3764.312 3616.772 3900.295 
##     2282     2283     2287     2294     2295     2296     2298     2300 
## 3906.458 4697.317 4032.811 6188.122 3186.095 4420.728 3743.124 4148.762 
##     2301     2302     2305     2307     2309     2311     2312     2313 
## 4144.139 4057.465 4282.819 3564.767 4256.239 4788.229 3980.420 2622.517 
##     2316     2319     2326     2328     2331     2333     2335     2339 
## 4588.299 3601.748 4045.523 2622.517 4938.080 5072.907 4726.593 3793.588 
##     2344     2352     2353     2357     2360     2362     2363     2365 
## 2622.517 3594.044 3684.956 3878.337 3799.752 4420.343 4032.040 3784.728 
##     2366     2368     2369     2372     2373     2376     2377     2378 
## 5585.636 3723.093 2721.133 4756.255 5559.056 2622.517 2622.517 5774.394 
##     2393     2397     2398     2402     2403     2407     2408     2409 
## 3384.098 3539.342 2622.517 3114.444 4080.963 5463.906 4448.849 6206.998 
##     2412     2416     2417     2420     2421     2422     2425     2426 
## 3594.429 5894.583 5928.098 5495.495 4021.254 5399.960 5113.741 2843.248 
##     2427     2430     2431     2434     2435     2436     2437     2440 
## 5008.575 5139.165 5037.467 5361.052 2933.005 3671.088 4940.776 5044.401 
##     2442     2443     2444     2445     2446     2448     2450     2452 
## 3824.791 4359.863 2622.517 4055.153 3456.135 4869.510 3307.825 4768.968 
##     2454     2455     2462     2463     2466     2467     2468     2469 
## 4312.866 4621.043 5459.669 3024.687 3368.690 4643.771 4101.380 2860.968 
##     2474     2477     2479     2481     2482     2485     2486     2487 
## 3134.860 4197.685 2863.280 4091.749 6149.985 3282.785 3616.001 3934.194 
##     2488     2489     2494     2496     2497     2498     2499     2500 
## 3149.114 3276.622 2622.517 3911.466 4748.166 3629.484 5126.453 2622.517 
##     2501     2503     2504     2505     2507     2508     2509     2510 
## 4991.240 3643.352 4090.208 2622.517 3705.373 3778.179 2622.517 2888.319 
##     2511     2514     2517     2518     2520     2521     2524     2525 
## 5361.052 2793.555 3570.160 4923.441 3060.898 2807.037 3759.304 3998.141 
##     2526     2527     2535     2537     2541     2542     2543     2544 
## 4990.470 3936.120 5109.118 3937.661 4008.156 4721.586 2647.171 2622.517 
##     2548     2549     2551     2552     2553     2555     2557     2558 
## 3200.733 2682.996 5311.744 4633.755 4433.440 2622.517 3755.451 2622.517 
##     2560     2561     2563     2565     2566     2569     2571     2572 
## 2815.127 5030.148 3826.332 4260.861 5072.137 4363.330 3761.615 3506.984 
##     2573     2574     2575     2576     2577     2578     2580     2581 
## 3778.179 4639.534 3535.875 3361.370 2622.517 4427.662 3136.016 3937.661 
##     2582     2583     2586     2587     2590     2594     2595     2596 
## 5036.311 3750.058 4083.660 3858.691 4066.325 4385.288 3367.149 3847.904 
##     2597     2598     2599     2600     2601     2602     2603     2604 
## 3649.516 4677.670 4310.170 4323.652 4777.443 4247.764 4882.223 4505.091 
##     2605     2606     2607     2608     2609     2610     2611     2612 
## 4313.637 4589.070 4103.691 4588.684 4424.580 4196.915 4859.495 4553.244 
##     2613     2614     2615     2617     2618     2620     2621     2624 
## 4611.412 3871.403 4902.254 4072.874 4631.059 3349.814 4446.538 4424.195 
##     2625     2626     2630     2631     2632     2636     2640     2642 
## 2622.517 2622.517 2622.517 5327.538 4242.371 4890.698 3334.020 5567.916 
##     2643     2644     2645     2646     2647     2648     2651     2653 
## 3399.122 3517.385 3694.201 5203.882 4294.761 3417.998 2939.939 2622.517 
##     2654     2655     2657     2658     2659     2660     2664     2666 
## 2622.517 2622.517 3264.680 3323.619 2622.517 2622.517 4060.932 4993.166 
##     2668     2669     2672     2675     2677     2679     2681     2686 
## 3807.841 2938.783 4810.186 3041.252 3852.912 2849.027 5091.783 4170.720 
##     2691     2692     2694     2696     2697     2700     2702     2704 
## 5639.952 6035.189 3497.739 4587.143 4397.230 4536.294 3889.123 3658.376 
##     2705     2710     2713     2714     2716     2718     2720     2721 
## 4079.422 3385.639 3274.310 4847.168 4087.897 3939.972 3999.682 4852.946 
##     2722     2726     2727     2728     2734     2735     2738     2739 
## 4082.889 2622.517 4114.477 4319.800 4700.398 4669.966 4278.967 3657.220 
##     2740     2741     2742     2743     2744     2745     2746     2747 
## 5376.846 4005.845 4135.279 4809.801 4810.572 4486.986 4423.039 4219.257 
##     2749     2750     2751     2752     2755     2758     2763     2764 
## 4051.301 3652.597 4655.328 4700.013 3452.668 5015.124 3622.935 4169.179 
##     2767     2770     2775     2780     2782     2788     2791     2792 
## 4188.440 4273.959 3600.978 5149.181 3709.995 3583.258 4157.237 4814.039 
##     2795     2799     2803     2805     2807     2810     2814     2817 
## 4123.723 3995.444 3444.963 4252.772 3161.826 3287.408 5070.596 2997.337 
##     2819     2821     2822     2823     2828     2830     2833     2834 
## 3627.558 2622.517 2787.776 4909.573 5537.098 3679.178 3585.569 4010.468 
##     2836     2839     2842     2843     2844     2848     2849     2852 
## 4316.333 4418.802 3312.062 2622.517 3672.629 4998.945 3605.215 5021.673 
##     2855     2856     2858     2862     2865     2867     2868     2871 
## 3559.374 4220.798 3555.522 3955.381 3894.131 4783.991 3230.780 3060.128 
##     2876     2877     2878     2884     2887     2888     2890     2891 
## 4201.537 3982.732 4335.594 3702.291 2622.517 3437.259 3906.458 3214.986 
##     2893     2894     2900     2902     2903     2904     2911     2913 
## 3583.258 4083.274 3484.256 3280.859 3036.244 2729.608 3224.232 5509.362 
##     2914     2915     2922     2923     2924     2927     2931     2935 
## 2687.619 3802.834 3988.125 3711.151 3798.981 4277.426 3938.431 3628.329 
##     2936     2937     2938     2940     2948     2951     2954     2956 
## 3641.426 3547.817 3099.420 3530.097 3026.999 5214.283 4680.752 3832.496 
##     2966     2971     2974     2975     2976     2979     2981     2982 
## 4434.596 3613.690 2622.517 3612.534 3573.627 2622.517 2849.027 3382.172 
##     2984     2988     3000     3004     3005     3016     3018     3019 
## 3392.959 3944.980 3473.084 4379.895 2825.528 3951.144 2622.517 3366.763 
##     3022     3023     3025     3026     3029     3030     3031     3033 
## 5028.607 2800.874 2954.577 4198.456 3656.835 3651.827 3265.836 4819.817 
##     3034     3041     3044     3049     3053     3054     3058     3060 
## 4059.391 2995.410 2730.764 4428.047 3513.533 3585.184 3923.408 4008.927 
##     3062     3063     3065     3067     3068     3071     3074     3076 
## 4182.661 3587.495 4144.910 3864.084 3341.724 3402.204 3508.140 4443.456 
##     3078     3081     3082     3083     3086     3103     3104     3107 
## 3872.559 3444.193 3359.059 3190.332 4923.827 2622.517 4447.693 4002.378 
##     3109     3110     3112     3114     3115     3118     3123     3125 
## 3878.722 3479.248 3183.784 3908.384 2862.509 2622.517 4291.679 2972.682 
##     3126     3128     3129     3130     3131     3132     3133     3140 
## 3704.602 4169.564 4527.819 3479.248 3589.421 3302.432 3375.624 3803.989 
##     3141     3142     3147     3151     3152     3156     3157     3162 
## 4050.531 4982.765 3494.272 4443.071 5034.770 3342.495 3056.275 4239.674 
##     3164     3167     3169     3171     3179     3181     3183     3184 
## 4545.925 3709.995 3406.441 3593.659 3142.950 4209.627 2849.027 3092.101 
##     3185     3186     3187     3192     3193     3195     3196     3197 
## 3072.840 4915.737 5291.327 3574.783 3020.450 2980.772 5527.083 4458.865 
##     3199     3200     3204     3205     3207     3210     3211     3214 
## 4459.635 3596.740 2903.343 2790.088 6280.190 3557.063 4622.199 3546.662 
##     3217     3218     3219     3220     3221     3237     3238     3239 
## 3660.302 3336.716 4079.422 2649.482 3746.591 4273.574 3392.959 4975.061 
##     3240     3241     3242     3247     3248     3250     3252     3253 
## 3482.715 3737.346 4724.667 3532.408 2863.280 5523.616 3652.597 3962.315 
##     3255     3256     3260     3261     3262     3263     3265     3266 
## 3549.358 2825.528 4808.646 3617.542 2928.767 3883.345 3405.671 2855.960 
##     3267     3269     3270     3275     3278     3282     3283     3284 
## 3461.143 5328.694 4184.202 3756.992 5154.574 5428.466 2877.148 3195.725 
##     3288     3289     3290     3291     3294     3295     3296     3297 
## 3692.660 4403.778 2980.772 3617.157 3379.861 3393.729 4198.456 3827.873 
##     3298     3300     3301     3302     3303     3305     3306     3309 
## 3721.937 4216.561 3154.122 3624.862 4440.760 2852.108 2622.517 4414.564 
##     3313     3316     3317     3318     3319     3320     3321     3322 
## 3134.860 3345.576 3887.582 3246.575 3542.809 3195.725 3071.299 3351.740 
##     3323     3324     3325     3326     3327     3328     3329     3330 
## 3059.357 3312.833 3209.208 3060.898 3254.664 3162.596 4537.450 3553.210 
##     3331     3332     3333     3334     3336     3339     3343     3344 
## 3469.232 3418.383 3594.044 3263.909 3059.357 2695.323 4845.627 6075.252 
##     3345     3346     3347     3349     3351     3352     3353     3354 
## 4011.623 3795.900 2707.265 4245.067 3954.611 3604.060 3386.025 4428.432 
##     3355     3358     3359     3362     3366     3369     3371     3373 
## 3505.828 3991.592 3188.021 3749.673 5528.624 3105.584 3539.342 4245.067 
##     3374     3375     3376     3379     3380     3381     3383     3384 
## 3827.488 3213.831 3704.217 3498.509 3811.694 3119.452 3329.782 3272.384 
##     3385     3386     3388     3391     3392     3393     3394     3395 
## 3933.424 2622.517 2947.258 3462.298 5819.080 5556.745 3585.569 4096.757 
##     3396     3404     3405     3406     3408     3411     3412     3414 
## 3797.826 3271.229 2890.630 2748.484 4574.431 4870.281 3255.820 4414.564 
##     3415     3417     3420     3421     3422     3424     3428     3429 
## 4967.357 2866.747 3970.405 3445.734 5269.755 4722.356 6138.043 3582.487 
##     3430     3434     3435     3437     3438     3439     3440     3446 
## 3348.658 4045.523 3953.455 3515.844 5219.291 3472.314 3740.043 3719.626 
##     3447     3450     3451     3453     3456     3457     3458     3460 
## 4215.020 3354.051 4042.441 3469.232 3564.767 4788.614 4490.068 4513.952 
##     3461     3462     3463     3465     3468     3469     3474     3475 
## 5195.022 3429.554 4414.564 4141.443 4197.685 3827.873 4248.919 4471.577 
##     3480     3481     3484     3485     3486     3487     3488     3489 
## 4288.597 4184.202 4405.319 3953.070 4269.721 3963.086 4027.417 4418.031 
##     3490     3491     3492     3493     3494     3496     3502     3504 
## 4256.239 3733.494 4024.721 3218.068 4671.122 3946.521 4547.081 3732.723 
##     3505     3507     3509     3511     3512     3517     3521     3523 
## 3493.501 4113.707 2849.797 3231.166 3646.049 3687.267 3281.630 4280.893 
##     3525     3526     3528     3533     3536     3539     3540     3541 
## 3084.011 2930.308 2728.838 3053.194 4123.337 3035.859 4404.934 3288.178 
##     3542     3543     3544     3546     3548     3550     3552     3553 
## 4262.787 4609.486 4070.947 4559.793 2622.517 2622.517 4686.530 4333.668 
##     3557     3562     3564     3567     3572     3574     3577     3578 
## 2940.709 3260.057 2877.148 4712.340 4303.236 4291.294 4807.875 4465.799 
##     3579     3580     3583     3587     3589     3591     3593     3601 
## 3044.334 3609.838 3746.206 5008.575 4648.779 3698.824 4070.562 4458.480 
##     3605     3607     3609     3611     3621     3622     3623     3624 
## 4163.786 2671.440 2622.517 3982.347 3906.458 3497.739 3592.118 3649.516 
##     3628     3629     3630     3632     3633     3635     3641     3645 
## 2837.855 4233.896 3659.531 3703.447 3832.881 5970.472 4530.516 3298.965 
##     3649     3654     3656     3659     3660     3668     3671     3674 
## 4379.895 2622.517 4342.143 3909.540 4834.070 3189.177 3214.986 4694.620 
##     3675     3678     3681     3682     3683     3696     3699     3700 
## 5012.427 3195.340 4317.874 4643.001 4631.829 4286.671 5098.332 4265.099 
##     3702     3703     3704     3706     3707     3708     3711     3712 
## 3232.321 4326.734 4048.219 3311.292 4174.957 2884.082 2857.887 2884.852 
##     3715     3717     3722     3724     3727     3729     3731     3732 
## 3117.911 3438.800 4675.744 4571.735 2841.322 3396.425 4109.469 4548.621 
##     3735     3746     3748     3754     3755     3759     3760     3763 
## 4100.224 3956.152 3817.857 4567.112 4055.539 3008.893 4967.357 5893.043 
##     3766     3768     3769     3772     3774     3780     3783     3784 
## 3456.135 3431.866 3636.803 2871.755 4184.202 4456.168 5186.933 4605.634 
##     3785     3786     3787     3789     3790     3798     3799     3800 
## 4220.798 3666.465 4562.104 2876.762 4450.775 3255.435 3738.502 4109.469 
##     3801     3802     3803     3804     3806     3809     3810     3811 
## 4946.940 4088.668 2626.754 3255.049 4592.151 4322.497 3123.304 3550.514 
##     3813     3814     3816     3817     3818     3830     3832     3836 
## 4474.659 3927.260 5008.575 3188.406 4609.486 2709.577 3877.566 3489.264 
##     3838     3839     3850     3855     3859     3862     3864     3865 
## 4664.188 5131.846 2960.355 4123.723 2706.110 3338.257 2785.850 3885.656 
##     3866     3867     3868     3870     3871     3872     3873     3874 
## 3454.979 2944.561 4002.763 2622.517 3841.741 2797.407 2655.646 3331.323 
##     3875     3877     3879     3881     3882     3883     3885     3886 
## 5813.302 3942.284 3375.238 3948.447 2864.050 2679.144 3270.073 3645.663 
##     3888     3889     3891     3892     3893     3894     3897     3906 
## 2990.403 4177.268 2699.946 4632.600 5202.727 3399.892 4322.111 3711.921 
##     3907     3909     3910     3912     3913     3914     3916     3919 
## 4146.451 3650.671 3907.228 4653.787 5355.274 4299.383 3942.669 5614.913 
##     3920     3922     3924     3925     3926     3933     3935     3938 
## 3665.695 3903.376 2797.792 3519.311 3240.411 3944.980 3320.152 6089.505 
##     3941     3943     3944     3947     3949     3951     3953     3954 
## 3434.948 4150.303 3354.051 4437.678 5249.724 3804.374 3293.186 4661.491 
##     3960     3964     3966     3968     3969     3970     3973     3974 
## 2871.369 3823.636 3676.866 3572.086 5357.585 4764.345 3390.647 5554.433 
##     3975     3977     3980     3990     3997     3999     4002     4003 
## 3044.719 5725.086 2968.060 3144.106 3180.317 3609.067 2725.756 2664.891 
##     4006     4011     4013     4014     4020     4025     4028     4030 
## 3874.099 3621.395 2941.865 2886.778 3593.273 2771.982 3585.184 3420.309 
##     4032     4036     4037     4046     4047     4048     4051     4053 
## 3053.194 3261.983 3649.130 4248.534 3312.833 4347.921 3216.913 4894.935 
##     4054     4056     4058     4059     4061     4062     4065     4067 
## 3594.814 4834.455 3811.308 3906.458 4084.430 4997.789 4133.738 5020.132 
##     4068     4069     4070     4074     4077     4082     4087     4091 
## 4231.970 3912.622 4681.137 3526.630 3750.058 5228.536 2688.389 4878.371 
##     4093     4094     4095     4101     4102     4106     4108     4109 
## 3687.267 4089.438 3485.797 3169.916 4062.087 3963.471 4600.626 3804.760 
##     4111     4112     4113     4115     4116     4121     4122     4124 
## 3278.163 3360.600 3714.618 3569.775 3538.572 2837.855 4367.568 3664.539 
##     4125     4126     4127     4131     4132     4134     4140     4141 
## 3549.358 3518.541 3904.917 4198.841 3830.184 5116.052 4031.270 3876.411 
##     4143     4144     4148     4149     4153     4157     4158     4159 
## 3327.086 4648.779 2631.762 3811.308 3324.004 3250.812 3109.821 3535.875 
##     4160     4161     4162     4163     4164     4165     4166     4167 
## 3996.985 3379.861 3161.055 2622.517 2976.920 3062.824 4281.278 3025.072 
##     4168     4169     4170     4180     4191     4193     4195     4198 
## 2838.240 3025.458 3030.466 2712.658 3236.944 4532.442 2622.517 4823.669 
##     4199     4202     4204     4208     4209     4217     4218     4219 
## 3641.041 2935.701 3807.841 2902.572 3186.095 3133.320 2689.930 2783.539 
##     4220     4221     4222     4223     4224     4225     4226     4227 
## 3611.379 4028.188 4403.778 4716.193 5608.364 3922.252 3595.970 3623.706 
##     4228     4233     4234     4235     4236     4239     4240     4241 
## 4114.477 2622.517 3050.497 3015.057 3525.475 2989.632 3439.185 5476.619 
##     4242     4243     4244     4245     4246     4248     4249     4252 
## 3449.201 3292.031 4605.249 4938.465 3545.891 3637.574 5389.559 5392.641 
##     4254     4256     4258     4260     4261     4262     4263     4265 
## 4762.804 4305.547 2862.124 2735.386 6278.649 4190.751 3906.458 3533.949 
##     4267     4268     4272     4284     4298     4311     4319     4321 
## 2724.600 2745.402 4497.002 3335.175 2622.517 2882.926 3154.507 3264.680 
##     4330     4335     4338     4341     4343     4347     4352     4358 
## 4013.549 4214.635 3412.605 4353.314 2857.116 2746.943 4075.185 3189.177 
##     4363     4370     4371     4376     4382     4385     4386     4412 
## 4548.621 2838.626 3052.808 3421.465 3855.224 3656.064 4168.408 3260.057 
##     4429     4437     4440     4446     4462     4466     4470     4471 
## 3970.790 3958.078 4206.160 3415.687 3368.690 2939.939 2822.831 2708.036 
##     4472     4473     4485     4494     4500     4503     4505     4507 
## 2930.308 4094.061 3977.339 3612.920 2622.517 3737.731 4590.610 2903.728 
##     4509     4516     4540     4544     4552     4556     4565     4584 
## 4709.259 3530.097 2797.792 2622.517 3716.929 4026.262 4990.470 3675.711 
##     4601     4606     4613     4616     4617     4619     4627     4628 
## 4104.076 3401.048 3074.381 2902.572 3559.374 3503.132 3523.163 3425.702 
##     4629     4635     4636     4641     4643     4645     4672     4678 
## 3218.839 4665.729 3167.219 2622.517 4548.621 3811.308 2824.372 4420.343 
##     4680     4700     4707     4712     4717     4718     4719     4731 
## 2716.125 5478.545 4201.537 2622.517 3166.449 4080.963 2622.517 3585.569 
##     4739     4754     4757     4792     4795     4805     4807     4811 
## 5459.284 4800.556 3478.478 2622.517 3392.959 3906.458 4435.366 3477.707 
##     4813     4819     4820     4847     4851     4860     4875     4877 
## 3340.183 3416.457 2622.517 3012.745 3644.123 3802.834 3906.458 3260.828 
##     4888     4889     4890     4891     4892     4897     4902     4905 
## 2908.736 2991.173 3431.866 3013.131 2676.833 3486.952 3054.349 3501.976 
##     4906     4909     4910     4912     4914     4934     4941     4945 
## 4201.923 3776.639 2955.347 3906.458 2622.517 3585.569 4334.439 5248.953 
##     4947     4949     4950     4951     4953     4954     4958     4959 
## 4799.785 3778.179 4762.804 3723.093 3337.872 2689.545 3355.592 4948.481 
##     4960     4962     4964     4966     4967     4969     4970     4971 
## 2622.517 2622.517 2622.517 5456.972 3007.738 2691.471 2778.146 2776.605 
##     4972     4988     4989     4991     4993     4997     4998     5003 
## 2622.517 3585.569 2897.564 3528.942 3235.403 4208.856 2622.517 3322.848 
##     5009     5016     5036     5043     5047     5056     5072     5086 
## 3172.997 3111.747 3440.341 5341.791 2766.974 3518.926 3642.967 3825.947 
##     5088     5090     5102     5114     5126     5129     5130     5131 
## 2768.901 2749.639 4108.314 2909.891 3712.307 3358.289 3088.249 3651.827 
##     5132     5133     5135     5139     5146     5152     5165     5170 
## 3387.565 4295.146 3521.237 2622.517 2622.517 4580.210 3050.497 5203.882 
##     5176     5186     5188     5190     5195     5199     5201     5204 
## 2622.517 4607.175 2622.517 2840.552 5812.531 2622.517 4206.545 3874.099 
##     5215     5223     5224     5225     5226     5256     5263     5264 
## 3542.809 2771.982 3228.469 2751.951 2860.968 3528.942 3938.817 4012.394 
##     5265     5266     5267     5271     5272     5280     5281     5288 
## 4284.745 2987.321 2928.767 2702.643 3367.149 5289.401 5956.219 2622.517 
##     5293     5297     5308     5313     5315     5318     5327     5339 
## 2622.517 2622.517 3800.522 2732.690 2894.868 3307.825 3598.281 2622.517 
##     5348     5364     5366     5369     5381     5433     5434     5437 
## 4067.095 2863.280 4548.621 3515.074 3365.608 5215.439 6474.726 3327.856 
##     5443     5451     5454     5455     5456     5458     5466     5472 
## 2622.517 4371.805 3685.341 3255.049 3267.762 6012.461 4163.400 4241.215 
##     5473     5474     5477     5482     5495     5508     5519     5520 
## 3047.415 4845.627 3442.267 2674.521 2622.517 5134.928 3698.824 4232.355 
##     5524     5528     5532     5533     5537     5558     5572     5585 
## 4411.098 3975.413 3411.064 3992.362 2839.396 2687.234 3312.062 4450.775 
##     5600     5610     5616     5627     5632     5634     5638     5646 
## 3028.154 2622.517 3503.132 2966.519 3886.812 3585.569 3640.270 2622.517 
##     5663     5664     5685     5689     5700     5705     5712     5718 
## 3251.582 3825.562 4483.134 3097.109 3998.141 2964.978 3264.680 3784.728 
##     5734     5735     5736     5737     5755     5823     5829     5830 
## 2943.406 3089.404 2680.300 3837.118 4365.256 4762.804 2803.570 2807.037 
##     5831     5832     5833     5834     5835     5836     5856     5858 
## 2792.399 2683.767 3373.312 3068.602 3844.823 3799.367 5113.355 3436.874 
##     5890     5898     5903     5904     5905     5910     5912     5919 
## 2622.517 4987.773 2622.517 4607.175 2918.751 3313.988 5550.966 3075.536 
##     5945     5946     5947     5948     5949     5950     5951     5977 
## 2832.847 2812.045 3619.468 3076.692 3233.477 2826.684 4047.834 2662.580 
##     5978     5998     6026     6028     6029     6030     6051     6061 
## 2774.679 2872.525 3676.481 2622.517 2622.517 2785.465 5167.671 3337.487 
##     6062     6067     6068     6069     6070     6071     6072     6073 
## 3434.948 2733.460 3678.407 2883.696 3466.536 3279.318 2714.199 3861.772 
##     6104     6105     6106     6107     6181     6183     6186     6195 
## 3763.156 4163.400 3119.452 4548.621 3627.558 2642.163 2622.517 3282.785 
##     6197     6220     6266     6267     6268     6269     6270     6271 
## 3193.414 4758.567 2751.566 2998.492 2700.331 3083.241 3906.458 2807.808 
##     6301     6305     6309     6310     6311     6312     6317     6332 
## 5026.681 2622.517 2622.517 3067.062 4823.669 3162.211 3164.908 4471.577 
##     6336     6375     6384     6391     6393     6400     6401     6419 
## 3172.997 2962.281 5220.447 4273.574 2897.564 5832.563 5404.582 2622.517 
##     6421     6491     6507     6508     6509     6510     6512     6513 
## 2912.973 3501.206 3561.300 3961.545 3985.428 3602.519 2830.921 2622.517 
##     6514     6515     6516     6518     6519     6520     6521     6526 
## 2709.577 2709.962 2900.261 3113.673 2725.371 2735.001 5170.753 2622.517 
##     6527     6547     6548     6549     6572     6579     6583     6584 
## 2622.517 2622.517 2622.517 2622.517 3367.919 3010.049 4190.751 3740.813 
##     6591     6671     6682     6700     6701     6702     6711     6712 
## 5190.785 2622.517 2972.682 3104.043 3111.747 3209.593 4273.574 3050.497 
##     6713     6717     6748     6750     6783     6784     6786     6787 
## 3339.798 2678.374 2622.517 3230.780 2767.360 3036.629 2817.438 2977.305 
##     6834     6837     6845     6846     6847     6848     6881     6887 
## 2622.517 2622.517 4373.346 3906.458 3098.264 3172.997 2776.605 2622.517 
##     6889     6918     6932     6936     6937     6940     6941     6943 
## 2622.517 6046.746 3050.497 3233.092 2740.394 3839.044 2763.507 2906.039 
##     6944     6945     6946     6948     6949     6952     6997     7002 
## 3346.347 3318.611 2693.782 4237.363 3962.315 3392.959 4023.180 4023.180 
##     7007     7014     7018     7040     7042     7057     7058     7082 
## 2622.517 3089.404 4124.108 2622.517 2622.517 2771.597 2790.088 3526.245 
##     7083     7086     7104     7105     7106     7107     7108     7109 
## 4148.762 3565.923 3609.453 3139.483 3314.373 3813.235 3569.775 3570.160 
##     7110     7111     7112     7113     7114     7115     7116     7117 
## 3691.505 2870.984 2622.517 3778.179 3478.478 3547.047 3723.093 3063.209 
##     7118     7119     7120     7121     7122     7123     7124     7125 
## 3755.451 3184.939 3778.179 2622.517 3146.802 3817.857 3320.537 2622.517 
##     7126     7127     7128     7129     7140     7154     7179     7195 
## 3206.126 3153.736 3906.458 3798.211 4128.345 3050.497 3906.458 3906.458 
##     7224     7225     7228     7252     7260     7272 
## 2622.517 2622.517 5594.111 3312.062 3958.848 5832.563
reg5 <- lm(C150_4 ~ SAT_AVG, data=data2)
summary(reg5)
## 
## Call:
## lm(formula = C150_4 ~ SAT_AVG, data = data2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52185 -0.06537  0.00721  0.06898  0.46134 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.5741736  0.0237624  -24.16   <2e-16 ***
## SAT_AVG      0.0010598  0.0000222   47.74   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1049 on 1269 degrees of freedom
##   (6432 observations deleted due to missingness)
## Multiple R-squared:  0.6424, Adjusted R-squared:  0.6421 
## F-statistic:  2279 on 1 and 1269 DF,  p-value: < 2.2e-16
coefficients(reg5)
##  (Intercept)      SAT_AVG 
## -0.574173650  0.001059838
confint(reg5, level=0.95)
##                    2.5 %       97.5 %
## (Intercept) -0.620791597 -0.527555703
## SAT_AVG      0.001016287  0.001103389
lm.beta(reg5)
##   SAT_AVG 
## 0.8014783
fitted(reg5)
##         1         2         4         5         6         9        10 
## 0.3023124 0.5990670 0.7177689 0.3277485 0.6817344 0.4952029 0.7135295 
##        11        13        24        27        33        37        38 
## 0.6774950 0.4241937 0.5132201 0.5291177 0.4750660 0.5005021 0.5598530 
##        40        42        47        51        52        53        54 
## 0.5163996 0.4093560 0.6605376 0.5365366 0.6086055 0.4114757 0.2853550 
##        57        58        65        83       116       123       129 
## 0.5386562 0.4623479 0.5428956 0.6393408 0.5630325 0.4729463 0.5365366 
##       135       138       139       141       142       147       148 
## 0.6011867 0.6499392 0.3648428 0.5789301 0.4962627 0.5375964 0.4697668 
##       157       158       159       172       175       187       189 
## 0.6245031 0.4740061 0.7442648 0.6043662 0.5503144 0.4676471 0.4740061 
##       211       216       224       227       228       229       233 
## 0.5248783 0.6149646 0.4602282 1.0632760 0.6011867 0.7336664 0.3627231 
##       234       235       237       238       240       241       242 
## 0.5640923 0.4814250 0.3902789 0.5079209 0.5428956 0.3489452 0.3945183 
##       243       244       245       246       247       248       249 
## 0.4188945 0.8905224 0.7251877 0.6637171 0.8354109 0.6213236 0.8173936 
##       251       252       275       277       278       284       308 
## 0.7538033 0.6435802 0.7082303 0.5259382 0.4771856 0.9297364 0.5354767 
##       331       344       351       353       367       369       378 
## 0.4962627 1.0155833 0.3637830 0.4708266 0.3828600 0.5005021 0.4157150 
##       387       393       408       411       423       441       442 
## 0.5948276 0.7167090 0.4803651 0.6467597 0.3818002 0.4135953 0.8036157 
##       446       448       455       456       461       464       465 
## 0.4962627 0.3754412 0.5036816 0.6817344 0.7336664 0.6287425 0.9668308 
##       472       489       490       493       495       499       501 
## 0.6022465 0.6075457 0.7432050 0.4750660 0.6467597 0.4952029 0.5259382 
##       507       511       520       525       527       531       536 
## 0.8131543 0.8672060 0.5111004 0.6011867 0.4687069 0.4538692 0.6456999 
##       537       541       559       560       568       573       574 
## 0.8884028 0.7622820 0.6711360 0.5503144 0.4379716 0.5439554 0.5799899 
##       576       583       585       596       598       605       606 
## 0.7050508 0.8385904 0.6213236 0.7304869 0.5068611 0.4538692 0.4570487 
##       613       620       623       629       636       637       643 
## 0.5206390 0.6001268 0.4549290 0.4750660 0.3786207 0.5015619 0.7463845 
##       653       664       671       673       675       678       684 
## 0.4856643 0.5524341 0.3319878 0.5958875 0.4528094 0.4135953 0.4655274 
##       686       692       693       696       698       699       702 
## 1.0081645 0.3733215 0.6912729 0.3298681 0.7527435 0.6234433 0.3256288 
##       703       704       705       714       715       717       718 
## 0.8004362 0.9244373 0.5969473 0.4453905 0.4199544 0.2768762 0.4644676 
##       726       727       730       734       736       738       739 
## 0.4220741 0.6817344 0.4581085 0.6478195 0.3001927 0.4305528 0.5471349 
##       741       742       746       747       749       754       755 
## 0.5471349 0.5524341 0.4093560 0.6721958 0.5799899 0.6414605 0.7273074 
##       758       796       805       806       807       811       835 
## 0.7750001 0.8354109 0.6266228 0.3998175 0.6372212 0.5609128 0.6573581 
##       836       839       846       849       853       855       857 
## 0.3998175 0.4485700 0.5852891 0.3786207 0.3404665 0.4326724 0.5545538 
##       862       868       870       874       878       883       885 
## 0.4082962 0.3531846 0.4920234 0.3976978 0.3372870 0.6796147 0.4697668 
##       888       891       894       896       901       902       904 
## 0.4008773 0.4114757 0.4602282 0.6711360 0.4432708 0.8735650 0.3510649 
##       906       907       908       909       910       911       912 
## 0.9095995 0.4538692 0.6255629 0.5905883 0.5439554 0.7485042 0.3362272 
##       918       919       924       925       929       930       931 
## 0.5662120 0.5227587 0.7029311 0.4899037 0.6329818 0.2313032 0.4517495 
##       933       935       936       937       940       941       944 
## 0.4591684 0.5715112 0.3235091 0.4337323 0.4909635 0.6276826 0.4538692 
##       945       947       949       950       952       953       954 
## 0.4549290 0.5047414 0.4326724 0.4750660 0.4411511 0.4178347 0.5598530 
##       968       969       972       973       974       979       981 
## 0.4814250 0.5301775 0.5460751 0.5662120 0.4040568 0.5407759 0.5291177 
##       987       989       994       997      1011      1013      1022 
## 0.5545538 0.4962627 0.4740061 0.6573581 0.3478854 1.0208825 0.5185193 
##      1031      1033      1034      1041      1046      1049      1050 
## 0.4962627 0.5799899 0.5418357 0.5450153 0.5174595 0.6181441 0.5174595 
##      1052      1053      1057      1059      1067      1080      1081 
## 0.8311715 0.7495640 0.7675812 0.6022465 0.5704514 0.5598530 0.4920234 
##      1082      1085      1091      1094      1098      1099      1108 
## 0.6181441 0.7103500 0.4538692 0.5365366 0.5344169 0.5206390 0.6181441 
##      1109      1111      1113      1114      1117      1122      1130 
## 0.5121603 0.5174595 0.9742496 0.3690822 0.5969473 0.5111004 0.4952029 
##      1131      1132      1135      1137      1138      1150      1151 
## 0.5386562 0.5163996 0.5534940 0.4941430 0.5715112 0.5439554 0.5598530 
##      1156      1157      1160      1163      1164      1167      1169 
## 0.5704514 0.5513743 0.6011867 0.4538692 0.8152739 0.5365366 0.5556136 
##      1170      1171      1177      1181      1182      1183      1184 
## 0.5280579 0.7029311 0.7114098 0.6382810 0.5185193 0.6011867 0.6022465 
##      1187      1189      1191      1193      1194      1196      1197 
## 0.5927080 0.4528094 0.5216988 0.4877840 0.4962627 0.5047414 0.4485700 
##      1198      1199      1200      1201      1202      1203      1204 
## 0.4867242 0.3934584 0.4157150 0.4241937 0.6955123 0.3966379 0.4422110 
##      1205      1218      1219      1220      1228      1229      1231 
## 0.4252536 0.4856643 0.5238185 0.5715112 0.9625914 0.4432708 0.4485700 
##      1232      1235      1237      1238      1239      1240      1244 
## 0.4422110 0.8120944 0.4655274 0.4814250 0.4252536 0.6382810 0.6806745 
##      1245      1246      1249      1252      1253      1257      1258 
## 0.5683317 0.6499392 0.6213236 0.4909635 0.5354767 0.5927080 0.5163996 
##      1259      1260      1264      1265      1266      1268      1270 
## 0.6404007 0.6976319 0.5916481 0.7389656 0.4231339 0.5047414 0.4899037 
##      1272      1273      1274      1286      1287      1289      1295 
## 0.4199544 0.4506897 0.9074798 0.6393408 0.4750660 0.6594778 0.5789301 
##      1296      1300      1301      1304      1305      1312      1316 
## 0.6520589 0.5545538 0.5174595 0.5386562 0.5948276 0.5386562 0.6181441 
##      1322      1323      1324      1330      1332      1333      1334 
## 0.4326724 0.3934584 0.5916481 0.5481948 0.6128449 0.4528094 0.4856643 
##      1340      1348      1352      1355      1365      1366      1369 
## 0.4496298 0.4952029 0.5163996 0.3277485 0.6393408 0.5662120 0.5481948 
##      1374      1375      1376      1382      1384      1388      1389 
## 0.5174595 0.4909635 0.4962627 0.4962627 0.4877840 0.4930832 0.4623479 
##      1390      1395      1396      1400      1401      1404      1405 
## 0.5248783 0.4941430 0.6287425 0.6128449 0.6181441 0.5269980 0.4475102 
##      1407      1412      1413      1416      1427      1428      1429 
## 0.7644017 0.5259382 0.4941430 0.5937678 0.4962627 0.3616633 0.5079209 
##      1430      1431      1435      1440      1441      1443      1448 
## 0.6361613 0.4496298 0.6382810 0.5163996 0.5534940 0.5344169 0.4496298 
##      1459      1462      1463      1465      1466      1476      1484 
## 0.4506897 0.4665872 0.7294271 0.4538692 0.5354767 0.6011867 0.3648428 
##      1486      1492      1493      1495      1499      1501      1502 
## 0.3457657 0.4718864 0.6562982 0.5386562 0.4750660 0.5958875 0.6287425 
##      1503      1504      1505      1506      1509      1511      1524 
## 0.5174595 0.5725710 0.5185193 0.5174595 0.5142800 0.4962627 0.5174595 
##      1525      1526      1528      1530      1531      1540      1542 
## 0.3902789 0.2800558 0.5598530 0.8481289 0.5269980 0.8385904 0.4337323 
##      1547      1549      1550      1552      1556      1559      1571 
## 0.3786207 0.5683317 0.5111004 0.5630325 0.4485700 0.4835447 0.4008773 
##      1572      1573      1577      1578      1582      1591      1598 
## 0.3447059 0.5651522 0.3309280 0.3584838 0.4506897 0.9509332 0.7114098 
##      1599      1600      1601      1605      1606      1609      1615 
## 0.8195133 0.6605376 0.3182099 0.3521247 0.5365366 0.5365366 0.6849139 
##      1617      1619      1622      1624      1628      1629      1634 
## 0.8279920 0.5725710 0.4750660 0.5852891 0.3659026 0.9509332 0.7739403 
##      1636      1637      1640      1641      1647      1649      1650 
## 0.3531846 0.4337323 0.5015619 0.7474443 0.8884028 0.8036157 0.8767445 
##      1651      1661      1663      1666      1667      1668      1673 
## 0.4761258 0.4305528 0.3341075 0.3987576 0.7442648 0.5842293 0.4899037 
##      1674      1676      1681      1690      1692      1694      1698 
## 0.4973226 0.6562982 1.0166432 0.4581085 0.5768104 0.6393408 0.7156492 
##      1699      1701      1702      1703      1704      1714      1727 
## 0.5386562 0.5640923 0.5672719 1.0155833 0.5969473 0.3648428 0.4612881 
##      1731      1733      1734      1741      1743      1747      1749 
## 0.9307963 0.4284331 0.2525000 0.4687069 0.6658368 0.5121603 0.5121603 
##      1751      1753      1754      1755      1756      1757      1759 
## 0.5375964 0.9339758 0.8990011 0.6086055 0.5672719 0.4824848 0.4464503 
##      1760      1762      1763      1764      1767      1769      1770 
## 0.9647111 0.4824848 0.4952029 0.6181441 0.5927080 0.5715112 0.5810498 
##      1776      1780      1783      1785      1792      1795      1796 
## 0.6785548 0.5386562 0.4750660 0.4962627 0.6022465 0.5153398 0.4962627 
##      1799      1802      1805      1808      1812      1818      1820 
## 0.7220082 0.5397161 0.5799899 0.6817344 0.7389656 0.5153398 0.6202638 
##      1823      1824      1825      1826      1828      1829      1830 
## 0.5375964 0.2736967 0.4559889 0.8884028 0.6531187 0.7442648 0.5969473 
##      1831      1841      1844      1846      1847      1849      1854 
## 0.4782455 0.4962627 0.4899037 0.5598530 0.3976978 0.5174595 0.5174595 
##      1856      1860      1862      1868      1871      1879      1882 
## 0.5121603 0.5227587 0.3902789 0.5598530 0.5174595 0.5640923 0.4962627 
##      1883      1884      1887      1888      1891      1899      1909 
## 0.5598530 0.6404007 0.9180782 0.6615974 0.6181441 0.5927080 0.8608470 
##      1911      1918      1919      1921      1926      1927      1930 
## 0.4962627 0.7728804 0.4920234 0.5789301 0.6022465 0.6425204 0.5375964 
##      1935      1937      1939      1944      1947      1948      1949 
## 0.5513743 0.6022465 0.4475102 0.6753753 0.4962627 0.6499392 0.5566735 
##      1950      1951      1952      1953      1955      1958      1965 
## 0.7951370 0.5026217 0.5980072 0.4316126 0.5195791 0.4750660 0.5386562 
##      1968      1970      1977      1985      1988      1990      1991 
## 0.3500051 0.5174595 0.4517495 0.3913388 0.6743155 0.5895285 0.4729463 
##      1992      1993      1996      2000      2003      2005      2007 
## 0.3001927 0.6128449 0.6192039 0.2313032 0.5163996 0.3415264 0.5704514 
##      2010      2015      2018      2019      2022      2025      2027 
## 0.5259382 0.5005021 0.5386562 0.4962627 0.5386562 0.5969473 0.5058013 
##      2030      2031      2036      2037      2049      2055      2060 
## 0.4708266 0.6817344 0.5439554 0.5407759 0.5768104 0.5259382 0.6308621 
##      2064      2067      2071      2075      2076      2077      2078 
## 0.4538692 0.4687069 0.4750660 0.6615974 0.6223834 0.7855985 0.5969473 
##      2084      2085      2087      2093      2096      2101      2102 
## 0.7251877 0.5397161 0.5640923 0.6594778 0.7389656 0.4750660 0.6849139 
##      2105      2110      2111      2112      2117      2118      2120 
## 0.5598530 0.5534940 0.5386562 0.5810498 0.9922669 0.5969473 0.6064859 
##      2121      2122      2128      2141      2142      2143      2144 
## 0.6351015 0.5301775 0.6266228 0.6181441 0.6213236 0.5651522 0.3976978 
##      2145      2150      2151      2155      2156      2157      2158 
## 0.5185193 0.4750660 0.5386562 0.5566735 0.6976319 0.5492546 0.5534940 
##      2159      2162      2164      2167      2169      2173      2174 
## 0.5693915 0.5375964 0.5810498 0.4962627 0.5386562 0.6170842 0.6404007 
##      2179      2185      2192      2193      2196      2202      2205 
## 0.5174595 0.4538692 0.4856643 0.5715112 0.4962627 0.9562324 0.4316126 
##      2215      2216      2217      2227      2238      2241      2243 
## 0.5958875 0.4485700 0.4962627 0.4453905 0.2842951 0.4326724 0.4072363 
##      2254      2259      2260      2261      2263      2264      2271 
## 0.6107252 0.4263134 0.3478854 0.5185193 0.4273732 0.5948276 0.3690822 
##      2273      2279      2280      2287      2294      2296      2298 
## 0.3870994 0.5439554 0.4591684 0.6637171 1.0060448 0.5725710 0.5132201 
##      2300      2301      2302      2305      2307      2309      2311 
## 0.5121603 0.7135295 0.5227587 0.3786207 0.6266228 0.3192698 0.8523683 
##      2312      2316      2319      2326      2333      2335      2339 
## 0.5683317 0.7114098 0.4644676 0.4167749 0.6902131 0.5492546 0.4687069 
##      2353      2357      2360      2373      2393      2403      2407 
## 0.5831694 0.6605376 0.5534940 0.8491888 0.5757506 0.6923327 0.8767445 
##      2409      2412      2416      2417      2422      2425      2426 
## 0.9837882 0.3500051 0.8968815 0.9329160 0.7347263 0.5757506 0.4909635 
##      2427      2430      2431      2434      2437      2440      2442 
## 0.6234433 0.6552384 0.4538692 0.4803651 0.5810498 0.3796805 0.5227587 
##      2445      2450      2455      2462      2468      2469      2474 
## 0.3500051 0.5630325 0.7548632 0.9021807 0.6414605 0.6139047 0.5089808 
##      2481      2486      2487      2489      2496      2503      2504 
## 0.8354109 0.3945183 0.5609128 0.4326724 0.5884686 0.5545538 0.3160903 
##      2517      2520      2521      2526      2527      2535      2537 
## 0.5619727 0.4973226 0.4125355 0.4411511 0.6096654 0.8502486 0.5280579 
##      2541      2542      2543      2548      2552      2553      2561 
## 0.5587932 0.4220741 0.3892191 0.5428956 0.4369118 0.6351015 0.8799241 
##      2563      2565      2571      2572      2576      2581      2582 
## 0.5481948 0.7400254 0.5556136 0.4167749 0.4411511 0.6202638 0.7410853 
##      2583      2587      2590      2594      2597      2598      2599 
## 0.5185193 0.5821096 0.5990670 0.4665872 0.3553043 0.4665872 0.3743813 
##      2600      2601      2602      2603      2604      2605      2606 
## 0.5895285 0.7898378 0.6605376 0.7548632 0.6902131 0.5905883 0.5450153 
##      2607      2609      2610      2611      2612      2613      2615 
## 0.4210142 0.5450153 0.7198885 0.6149646 0.5768104 0.5980072 0.5863489 
##      2617      2618      2621      2624      2642      2644      2646 
## 0.4803651 0.5185193 0.5980072 0.6806745 0.9127790 0.5163996 0.9307963 
##      2647      2658      2664      2666      2668      2675      2677 
## 0.5418357 0.7198885 0.6425204 0.4453905 0.4856643 0.4538692 0.5121603 
##      2686      2691      2692      2694      2696      2697      2700 
## 0.2450811 0.8428297 0.9668308 0.5238185 0.3436460 0.7241279 0.3712018 
##      2702      2704      2710      2714      2720      2722      2728 
## 0.5068611 0.3542444 0.5874088 0.2821754 0.1889097 0.4051166 0.4453905 
##      2734      2735      2738      2739      2740      2741      2742 
## 0.5026217 0.3818002 0.3902789 0.6880934 0.8332912 0.5693915 0.5312374 
##      2743      2744      2745      2746      2747      2749      2750 
## 0.3648428 0.6086055 0.7538033 0.4040568 0.6393408 0.3690822 0.4114757 
##      2751      2752      2755      2758      2763      2764      2770 
## 0.4305528 0.4188945 0.5397161 0.4676471 0.2101065 0.5937678 0.4220741 
##      2782      2788      2791      2792      2795      2799      2803 
## 0.6276826 0.4867242 0.3362272 0.5227587 0.4400913 0.6743155 0.5386562 
##      2805      2807      2810      2814      2817      2822      2828 
## 0.5227587 0.5810498 0.5831694 0.4284331 0.5068611 0.5386562 0.4443307 
##      2830      2833      2836      2839      2844      2848      2849 
## 0.5365366 0.5757506 0.5163996 0.4983824 0.5916481 0.8831036 0.6838540 
##      2852      2855      2856      2858      2862      2865      2868 
## 0.2779361 0.4294929 0.4528094 0.6605376 0.4114757 0.5365366 0.5005021 
##      2871      2876      2877      2884      2888      2893      2894 
## 0.5322972 0.6912729 0.4591684 0.5227587 0.3902789 0.5142800 0.4899037 
##      2902      2911      2913      2915      2922      2923      2924 
## 0.6086055 0.5386562 0.8375305 0.4496298 0.4326724 0.5333570 0.5969473 
##      2931      2935      2936      2937      2938      2940      2948 
## 0.7400254 0.5174595 0.5460751 0.5344169 0.4909635 0.4952029 0.4188945 
##      2951      2954      2956      2966      2971      2976      2981 
## 0.8555478 0.4909635 0.6764352 0.7951370 0.5980072 0.5852891 0.7824190 
##      3000      3005      3016      3019      3022      3023      3026 
## 0.6796147 0.5185193 0.5005021 0.5312374 0.2048073 0.4538692 0.7283672 
##      3029      3031      3033      3034      3041      3044      3049 
## 0.6054260 0.4697668 0.3213894 0.4846045 0.4750660 0.4909635 0.4220741 
##      3054      3058      3060      3062      3063      3065      3067 
## 0.4952029 0.4114757 0.6202638 0.3902789 0.6308621 0.6668966 0.6605376 
##      3068      3071      3074      3078      3081      3082      3083 
## 0.6859737 0.4962627 0.3266886 0.5269980 0.4538692 0.4655274 0.4962627 
##      3086      3104      3107      3110      3115      3123      3126 
## 0.7993764 0.5248783 0.4305528 0.5715112 0.5736309 0.5354767 0.4718864 
##      3128      3130      3131      3133      3140      3141      3142 
## 0.5322972 0.6043662 0.6086055 0.5810498 0.5174595 0.6923327 0.8915823 
##      3147      3152      3156      3157      3162      3167      3169 
## 0.5163996 0.5026217 0.7071705 0.4867242 0.3796805 0.6658368 0.5206390 
##      3171      3179      3181      3184      3186      3187      3192 
## 0.4538692 0.4899037 0.5969473 0.4538692 0.8173936 0.8216330 0.3765010 
##      3193      3195      3196      3197      3200      3204      3210 
## 0.4157150 0.4231339 0.9477537 0.4909635 0.4517495 0.4093560 0.4750660 
##      3214      3217      3218      3219      3220      3221      3240 
## 0.6827942 0.6382810 0.4369118 0.5259382 0.4093560 0.6266228 0.5248783 
##      3241      3247      3250      3252      3255      3256      3262 
## 0.5619727 0.4443307 0.9329160 0.4061765 0.4453905 0.4411511 0.4019371 
##      3265      3266      3267      3269      3270      3278      3282 
## 0.4432708 0.4072363 0.4793053 0.8036157 0.4814250 0.8311715 0.3394067 
##      3283      3288      3290      3291      3295      3297      3298 
## 0.4294929 0.5312374 0.4326724 0.5174595 0.6181441 0.4983824 0.5640923 
##      3301      3302      3305      3313      3316      3317      3318 
## 0.5089808 0.3934584 0.3298681 0.5428956 0.4581085 0.3637830 0.4475102 
##      3319      3320      3321      3322      3323      3324      3325 
## 0.4422110 0.4888438 0.4867242 0.4369118 0.4570487 0.5111004 0.4517495 
##      3326      3327      3328      3329      3330      3331      3332 
## 0.4061765 0.3945183 0.4284331 0.6933926 0.4506897 0.4305528 0.4337323 
##      3333      3334      3344      3345      3346      3347      3349 
## 0.3786207 0.5079209 0.9647111 0.5640923 0.4920234 0.4782455 0.6647770 
##      3351      3352      3353      3354      3362      3371      3373 
## 0.4697668 0.4973226 0.5005021 0.7771198 0.4803651 0.5397161 0.4782455 
##      3374      3376      3379      3384      3385      3392      3395 
## 0.5206390 0.5216988 0.6181441 0.4655274 0.4846045 0.9445742 0.6181441 
##      3396      3405      3408      3412      3414      3417      3420 
## 0.4538692 0.4231339 0.8173936 0.4941430 0.5693915 0.5439554 0.5100406 
##      3421      3422      3424      3428      3435      3437      3438 
## 0.5333570 0.4602282 0.5386562 0.9466939 0.3987576 0.5672719 0.7548632 
##      3446      3447      3450      3453      3456      3457      3458 
## 0.5259382 0.4824848 0.5407759 0.6308621 0.5630325 0.2800558 0.7622820 
##      3460      3461      3462      3463      3465      3468      3474 
## 0.4771856 0.5227587 0.5206390 0.5333570 0.5026217 0.4146552 0.4178347 
##      3475      3480      3481      3484      3485      3486      3487 
## 0.5068611 0.4273732 0.6467597 0.5810498 0.4538692 0.4146552 0.7156492 
##      3492      3493      3494      3504      3505      3507      3509 
## 0.4814250 0.2842951 0.4294929 0.5418357 0.6912729 0.6573581 0.4337323 
##      3511      3512      3517      3521      3523      3525      3526 
## 0.5132201 0.5322972 0.4750660 0.5121603 0.4644676 0.6774950 0.5577333 
##      3528      3533      3536      3539      3540      3541      3542 
## 0.5153398 0.5322972 0.6160244 0.4962627 0.6022465 0.6721958 0.4114757 
##      3543      3544      3546      3552      3553      3557      3562 
## 0.5545538 0.5736309 0.5969473 0.5322972 0.6711360 0.5174595 0.4284331 
##      3564      3567      3572      3574      3577      3578      3579 
## 0.6096654 0.3192698 0.5216988 0.5301775 0.2334229 0.2048073 0.5662120 
##      3580      3583      3587      3589      3591      3593      3601 
## 0.5439554 0.5375964 0.5121603 0.5163996 0.5195791 0.5884686 0.5386562 
##      3605      3621      3622      3623      3624      3628      3629 
## 0.7993764 0.4877840 0.5789301 0.6955123 0.5386562 0.5969473 0.4453905 
##      3630      3632      3633      3635      3641      3645      3649 
## 0.5556136 0.4750660 0.6658368 0.9954464 0.5821096 0.4602282 0.6541786 
##      3656      3668      3671      3674      3675      3678      3681 
## 0.7262476 0.5079209 0.4538692 0.5651522 0.4814250 0.7092901 0.4347921 
##      3683      3696      3699      3702      3704      3706      3707 
## 0.3892191 0.5248783 0.5428956 0.3733215 0.6329818 0.4602282 0.2885345 
##      3708      3717      3722      3724      3727      3729      3731 
## 0.4464503 0.4464503 0.3860396 0.6732557 0.4962627 0.5534940 0.3807404 
##      3735      3746      3754      3755      3759      3760      3763 
## 0.4803651 0.5874088 0.4231339 0.4358519 0.5598530 0.3266886 0.9731898 
##      3766      3768      3769      3772      3774      3780      3784 
## 0.6086055 0.6033063 0.4856643 0.4824848 0.5206390 0.8205731 0.6541786 
##      3785      3786      3787      3789      3790      3798      3799 
## 0.4835447 0.5195791 0.3849797 0.3690822 0.4443307 0.4029970 0.7039910 
##      3800      3801      3802      3804      3806      3809      3810 
## 0.5418357 0.7993764 0.7601624 0.5397161 0.7050508 0.5068611 0.4464503 
##      3811      3813      3814      3816      3817      3818      3830 
## 0.5248783 0.2864148 0.6022465 0.4687069 0.4358519 0.7834788 0.4284331 
##      3832      3838      3839      3855      3859      3862      3864 
## 0.4538692 0.7930173 0.6022465 0.5524341 0.5566735 0.6245031 0.6149646 
##      3867      3868      3872      3873      3875      3877      3882 
## 0.4506897 0.6446400 0.4231339 0.4188945 0.8873429 0.5418357 0.3256288 
##      3886      3889      3891      3892      3893      3894      3897 
## 0.6880934 0.4040568 0.3870994 0.5450153 0.8809839 0.5556136 0.6467597 
##      3906      3907      3909      3910      3912      3913      3914 
## 0.4803651 0.4888438 0.3288083 0.6467597 0.5895285 0.4846045 0.5725710 
##      3916      3919      3920      3922      3924      3925      3926 
## 0.6478195 0.5280579 0.4909635 0.4835447 0.4634077 0.6064859 0.4867242 
##      3933      3935      3941      3943      3944      3949      3951 
## 0.3436460 0.4930832 0.4517495 0.5768104 0.5768104 0.8428297 0.5778702 
##      3953      3954      3960      3964      3966      3968      3969 
## 0.4793053 0.5450153 0.5450153 0.4284331 0.7135295 0.5969473 0.8640265 
##      3970      3973      3974      3975      3977      3990      3999 
## 0.6573581 0.3129107 0.2482606 0.4761258 0.9043003 0.4623479 0.4411511 
##      4003      4006      4025      4028      4030      4032      4036 
## 0.5312374 0.7050508 0.5047414 0.6075457 0.7294271 0.5460751 0.6340416 
##      4037      4046      4047      4048      4051      4053      4056 
## 0.6796147 0.5651522 0.5174595 0.7400254 0.6022465 0.8279920 0.4750660 
##      4058      4061      4062      4065      4067      4068      4069 
## 0.4930832 0.3860396 0.4082962 0.4729463 0.4846045 0.4708266 0.4485700 
##      4070      4074      4082      4087      4091      4093      4094 
## 0.3796805 0.5079209 0.4263134 0.4846045 0.4241937 0.4485700 0.4676471 
##      4095      4101      4102      4106      4108      4111      4112 
## 0.4909635 0.5587932 0.5195791 0.4114757 0.5386562 0.4888438 0.5810498 
##      4113      4115      4116      4122      4126      4127      4132 
## 0.5958875 0.5799899 0.5365366 0.4316126 0.4326724 0.7188287 0.7432050 
##      4134      4140      4141      4143      4144      4149      4153 
## 0.4114757 0.5757506 0.6001268 0.6181441 0.2948935 0.5799899 0.5386562 
##      4157      4158      4159      4160      4161      4162      4164 
## 0.6022465 0.5386562 0.6393408 0.5693915 0.5174595 0.4750660 0.5386562 
##      4165      4166      4167      4168      4169      4170      4180 
## 0.4962627 0.7887780 0.4962627 0.5810498 0.5386562 0.5386562 0.6107252 
##      4239      4242      4243      4249      4260      4261      4262 
## 0.5428956 0.4994422 0.6414605 0.6849139 0.2694574 0.9784890 0.7114098 
##      4386      4473      4628      4629      4739      4754      4811 
## 0.7760599 0.4305528 0.4952029 0.4634077 0.4856643 0.7220082 0.5863489 
##      5056      5201      5263      5264      5265      5339      5458 
## 0.6319220 0.5481948 0.4899037 0.5386562 0.4867242 0.5026217 0.9890874 
##      5528      5632      5685      5856      5858      5912      6104 
## 0.7092901 0.5185193 0.5757506 0.6573581 0.5736309 0.5185193 0.6202638 
##      6700      6948      7082      7129 
## 0.5768104 0.5280579 0.5174595 0.5026217
reg6 <- lm(C150_4 ~ ADM_RATE, data=data2)
summary(reg6)
## 
## Call:
## lm(formula = C150_4 ~ ADM_RATE, data = data2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.58476 -0.12368  0.00175  0.13908  0.57278 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.73479    0.01509   48.68   <2e-16 ***
## ADM_RATE    -0.30757    0.02143  -14.36   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.182 on 1804 degrees of freedom
##   (5897 observations deleted due to missingness)
## Multiple R-squared:  0.1025, Adjusted R-squared:  0.102 
## F-statistic: 206.1 on 1 and 1804 DF,  p-value: < 2.2e-16
coefficients(reg6)
## (Intercept)    ADM_RATE 
##   0.7347908  -0.3075745
confint(reg6, level=0.95)
##                  2.5 %     97.5 %
## (Intercept)  0.7051859  0.7643956
## ADM_RATE    -0.3495969 -0.2655521
lm.beta(reg6)
##   ADM_RATE 
## -0.3201865
fitted(reg6)
##         1         2         4         5         6         9        10 
## 0.5731296 0.4712302 0.4824874 0.5709766 0.5777740 0.4882083 0.4780583 
##        11        13        23        24        25        27        31 
## 0.5705767 0.5709151 0.4272163 0.5551980 0.4272163 0.4787043 0.5340984 
##        33        37        38        40        42        47        51 
## 0.5133679 0.5549520 0.5062629 0.5260092 0.5875549 0.5516609 0.4784274 
##        52        53        54        57        58        65        83 
## 0.5755595 0.4272163 0.5532911 0.5990274 0.5834026 0.6053942 0.4754132 
##        85        96        99       103       104       108       116 
## 0.5052787 0.4882391 0.5577201 0.4469626 0.4520991 0.4856862 0.5233948 
##       123       129       135       138       139       141       142 
## 0.5603038 0.5524606 0.5458785 0.5439716 0.6158210 0.5121376 0.4694770 
##       147       148       157       158       159       162       172 
## 0.4448711 0.5595656 0.4299229 0.5416955 0.4800576 0.5201653 0.5176124 
##       175       187       189       192       194       208       211 
## 0.4612955 0.5179815 0.5151211 0.5616571 0.4703075 0.4859630 0.4831026 
##       215       216       217       224       225       227       228 
## 0.5291465 0.5028796 0.4299229 0.4897462 0.5388966 0.7076319 0.5472626 
##       229       231       232       233       234       235       236 
## 0.6397810 0.5176432 0.5111226 0.4750441 0.5752519 0.5165359 0.6045637 
##       237       238       239       240       241       242       243 
## 0.5520915 0.5980124 0.5185351 0.6257249 0.5469550 0.5722069 0.5113379 
##       244       245       246       247       248       249       251 
## 0.6855173 0.6106229 0.6196964 0.6777049 0.5555056 0.6323992 0.6230182 
##       252       258       259       275       277       278       284 
## 0.5634103 0.6596811 0.5296386 0.5901077 0.4700307 0.5640869 0.7016650 
##       288       293       308       319       320       331       344 
## 0.6000731 0.4933756 0.4859015 0.5755287 0.5690696 0.5298846 0.6909614 
##       351       353       360       361       362       365       367 
## 0.5592888 0.4993425 0.4441944 0.4462244 0.4585889 0.6072704 0.5307766 
##       369       370       378       387       393       408       411 
## 0.5915841 0.5549520 0.6097925 0.5014032 0.5726683 0.5961977 0.5006036 
##       423       426       435       441       442       446       448 
## 0.4939599 0.4441329 0.4333678 0.4957746 0.6054865 0.5303152 0.6394427 
##       455       456       461       462       464       465       472 
## 0.5888774 0.5659324 0.6257249 0.6947446 0.5209342 0.6972974 0.5099846 
##       489       490       491       492       493       495       499 
## 0.6287391 0.5925376 0.4423489 0.6201578 0.5318839 0.5500923 0.5016186 
##       501       507       511       514       520       525       527 
## 0.5507074 0.5830028 0.6474396 0.4272163 0.5583660 0.5011879 0.4886697 
##       531       536       537       541       559       560       565 
## 0.5563976 0.4863013 0.6793658 0.4804267 0.4906997 0.5444637 0.5103537 
##       568       573       574       576       577       578       583 
## 0.5339754 0.5102922 0.4505919 0.4759361 0.4446865 0.6797349 0.6226184 
##       585       596       598       605       606       608       613 
## 0.4872548 0.4995270 0.4554516 0.4817492 0.5345290 0.5193041 0.5167820 
##       620       622       623       629       636       637       640 
## 0.4393962 0.4272163 0.4494232 0.4351825 0.5480315 0.5488927 0.6191428 
##       643       646       647       653       660       664       671 
## 0.5811266 0.5407113 0.5147827 0.5129373 0.5193656 0.4860860 0.4669857 
##       673       674       675       677       678       681       683 
## 0.5320684 0.5590119 0.4888235 0.6164976 0.5147520 0.6331682 0.6612497 
##       684       686       692       693       694       696       698 
## 0.6116687 0.7154136 0.6002577 0.5261630 0.5780816 0.5603960 0.5937986 
##       699       702       703       704       705       709       714 
## 0.5074625 0.5338831 0.6001039 0.6814266 0.5858940 0.4553593 0.5639024 
##       715       717       718       724       726       727       730 
## 0.5929682 0.5388351 0.5045098 0.6262477 0.6261247 0.5822031 0.5443406 
##       734       736       737       738       739       741       742 
## 0.5110611 0.5719301 0.5100768 0.5842331 0.5316993 0.5875241 0.4992195 
##       746       747       749       751       754       755       758 
## 0.4272163 0.5454172 0.5724530 0.6716150 0.5969666 0.5644253 0.5945060 
##       774       775       777       787       796       799       805 
## 0.4931910 0.5623338 0.5850635 0.5847559 0.6173588 0.5121991 0.5484929 
##       806       807       811       820       822       824       832 
## 0.6124069 0.5846637 0.4417646 0.4726758 0.5585813 0.5128450 0.4272163 
##       835       836       838       839       846       849       853 
## 0.5712842 0.4736600 0.5464322 0.5996425 0.5752211 0.5389273 0.6548214 
##       855       857       862       863       868       870       874 
## 0.5792811 0.6066245 0.4971587 0.5265013 0.5893388 0.5255478 0.5751904 
##       878       883       885       888       891       894       896 
## 0.4743675 0.5476932 0.5016186 0.4507457 0.6042254 0.5649481 0.4375508 
##       901       902       904       906       907       908       909 
## 0.5837102 0.6522993 0.6603885 0.6321224 0.5205959 0.5002960 0.5407113 
##       910       911       912       918       919       921       923 
## 0.5519685 0.5634103 0.5859555 0.5703922 0.5648559 0.5591657 0.4272163 
##       924       925       929       930       931       933       935 
## 0.5295771 0.4763359 0.4941752 0.6677088 0.5577817 0.4579122 0.5300999 
##       936       937       940       941       943       944       945 
## 0.4960207 0.5218877 0.5687005 0.4916224 0.5494156 0.6208344 0.4385043 
##       947       949       950       952       953       954       956 
## 0.5682699 0.5852788 0.5801116 0.4714455 0.5153671 0.4923606 0.5446175 
##       965       968       969       972       973       974       975 
## 0.5167205 0.4495154 0.4979584 0.5272395 0.4490541 0.4301690 0.5028488 
##       979       981       987       988       989       994       997 
## 0.5346520 0.4283851 0.5221030 0.5699001 0.4853479 0.5345598 0.5370204 
##      1011      1013      1021      1022      1027      1031      1033 
## 0.6426415 0.7078472 0.4624951 0.5691619 0.5198577 0.5817417 0.5265321 
##      1034      1041      1046      1049      1050      1052      1053 
## 0.5364667 0.5635333 0.4492386 0.5057093 0.4974355 0.5531988 0.5489235 
##      1055      1057      1059      1067      1070      1072      1075 
## 0.5683007 0.5791581 0.5075547 0.5098923 0.4779353 0.5249019 0.5650097 
##      1080      1081      1082      1085      1087      1091      1094 
## 0.5443714 0.5884468 0.5618109 0.5399731 0.5590427 0.4937446 0.5467090 
##      1097      1098      1099      1100      1105      1108      1109 
## 0.4641252 0.5418493 0.5223798 0.5131218 0.4350902 0.5507382 0.5668243 
##      1111      1113      1114      1117      1122      1127      1130 
## 0.5782661 0.6944678 0.5575971 0.5056785 0.4612648 0.6599579 0.5662399 
##      1131      1132      1135      1137      1138      1141      1150 
## 0.4959899 0.5481853 0.5792811 0.5821108 0.5453864 0.6200347 0.4840253 
##      1151      1153      1156      1157      1160      1163      1164 
## 0.4673240 0.4272163 0.4572971 0.4272163 0.5007573 0.5205959 0.5221030 
##      1167      1169      1170      1171      1172      1177      1180 
## 0.5659016 0.5506152 0.5178585 0.5242253 0.6308921 0.5607036 0.5363437 
##      1181      1182      1183      1184      1187      1189      1191 
## 0.4796577 0.5218877 0.5687005 0.4883621 0.5364975 0.4482544 0.4361052 
##      1193      1194      1195      1196      1197      1198      1199 
## 0.4552978 0.5179815 0.4272163 0.5303152 0.5177355 0.5153671 0.4809188 
##      1200      1201      1202      1203      1204      1205      1206 
## 0.5279162 0.5092464 0.5007573 0.4986351 0.4877469 0.5386813 0.4936831 
##      1208      1209      1210      1218      1219      1220      1228 
## 0.4910072 0.4999884 0.4460706 0.5063244 0.5611957 0.4424412 0.6697695 
##      1229      1231      1232      1235      1237      1238      1239 
## 0.5655018 0.5512303 0.5117685 0.5539677 0.4368741 0.5305306 0.4272163 
##      1240      1244      1245      1246      1249      1250      1251 
## 0.4784582 0.4640329 0.5010649 0.4814724 0.5195501 0.7347908 0.5526452 
##      1252      1253      1257      1258      1259      1260      1263 
## 0.5450481 0.5259784 0.5228719 0.5179815 0.5647021 0.5083237 0.4551748 
##      1264      1265      1266      1268      1270      1272      1273 
## 0.5102922 0.5217647 0.4952518 0.6124992 0.5277009 0.5814956 0.4312148 
##      1274      1286      1287      1289      1295      1296      1297 
## 0.6486392 0.4674778 0.6084699 0.4858092 0.4421952 0.5159208 0.6176049 
##      1299      1300      1301      1304      1305      1312      1313 
## 0.4374585 0.5600269 0.5599962 0.4957439 0.4954055 0.4393040 0.6609729 
##      1316      1322      1323      1324      1328      1330      1332 
## 0.4719684 0.5196732 0.5230257 0.4923298 0.5515071 0.5209342 0.4340444 
##      1333      1334      1340      1348      1350      1351      1352 
## 0.4350594 0.5837717 0.5821416 0.4995270 0.4644636 0.5700231 0.5460015 
##      1355      1362      1365      1366      1368      1369      1374 
## 0.5560900 0.4272163 0.4536062 0.5723607 0.4428103 0.5457247 0.5530450 
##      1375      1376      1380      1382      1384      1388      1389 
## 0.4294308 0.5225951 0.4288464 0.4912225 0.5886929 0.4643405 0.5983200 
##      1390      1393      1395      1396      1400      1401      1404 
## 0.4712609 0.4409649 0.6235411 0.5234871 0.4782736 0.6312612 0.5832488 
##      1405      1407      1412      1413      1416      1427      1428 
## 0.5111226 0.5146597 0.5309304 0.5075855 0.4618184 0.5687005 0.5881085 
##      1429      1430      1431      1434      1435      1439      1440 
## 0.5480315 0.5126912 0.5879547 0.4601575 0.5076163 0.5557209 0.4751056 
##      1441      1443      1448      1459      1462      1463      1465 
## 0.4888542 0.4557592 0.4272163 0.5941985 0.4478853 0.4806727 0.5034025 
##      1466      1476      1484      1486      1492      1493      1495 
## 0.4477623 0.5328066 0.6099463 0.5996118 0.5670089 0.4990964 0.4989734 
##      1499      1501      1502      1503      1504      1505      1506 
## 0.5469858 0.5347751 0.4572048 0.5032795 0.6007806 0.4629872 0.4972817 
##      1509      1510      1511      1524      1525      1526      1528 
## 0.5103229 0.5619954 0.5114917 0.4772587 0.5697771 0.6711228 0.5631642 
##      1530      1531      1534      1535      1537      1540      1542 
## 0.6488237 0.5318224 0.5161053 0.6566053 0.6889314 0.6485161 0.5134909 
##      1546      1547      1549      1550      1552      1555      1556 
## 0.4747365 0.5053094 0.4808265 0.4929449 0.4712609 0.4354285 0.4932525 
##      1559      1560      1561      1571      1572      1573      1577 
## 0.4765820 0.5063244 0.4484389 0.5439716 0.5654403 0.5179508 0.5966283 
##      1578      1582      1584      1588      1591      1594      1598 
## 0.6021646 0.5548289 0.5019876 0.4866089 0.6853328 0.5513841 0.5514456 
##      1599      1600      1601      1605      1606      1607      1609 
## 0.5873703 0.5682084 0.5463399 0.5340984 0.5291157 0.4950672 0.5826644 
##      1614      1615      1617      1619      1622      1623      1624 
## 0.5665783 0.4922068 0.4673240 0.5526759 0.5431411 0.5635948 0.5006343 
##      1628      1629      1631      1633      1634      1636      1637 
## 0.5269627 0.6922225 0.4962052 0.4847327 0.6538679 0.5074625 0.5408651 
##      1638      1640      1641      1642      1647      1648      1649 
## 0.5797425 0.5426490 0.5929682 0.6105922 0.6304923 0.6147137 0.6286468 
##      1650      1651      1658      1659      1661      1663      1666 
## 0.6264630 0.4908534 0.4564974 0.5686083 0.4675701 0.5236101 0.5721761 
##      1667      1668      1669      1672      1673      1674      1676 
## 0.5835256 0.5216416 0.5098000 0.5331142 0.5123837 0.5432949 0.4629872 
##      1680      1681      1685      1690      1692      1694      1698 
## 0.5298231 0.7164593 0.6014880 0.5000499 0.5149058 0.5440638 0.5459708 
##      1699      1701      1702      1703      1704      1709      1713 
## 0.5171203 0.4763974 0.5104459 0.7105539 0.5453249 0.4955901 0.5665475 
##      1714      1717      1720      1725      1726      1727      1731 
## 0.5241330 0.4568972 0.6451636 0.5186889 0.5001730 0.5125067 0.6356903 
##      1733      1734      1738      1741      1743      1744      1745 
## 0.4918992 0.5261322 0.5013110 0.5177355 0.5743599 0.4598499 0.6049636 
##      1747      1749      1750      1751      1753      1754      1755 
## 0.5168127 0.4985120 0.4980814 0.4767050 0.6817649 0.6421801 0.4806112 
##      1756      1757      1758      1759      1760      1761      1762 
## 0.4882698 0.5054632 0.5206267 0.4656016 0.6753674 0.6001347 0.5462476 
##      1763      1764      1767      1769      1770      1776      1780 
## 0.5444329 0.5478162 0.5133987 0.6213573 0.5345905 0.5098308 0.5217339 
##      1783      1785      1786      1792      1795      1796      1799 
## 0.4909150 0.5945060 0.4475777 0.5223798 0.5229642 0.4935909 0.5144444 
##      1801      1802      1805      1808      1809      1812      1818 
## 0.5150903 0.5230565 0.4874086 0.4966974 0.4488695 0.5205651 0.4546212 
##      1820      1823      1824      1825      1826      1828      1829 
## 0.5581815 0.5545829 0.5858632 0.6099463 0.6356288 0.5315148 0.5025720 
##      1830      1831      1841      1844      1846      1847      1849 
## 0.5420338 0.4929142 0.5130603 0.5211188 0.5287159 0.5458478 0.5174894 
##      1853      1854      1856      1860      1862      1868      1871 
## 0.5590427 0.4888542 0.5064475 0.5298231 0.5949982 0.4969434 0.4762437 
##      1879      1882      1883      1884      1887      1888      1889 
## 0.5255786 0.4471164 0.4958669 0.4412724 0.6647561 0.5370819 0.5710381 
##      1891      1898      1899      1909      1911      1917      1918 
## 0.4354593 0.5469550 0.5207497 0.6229874 0.5300077 0.4272163 0.5953057 
##      1919      1921      1923      1925      1926      1927      1930 
## 0.5134602 0.5366820 0.4272163 0.4569895 0.4986351 0.5392042 0.4758438 
##      1935      1937      1939      1944      1947      1948      1949 
## 0.4542828 0.5209035 0.5297309 0.4820261 0.4819953 0.4925451 0.5064475 
##      1950      1951      1952      1953      1955      1958      1962 
## 0.5770666 0.6474396 0.5312380 0.4683697 0.5280700 0.5289004 0.5121068 
##      1965      1968      1969      1970      1977      1985      1988 
## 0.5408958 0.4935293 0.5142906 0.5655325 0.4507765 0.5180430 0.5589197 
##      1990      1991      1992      1993      1996      2000      2003 
## 0.4849788 0.4468703 0.6845639 0.5408958 0.5163514 0.6152981 0.5295156 
##      2005      2007      2010      2011      2014      2015      2017 
## 0.6108383 0.5797117 0.5749136 0.5442176 0.5670089 0.4272163 0.6043792 
##      2018      2019      2022      2025      2027      2030      2031 
## 0.5486159 0.4950365 0.4272163 0.4272163 0.5175509 0.5572588 0.5059246 
##      2036      2037      2041      2049      2050      2055      2060 
## 0.5363130 0.4560975 0.5466167 0.5503383 0.4272163 0.5721454 0.5131834 
##      2064      2067      2071      2072      2073      2075      2076 
## 0.4999269 0.5495387 0.4395193 0.4272163 0.6001347 0.4958977 0.5371434 
##      2077      2078      2084      2085      2087      2088      2089 
## 0.4707381 0.5017108 0.5057093 0.4992502 0.7092313 0.5298539 0.4272163 
##      2093      2096      2101      2105      2110      2111      2112 
## 0.4981430 0.5469243 0.4477315 0.5445559 0.5699308 0.4740291 0.4732602 
##      2117      2118      2120      2121      2122      2128      2136 
## 0.6821033 0.5131526 0.5307459 0.5415417 0.5001114 0.5578432 0.5326836 
##      2141      2142      2143      2144      2145      2150      2151 
## 0.4556669 0.4768896 0.4496077 0.4272163 0.5391426 0.5461246 0.5585506 
##      2155      2156      2157      2158      2159      2162      2164 
## 0.4991580 0.5112764 0.4907304 0.5975510 0.5205651 0.4760899 0.4807035 
##      2167      2169      2173      2174      2177      2179      2185 
## 0.5496924 0.4933448 0.4944521 0.5198270 0.5722377 0.5744214 0.6094234 
##      2192      2193      2196      2199      2201      2202      2205 
## 0.4675393 0.4767973 0.5325913 0.4562513 0.5413572 0.6994197 0.4755055 
##      2209      2211      2213      2215      2216      2217      2218 
## 0.4272163 0.4403497 0.4757823 0.4886697 0.4930680 0.5192426 0.5034948 
##      2227      2228      2231      2238      2241      2243      2254 
## 0.5423722 0.5007573 0.5010342 0.5397885 0.5381584 0.4828565 0.5189658 
##      2259      2260      2261      2263      2264      2271      2273 
## 0.4883928 0.4759361 0.4864244 0.5254556 0.6007806 0.4992195 0.5183814 
##      2279      2280      2287      2294      2295      2296      2298 
## 0.5066013 0.5292387 0.5398193 0.7119072 0.4722144 0.5707921 0.5166897 
##      2300      2301      2302      2305      2307      2309      2311 
## 0.5490773 0.5487082 0.5417878 0.5597809 0.5024490 0.5576586 0.6001347 
##      2312      2313      2316      2319      2326      2328      2333 
## 0.5356363 0.4272163 0.5841715 0.5054017 0.5408343 0.4272163 0.6228644 
##      2335      2339      2344      2352      2353      2357      2360 
## 0.5952135 0.5207189 0.4272163 0.5047866 0.5120453 0.5274856 0.5212110 
##      2366      2372      2373      2376      2393      2397      2398 
## 0.6638026 0.5975818 0.6616803 0.4272163 0.4880238 0.5004190 0.4272163 
##      2403      2407      2408      2409      2412      2416      2417 
## 0.5436640 0.6540832 0.5730373 0.7134143 0.5048173 0.6884701 0.6911459 
##      2421      2422      2425      2426      2427      2430      2431 
## 0.5388966 0.6489775 0.6261247 0.4448403 0.6177279 0.6281547 0.6200347 
##      2434      2435      2436      2437      2440      2442      2443 
## 0.6458710 0.4520068 0.5109381 0.6123146 0.6205884 0.5232103 0.5659324 
##      2444      2445      2446      2450      2452      2454      2455 
## 0.4272163 0.5416032 0.4937754 0.4819338 0.5985968 0.5621800 0.5867859 
##      2462      2463      2466      2467      2468      2469      2474 
## 0.6537449 0.4593271 0.4867935 0.5886006 0.5452941 0.4462551 0.4681237 
##      2477      2479      2481      2482      2485      2486      2487 
## 0.5529835 0.4464397 0.5445252 0.7088622 0.4799345 0.5065397 0.5319454 
##      2488      2489      2494      2496      2497      2498      2499 
## 0.4692617 0.4794424 0.4272163 0.5301307 0.5969359 0.5076163 0.6271397 
##      2501      2503      2504      2507      2508      2509      2510 
## 0.6163438 0.5087235 0.5444022 0.5136755 0.5194886 0.4272163 0.4484389 
##      2514      2517      2518      2520      2521      2524      2526 
## 0.4408726 0.5028796 0.6109305 0.4622183 0.4419491 0.5179815 0.6162823 
##      2527      2535      2537      2541      2542      2543      2544 
## 0.5320992 0.6257556 0.5322222 0.5378508 0.5948136 0.4291848 0.4272163 
##      2548      2549      2551      2552      2553      2555      2557 
## 0.4733832 0.4320452 0.6419340 0.5878009 0.5718070 0.4272163 0.5176739 
##      2558      2560      2561      2563      2565      2566      2569 
## 0.4272163 0.4425950 0.6194503 0.5233333 0.5580277 0.6228029 0.5662092 
##      2571      2572      2574      2575      2576      2578      2580 
## 0.5181661 0.4978354 0.5882623 0.5001422 0.4862091 0.5713457 0.4682160 
##      2581      2582      2583      2587      2590      2594      2595 
## 0.5322222 0.6199425 0.5172433 0.5259169 0.5424952 0.5679624 0.4866704 
##      2596      2597      2598      2599      2600      2601      2602 
## 0.5250557 0.5092156 0.5913073 0.5619647 0.5630412 0.5992734 0.5569820 
##      2603      2604      2605      2606      2607      2608      2609 
## 0.6076395 0.5775279 0.5622415 0.5842331 0.5454787 0.5842023 0.5710996 
##      2610      2611      2612      2613      2614      2615      2617 
## 0.5529220 0.6058248 0.5813726 0.5860170 0.5269319 0.6092389 0.5430181 
##      2618      2620      2621      2624      2625      2626      2630 
## 0.5875856 0.4852863 0.5728528 0.5710689 0.4272163 0.4272163 0.4272163 
##      2631      2632      2636      2640      2642      2643      2644 
## 0.6431951 0.5565514 0.6083161 0.4840253 0.6623877 0.4892233 0.4986658 
##      2645      2646      2647      2648      2653      2654      2655 
## 0.5127835 0.6333219 0.5607344 0.4907304 0.4272163 0.4272163 0.4272163 
##      2657      2658      2659      2660      2664      2666      2668 
## 0.4784889 0.4831948 0.4272163 0.4272163 0.5420646 0.6164976 0.5218570 
##      2669      2672      2675      2677      2681      2686      2691 
## 0.4524681 0.6018878 0.4606496 0.5254556 0.6243715 0.5508305 0.6681394 
##      2692      2694      2696      2697      2700      2702      2704 
## 0.6996965 0.4970972 0.5840793 0.5689158 0.5800193 0.5283468 0.5099231 
##      2705      2710      2713      2714      2716      2718      2720 
## 0.5435410 0.4881468 0.4792579 0.6048405 0.5442176 0.5324068 0.5371742 
##      2722      2727      2728      2734      2735      2738      2739 
## 0.5438178 0.5463399 0.5627336 0.5931220 0.5906921 0.5594733 0.5098308 
##      2740      2741      2742      2743      2744      2745      2746 
## 0.6471320 0.5376663 0.5480008 0.6018571 0.6019186 0.5760823 0.5709766 
##      2747      2749      2750      2751      2752      2755      2758 
## 0.5547059 0.5412957 0.5094617 0.5895233 0.5930912 0.4934986 0.6182508 
##      2763      2764      2767      2770      2775      2780      2782 
## 0.5070934 0.5507074 0.5522453 0.5590735 0.5053402 0.6289544 0.5140446 
##      2788      2791      2792      2795      2799      2803      2805 
## 0.5039254 0.5497540 0.6021954 0.5470781 0.5368358 0.4928834 0.5573818 
##      2807      2810      2814      2817      2819      2821      2822 
## 0.4702767 0.4803036 0.6226799 0.4571433 0.5074625 0.4272163 0.4404112 
##      2828      2830      2833      2834      2836      2839      2844 
## 0.6599271 0.5115840 0.5041099 0.5380354 0.5624568 0.5706383 0.5110611 
##      2848      2849      2852      2855      2856      2858      2862 
## 0.6169590 0.5056785 0.6187737 0.5020184 0.5548289 0.5017108 0.5336371 
##      2865      2867      2868      2871      2876      2877      2878 
## 0.5287466 0.5997963 0.4757823 0.4621567 0.5532911 0.5358208 0.5639947 
##      2884      2887      2888      2893      2894      2900      2902 
## 0.5134294 0.4272163 0.4922683 0.5039254 0.5438485 0.4960207 0.4797808 
##      2903      2911      2913      2914      2915      2922      2923 
## 0.4602498 0.4752594 0.6577126 0.4324143 0.5214571 0.5362514 0.5141368 
##      2924      2927      2931      2935      2936      2937      2938 
## 0.5211495 0.5593503 0.5322837 0.5075240 0.5085697 0.5010957 0.4652940 
##      2940      2948      2951      2954      2956      2966      2971 
## 0.4996808 0.4595116 0.6341524 0.5915533 0.5238254 0.5718993 0.5063552 
##      2975      2976      2981      2984      3000      3004      3005 
## 0.5062629 0.5031564 0.4453017 0.4887312 0.4951287 0.5675318 0.4434255 
##      3016      3019      3022      3023      3025      3026      3029 
## 0.5332987 0.4866397 0.6193273 0.4414570 0.4537292 0.5530450 0.5098000 
##      3030      3031      3033      3034      3041      3044      3049 
## 0.5094002 0.4785812 0.6026568 0.5419416 0.4569895 0.4358591 0.5713764 
##      3053      3054      3058      3060      3062      3063      3065 
## 0.4983583 0.5040791 0.5310842 0.5379123 0.5517839 0.5042637 0.5487697 
##      3067      3068      3071      3074      3076      3078      3081 
## 0.5263475 0.4846404 0.4894694 0.4979277 0.5726067 0.5270242 0.4928219 
##      3082      3083      3086      3104      3107      3109      3110 
## 0.4860245 0.4725528 0.6109613 0.5729451 0.5373895 0.5275163 0.4956208 
##      3112      3114      3115      3118      3123      3126      3128 
## 0.4720299 0.5298846 0.4463782 0.4272163 0.5604883 0.5136140 0.5507382 
##      3129      3130      3131      3132      3133      3140      3141 
## 0.5793426 0.4956208 0.5044175 0.4815032 0.4873471 0.5215494 0.5412341 
##      3142      3147      3151      3152      3156      3157      3162 
## 0.6156672 0.4968204 0.5725760 0.6198194 0.4847020 0.4618492 0.5563361 
##      3164      3167      3169      3171      3179      3181      3184 
## 0.5807882 0.5140446 0.4898077 0.5047558 0.4687696 0.5539370 0.4647096 
##      3186      3187      3192      3193      3195      3196      3197 
## 0.6103154 0.6403039 0.5032487 0.4589887 0.4558207 0.6591274 0.5738370 
##      3199      3200      3204      3207      3210      3211      3214 
## 0.5738986 0.5050019 0.4496385 0.7192583 0.5018339 0.5868782 0.5010034 
##      3217      3218      3219      3220      3221      3237      3239 
## 0.5100768 0.4842406 0.5435410 0.4293693 0.5169665 0.5590427 0.6150520 
##      3240      3241      3242      3247      3250      3252      3253 
## 0.4958977 0.5162283 0.5950597 0.4998654 0.6588506 0.5094617 0.5341907 
##      3255      3256      3261      3262      3263      3265      3266 
## 0.5012187 0.4434255 0.5066628 0.4516685 0.5278854 0.4897462 0.4458553 
##      3267      3269      3270      3275      3278      3282      3283 
## 0.4941752 0.6432874 0.5519070 0.5177970 0.6293850 0.6512535 0.4475470 
##      3288      3290      3291      3294      3295      3297      3298 
## 0.5126605 0.4558207 0.5066320 0.4876854 0.4887927 0.5234563 0.5149980 
##      3300      3301      3302      3303      3305      3313      3316 
## 0.5544906 0.4696616 0.5072472 0.5723914 0.4455477 0.4681237 0.4849480 
##      3317      3318      3319      3320      3321      3322      3323 
## 0.5282237 0.4770433 0.5006958 0.4729834 0.4630487 0.4854401 0.4620952 
##      3324      3325      3326      3327      3328      3329      3330 
## 0.4823336 0.4740599 0.4622183 0.4776893 0.4703382 0.5801116 0.5015263 
##      3331      3332      3333      3334      3339      3343      3344 
## 0.4948212 0.4907612 0.5047866 0.4784274 0.4330294 0.6047175 0.7028953 
##      3345      3346      3347      3349      3351      3352      3353 
## 0.5381276 0.5209035 0.4339829 0.5567667 0.5335755 0.5055863 0.4881775 
##      3354      3362      3369      3371      3373      3374      3375 
## 0.5714072 0.5172126 0.4657861 0.5004190 0.5567667 0.5234256 0.4744290 
##      3376      3379      3380      3384      3385      3386      3391 
## 0.5135832 0.4971587 0.5221645 0.4791041 0.5318839 0.4272163 0.4942675 
##      3392      3394      3395      3396      3404      3405      3408 
## 0.6824416 0.5041099 0.5449250 0.5210573 0.4790118 0.4486235 0.5830643 
##      3411      3412      3414      3417      3420      3421      3422 
## 0.6066860 0.4777815 0.5702999 0.4467165 0.5348366 0.4929449 0.6385815 
##      3424      3428      3429      3430      3434      3435      3437 
## 0.5948751 0.7079088 0.5038638 0.4851941 0.5408343 0.5334833 0.4985428 
##      3438      3439      3440      3446      3447      3450      3451 
## 0.6345522 0.4950672 0.5164436 0.5148135 0.5543676 0.4856247 0.5405882 
##      3453      3456      3457      3458      3460      3461      3462 
## 0.4948212 0.5024490 0.6001654 0.5763284 0.5782354 0.6326145 0.4916531 
##      3463      3465      3468      3469      3474      3475      3480 
## 0.5702999 0.5484929 0.5529835 0.5234563 0.5570742 0.5748520 0.5602422 
##      3481      3484      3485      3486      3487      3492      3493 
## 0.5519070 0.5695618 0.5334525 0.5587351 0.5342522 0.5391734 0.4747673 
##      3494      3502      3504      3505      3507      3509      3511 
## 0.5907844 0.5808805 0.5158592 0.4967589 0.5462784 0.4453632 0.4758131 
##      3512      3517      3521      3523      3525      3526      3528 
## 0.5089388 0.5122299 0.4798423 0.5596271 0.4640637 0.4517915 0.4357053 
##      3533      3536      3539      3540      3541      3542      3543 
## 0.4616031 0.5470473 0.4602190 0.5695310 0.4803652 0.5581815 0.5858632 
##      3544      3546      3552      3553      3557      3562      3564 
## 0.5428643 0.5818955 0.5920147 0.5638409 0.4526219 0.4781199 0.4475470 
##      3567      3572      3574      3577      3578      3579      3580 
## 0.5940754 0.5614110 0.5604575 0.6017033 0.5743907 0.4608957 0.5060476 
##      3583      3587      3589      3591      3593      3601      3605 
## 0.5169358 0.6177279 0.5890005 0.5131526 0.5428335 0.5738063 0.5502768 
##      3611      3621      3622      3623      3624      3628      3629 
## 0.5357901 0.5297309 0.4970972 0.5046328 0.5092156 0.4444097 0.5558747 
##      3630      3632      3633      3635      3641      3645      3649 
## 0.5100153 0.5135217 0.5238562 0.6945293 0.5795579 0.4812264 0.5675318 
##      3656      3659      3668      3671      3674      3675      3678 
## 0.5645175 0.5299769 0.4724605 0.4745212 0.5926606 0.6180355 0.4729526 
##      3681      3683      3696      3699      3702      3704      3706 
## 0.5625798 0.5876471 0.5600885 0.6248944 0.4759053 0.5410496 0.4822106 
##      3707      3708      3711      3712      3717      3722      3724 
## 0.5511688 0.4481006 0.4460091 0.4481621 0.4923913 0.5911535 0.5828490 
##      3727      3729      3731      3735      3746      3748      3754 
## 0.4446865 0.4890080 0.5459400 0.5452019 0.5336986 0.5226566 0.5824799 
##      3755      3759      3760      3763      3766      3768      3769 
## 0.5416340 0.4580660 0.6144369 0.6883470 0.4937754 0.4918377 0.5082006 
##      3772      3774      3780      3783      3784      3785      3786 
## 0.4471164 0.5519070 0.5736217 0.6319686 0.5855556 0.5548289 0.5105690 
##      3787      3789      3790      3798      3799      3800      3801 
## 0.5820800 0.4475162 0.5731911 0.4777508 0.5163206 0.5459400 0.6128067 
##      3802      3803      3804      3806      3809      3810      3811 
## 0.5442791 0.4275546 0.4777200 0.5844791 0.5629489 0.4672010 0.5013110 
##      3813      3814      3816      3817      3818      3830      3832 
## 0.5750981 0.5313918 0.6177279 0.4723990 0.5858632 0.4341675 0.5274240 
##      3838      3839      3850      3855      3859      3862      3864 
## 0.5902308 0.6275703 0.4541906 0.5470781 0.4338906 0.4843636 0.4402574 
##      3865      3866      3867      3868      3870      3871      3872 
## 0.5280700 0.4936831 0.4529295 0.5374202 0.4272163 0.5245636 0.4411802 
##      3873      3874      3875      3877      3879      3881      3882 
## 0.4298614 0.4838100 0.6819802 0.5325913 0.4873163 0.5330834 0.4465012 
##      3883      3885      3886      3889      3891      3892      3893 
## 0.4317376 0.4789196 0.5089081 0.5513533 0.4333985 0.5877086 0.6332297 
##      3894      3897      3906      3907      3909      3910      3912 
## 0.4892848 0.5629181 0.5141983 0.5488927 0.5093079 0.5297924 0.5894003 
##      3913      3914      3916      3919      3920      3922      3924 
## 0.6454096 0.5611035 0.5326221 0.6661401 0.5105075 0.5294848 0.4412109 
##      3925      3926      3933      3935      3941      3943      3944 
## 0.4988196 0.4765512 0.5328066 0.4829180 0.4920837 0.5492003 0.4856247 
##      3949      3951      3953      3954      3960      3964      3966 
## 0.6369821 0.5215801 0.4807650 0.5900155 0.4470856 0.5231180 0.5113994 
##      3968      3969      3970      3973      3974      3975      3977 
## 0.5030334 0.6455942 0.5982277 0.4885466 0.6613112 0.4609264 0.6749368 
##      3990      3997      3999      4003      4006      4013      4014 
## 0.4688619 0.4717531 0.5059861 0.4305996 0.5271472 0.4527142 0.4483159 
##      4020      4025      4028      4030      4032      4036      4037 
## 0.5047251 0.4391502 0.5040791 0.4909150 0.4616031 0.4782736 0.5091849 
##      4046      4047      4048      4051      4053      4054      4056 
## 0.5570435 0.4823336 0.5649789 0.4746750 0.6086545 0.5048481 0.6038256 
##      4058      4061      4062      4065      4067      4068      4069 
## 0.5221338 0.5439408 0.6168667 0.5478778 0.6186506 0.5557209 0.5302230 
##      4070      4074      4082      4087      4091      4093      4094 
## 0.5915841 0.4994040 0.6352904 0.4324758 0.6073319 0.5122299 0.5443406 
##      4095      4101      4102      4106      4108      4109      4111 
## 0.4961437 0.4709226 0.5421569 0.5342830 0.5851558 0.5216109 0.4795655 
##      4112      4113      4115      4116      4121      4122      4124 
## 0.4861476 0.5144136 0.5028488 0.5003575 0.4444097 0.5665475 0.5104152 
##      4125      4126      4127      4131      4132      4134      4140 
## 0.5012187 0.4987581 0.5296078 0.5530758 0.5236409 0.6263092 0.5396963 
##      4141      4143      4144      4149      4153      4157      4158 
## 0.5273318 0.4834717 0.5890005 0.5221338 0.4832256 0.4773817 0.4661245 
##      4159      4160      4161      4162      4163      4164      4165 
## 0.5001422 0.5369589 0.4876854 0.4702152 0.4272163 0.4555131 0.4623720 
##      4166      4167      4168      4169      4170      4180      4191 
## 0.5596579 0.4593578 0.4444405 0.4593886 0.4597884 0.4344135 0.4762744 
##      4193      4198      4199      4202      4204      4208      4220 
## 0.5797117 0.6029643 0.5085390 0.4522221 0.5218570 0.4495769 0.5061707 
##      4221      4222      4223      4224      4225      4226      4227 
## 0.5394502 0.5694387 0.5943830 0.6656173 0.5309919 0.5049404 0.5071549 
##      4228      4235      4236      4239      4240      4241      4242 
## 0.5463399 0.4585581 0.4993117 0.4565281 0.4924221 0.6550982 0.4932218 
##      4243      4244      4245      4246      4248      4249      4252 
## 0.4806727 0.5855249 0.6121301 0.5009419 0.5082622 0.6481470 0.6483931 
##      4254      4256      4260      4261      4262      4265      4267 
## 0.5981047 0.5615956 0.4362282 0.7191352 0.5524299 0.4999884 0.4353670 
##      4268      4284      4319      4321      4338      4352      4363 
## 0.4370279 0.4841176 0.4696923 0.4784889 0.4902998 0.5432026 0.5810035 
##      4370      4376      4382      4386      4412      4466      4470 
## 0.4444712 0.4910072 0.5256401 0.5506459 0.4781199 0.4525604 0.4432102 
##      4471      4472      4473      4485      4494      4505      4507 
## 0.4340444 0.4517915 0.5447097 0.5353902 0.5062937 0.5843561 0.4496692 
##      4516      4552      4556      4616      4627      4628      4629 
## 0.4996808 0.5145982 0.5392964 0.4495769 0.4991272 0.4913456 0.4748288 
##      4636      4643      4672      4707      4712      4717      4719 
## 0.4707073 0.5810035 0.4433332 0.5532911 0.4272163 0.4706458 0.4272163 
##      4739      4754      4757      4792      4795      4811      4813 
## 0.6537141 0.6011189 0.4955593 0.4272163 0.4887312 0.4954978 0.4845174 
##      4819      4851      4860      4877      4888      4889      4890 
## 0.4906074 0.5087850 0.5214571 0.4781814 0.4500691 0.4566512 0.4918377 
##      4891      4892      4902      4905      4906      4909      4912 
## 0.4584043 0.4315531 0.4616954 0.4974355 0.5533218 0.5193656 0.5297309 
##      4954      4972      5043      5056      5086      5090      5114 
## 0.4325681 0.4272163 0.6443331 0.4987889 0.5233026 0.4373662 0.4501613 
##      5126      5131      5132      5135      5176      5188      5199 
## 0.5142291 0.5094002 0.4883006 0.4989734 0.4272163 0.4272163 0.4272163 
##      5201      5204      5215      5223      5224      5263      5264 
## 0.5536909 0.5271472 0.5006958 0.4391502 0.4755977 0.5323145 0.5381892 
##      5265      5266      5267      5271      5315      5318      5339 
## 0.5599347 0.4563436 0.4516685 0.4336138 0.4489618 0.4819338 0.4272163 
##      5348      5364      5451      5454      5455      5456      5458 
## 0.5425567 0.4464397 0.5668859 0.5120761 0.4777200 0.4787350 0.6978818 
##      5472      5474      5495      5508      5528      5532      5533 
## 0.5564591 0.6047175 0.4272163 0.6278164 0.5352364 0.4901768 0.5365898 
##      5558      5585      5627      5632      5663      5664      5685 
## 0.4323835 0.5731911 0.4546827 0.5281622 0.4774432 0.5232718 0.5757748 
##      5700      5718      5734      5735      5736      5737      5755 
## 0.5370511 0.5200115 0.4528372 0.4644943 0.4318299 0.5241945 0.5663630 
##      5823      5829      5830      5832      5833      5834      5835 
## 0.5981047 0.4416723 0.4419491 0.4321067 0.4871625 0.4628334 0.5248097 
##      5836      5856      5858      5904      5912      5945      5946 
## 0.5211803 0.6260939 0.4922375 0.5856787 0.6610344 0.4440098 0.4423489 
##      5947      5948      5949      5950      5951      5998      6029 
## 0.5068166 0.4634793 0.4759976 0.4435177 0.5410188 0.4471779 0.4272163 
##      6030      6062      6067      6068      6069      6070      6071 
## 0.4402267 0.4920837 0.4360744 0.5115224 0.4480698 0.4946059 0.4796577 
##      6072      6073      6104      6105      6106      6107      6186 
## 0.4345366 0.5261630 0.5182891 0.5502461 0.4668934 0.5810035 0.4272163 
##      6220      6336      6421      6579      6671      6700      6711 
## 0.5977663 0.4711687 0.4504074 0.4581583 0.4272163 0.4656631 0.5590427 
##      6834      6837      6887      6889      6948      7040      7042 
## 0.4272163 0.4272163 0.4272163 0.4272163 0.5561515 0.4272163 0.4272163 
##      7082      7083      7104      7105      7106      7107      7108 
## 0.4993733 0.5490773 0.5060169 0.4684928 0.4824567 0.5222876 0.5028488 
##      7109      7110      7111      7112      7113      7114      7115 
## 0.5028796 0.5125682 0.4470548 0.4272163 0.5194886 0.4955593 0.5010342 
##      7116      7117      7118      7119      7120      7121      7122 
## 0.5150903 0.4624028 0.5176739 0.4721222 0.5194886 0.4272163 0.4690772 
##      7123      7124      7125      7126      7127      7128      7129 
## 0.5226566 0.4829488 0.4272163 0.4738138 0.4696308 0.5297309 0.5210880
reg7 <- lm(PCTFLOAN ~ SAT_AVG, data=data2)
summary(reg7)
## 
## Call:
## lm(formula = PCTFLOAN ~ SAT_AVG, data = data2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.72338 -0.07918  0.01720  0.10087  0.34595 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.276e+00  3.239e-02    39.4   <2e-16 ***
## SAT_AVG     -6.493e-04  3.035e-05   -21.4   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.146 on 1300 degrees of freedom
##   (6401 observations deleted due to missingness)
## Multiple R-squared:  0.2604, Adjusted R-squared:  0.2599 
## F-statistic: 457.8 on 1 and 1300 DF,  p-value: < 2.2e-16
coefficients(reg7)
##   (Intercept)       SAT_AVG 
##  1.2759380530 -0.0006493094
confint(reg7, level=0.95)
##                     2.5 %        97.5 %
## (Intercept)  1.2124004368  1.3394756691
## SAT_AVG     -0.0007088428 -0.0005897761
lm.beta(reg7)
##    SAT_AVG 
## -0.5103375
fitted(reg7)
##         1         2         4         5         6         9        10 
## 0.7389591 0.5571525 0.4844298 0.7233757 0.5065064 0.6207848 0.4870271 
##        11        13        24        27        33        35        37 
## 0.5091036 0.6642886 0.6097466 0.6000069 0.6331217 0.5909166 0.6175383 
##        38        40        42        47        51        52        53 
## 0.5811769 0.6077986 0.6733789 0.5194925 0.5954618 0.5513087 0.6720803 
##        54        57        58        65        83       116       123 
## 0.7493481 0.5941631 0.6409134 0.5915659 0.5324787 0.5792290 0.6344203 
##       129       135       138       139       141       142       145 
## 0.5954618 0.5558539 0.5259856 0.7006499 0.5694894 0.6201355 0.6331217 
##       147       148       157       158       159       172       175 
## 0.5948124 0.6363682 0.5415691 0.6337710 0.4681971 0.5539059 0.5870207 
##       176       187       189       211       216       224       227 
## 0.6720803 0.6376669 0.6337710 0.6026042 0.5474129 0.6422120 0.2727550 
##       228       229       233       234       235       237       238 
## 0.5558539 0.4746902 0.7019485 0.5785797 0.6292258 0.6850665 0.6129931 
##       240       241       242       243       244       245       246 
## 0.5915659 0.7103895 0.6824692 0.6675351 0.3785924 0.4798847 0.5175446 
##       247       248       249       251       252       275       277 
## 0.4123565 0.5435170 0.4233947 0.4623533 0.5298815 0.4902736 0.6019548 
##       278       284       308       331       344       351       353 
## 0.6318231 0.3545679 0.5961111 0.6201355 0.3019739 0.7012992 0.6357189 
##       367       369       378       387       393       408       411 
## 0.6896116 0.6175383 0.6694830 0.5597497 0.4850791 0.6298752 0.5279336 
##       423       441       442       446       448       455       456 
## 0.6902609 0.6707816 0.4318358 0.6201355 0.6941568 0.6155903 0.5065064 
##       461       464       465       472       489       490       493 
## 0.4746902 0.5389718 0.3318421 0.5552046 0.5519580 0.4688464 0.6331217 
##       495       499       501       507       511       520       525 
## 0.5279336 0.6207848 0.6019548 0.4259920 0.3928772 0.6110452 0.5558539 
##       527       531       536       537       541       559       560 
## 0.6370176 0.6461079 0.5285829 0.3798910 0.4571588 0.5129995 0.5870207 
##       568       573       574       576       583       585       596 
## 0.6558475 0.5909166 0.5688401 0.4922215 0.4104086 0.5435170 0.4766381 
##       598       605       606       613       620       623       629 
## 0.6136424 0.6461079 0.6441600 0.6052014 0.5565032 0.6454586 0.6331217 
##       636       637       643       653       664       671       673 
## 0.6922089 0.6168890 0.4668985 0.6266286 0.5857221 0.7207785 0.5591004 
##       675       678       684       686       692       693       696 
## 0.6467572 0.6707816 0.6389655 0.3065190 0.6954554 0.5006626 0.7220771 
##       698       699       702       703       704       705       714 
## 0.4630026 0.5422184 0.7246743 0.4337837 0.3578145 0.5584511 0.6513024 
##       715       717       718       726       727       730       734 
## 0.6668858 0.7545426 0.6396148 0.6655872 0.5065064 0.6435107 0.5272843 
##       736       738       739       741       742       746       747 
## 0.7402578 0.6603927 0.5889687 0.5889687 0.5857221 0.6733789 0.5123501 
##       749       754       755       758       796       805       806 
## 0.5688401 0.5311801 0.4785861 0.4493671 0.4123565 0.5402704 0.6792227 
##       807       811       835       836       839       846       849 
## 0.5337774 0.5805276 0.5214405 0.6792227 0.6493544 0.5655935 0.6922089 
##       853       855       857       862       868       869       870 
## 0.7155840 0.6590941 0.5844235 0.6740282 0.7077923 0.7577891 0.6227327 
##       874       878       883       885       888       891       894 
## 0.6805213 0.7175319 0.5078050 0.6363682 0.6785734 0.6720803 0.6422120 
##       896       901       902       904       906       907       908 
## 0.5129995 0.6526010 0.3889813 0.7090909 0.3669048 0.6461079 0.5409198 
##       909       910       911       912       918       919       924 
## 0.5623470 0.5909166 0.4655999 0.7181812 0.5772811 0.6039028 0.4935202 
##       925       929       930       931       933       935       936 
## 0.6240314 0.5363746 0.7824629 0.6474065 0.6428613 0.5740345 0.7259730 
##       937       940       941       944       945       947       949 
## 0.6584448 0.6233821 0.5396211 0.6461079 0.6454586 0.6149410 0.6590941 
##       950       952       953       954       968       969       972 
## 0.6331217 0.6538996 0.6681844 0.5811769 0.6292258 0.5993576 0.5896180 
##       973       974       979       981       987       989       994 
## 0.5772811 0.6766254 0.5928645 0.6000069 0.5844235 0.6201355 0.6337710 
##       997      1011      1013      1022      1031      1033      1034 
## 0.5214405 0.7110388 0.2987273 0.6065000 0.6201355 0.5688401 0.5922152 
##      1039      1040      1041      1046      1049      1050      1052 
## 0.6857158 0.6720803 0.5902673 0.6071493 0.5454649 0.6071493 0.4149537 
##      1053      1057      1059      1067      1080      1081      1082 
## 0.4649506 0.4539123 0.5552046 0.5746838 0.5811769 0.6227327 0.5454649 
##      1085      1091      1094      1096      1098      1099      1108 
## 0.4889750 0.6461079 0.5954618 0.6720803 0.5967604 0.6052014 0.5454649 
##      1109      1111      1113      1114      1117      1122      1130 
## 0.6103959 0.6071493 0.3272970 0.6980526 0.5584511 0.6110452 0.6207848 
##      1131      1132      1135      1137      1138      1150      1151 
## 0.5941631 0.6077986 0.5850728 0.6214341 0.5740345 0.5909166 0.5811769 
##      1156      1157      1160      1163      1164      1167      1169 
## 0.5746838 0.5863714 0.5558539 0.6461079 0.4246934 0.5954618 0.5837742 
##      1170      1171      1177      1181      1182      1183      1184 
## 0.6006562 0.4935202 0.4883257 0.5331280 0.6065000 0.5558539 0.5552046 
##      1187      1189      1191      1193      1194      1196      1197 
## 0.5610484 0.6467572 0.6045521 0.6253300 0.6201355 0.6149410 0.6493544 
##      1198      1199      1200      1201      1202      1203      1204 
## 0.6259793 0.6831185 0.6694830 0.6642886 0.4980653 0.6811706 0.6532503 
##      1205      1218      1219      1220      1228      1229      1231 
## 0.6636392 0.6266286 0.6032535 0.5740345 0.3344394 0.6526010 0.6493544 
##      1232      1235      1237      1238      1239      1240      1243 
## 0.6532503 0.4266413 0.6389655 0.6292258 0.6636392 0.5331280 0.6636392 
##      1244      1245      1246      1249      1252      1253      1257 
## 0.5071557 0.5759825 0.5259856 0.5435170 0.6233821 0.5961111 0.5610484 
##      1258      1259      1260      1264      1265      1266      1268 
## 0.6077986 0.5318294 0.4967667 0.5616977 0.4714436 0.6649379 0.6149410 
##      1270      1272      1273      1274      1286      1287      1289 
## 0.6240314 0.6668858 0.6480558 0.3682034 0.5324787 0.6331217 0.5201419 
##      1295      1296      1300      1301      1304      1305      1312 
## 0.5694894 0.5246870 0.5844235 0.6071493 0.5941631 0.5597497 0.5941631 
##      1316      1322      1323      1324      1330      1332      1333 
## 0.5454649 0.6590941 0.6831185 0.5616977 0.5883193 0.5487115 0.6467572 
##      1334      1340      1348      1352      1355      1365      1366 
## 0.6266286 0.6487051 0.6207848 0.6077986 0.7233757 0.5324787 0.5772811 
##      1369      1374      1375      1376      1382      1384      1388 
## 0.5883193 0.6071493 0.6233821 0.6201355 0.6201355 0.6253300 0.6220834 
##      1389      1390      1395      1396      1400      1401      1404 
## 0.6409134 0.6026042 0.6214341 0.5389718 0.5487115 0.5454649 0.6013055 
##      1405      1407      1412      1413      1416      1427      1428 
## 0.6500037 0.4558602 0.6019548 0.6214341 0.5603990 0.6201355 0.7025978 
##      1429      1430      1431      1435      1440      1441      1443 
## 0.6129931 0.5344267 0.6487051 0.5331280 0.6077986 0.5850728 0.5967604 
##      1448      1459      1462      1463      1465      1466      1476 
## 0.6487051 0.6480558 0.6383162 0.4772874 0.6461079 0.5961111 0.5558539 
##      1484      1486      1492      1493      1495      1499      1501 
## 0.7006499 0.7123375 0.6350696 0.5220898 0.5941631 0.6331217 0.5591004 
##      1502      1503      1504      1505      1506      1509      1511 
## 0.5389718 0.6071493 0.5733852 0.6065000 0.6071493 0.6090973 0.6201355 
##      1524      1525      1526      1528      1530      1531      1538 
## 0.6071493 0.6850665 0.7525946 0.5811769 0.4045648 0.6013055 0.6266286 
##      1540      1542      1547      1549      1550      1552      1556 
## 0.4104086 0.6584448 0.6922089 0.5759825 0.6110452 0.5792290 0.6493544 
##      1559      1571      1572      1573      1577      1578      1582 
## 0.6279272 0.6785734 0.7129868 0.5779304 0.7214278 0.7045457 0.6480558 
##      1591      1598      1599      1600      1601      1605      1606 
## 0.3415818 0.4883257 0.4220961 0.5194925 0.7292195 0.7084416 0.5954618 
##      1609      1615      1617      1619      1622      1624      1628 
## 0.5954618 0.5045584 0.4169017 0.5733852 0.6331217 0.5655935 0.7000006 
##      1629      1634      1636      1637      1640      1641      1647 
## 0.3415818 0.4500164 0.7077923 0.6584448 0.6168890 0.4662492 0.3798910 
##      1649      1650      1651      1661      1663      1666      1667 
## 0.4318358 0.3870334 0.6324724 0.6603927 0.7194799 0.6798720 0.4681971 
##      1668      1673      1674      1676      1681      1690      1692 
## 0.5662428 0.6240314 0.6194862 0.5220898 0.3013246 0.6435107 0.5707880 
##      1694      1698      1699      1701      1702      1703      1704 
## 0.5324787 0.4857285 0.5941631 0.5785797 0.5766318 0.3019739 0.5584511 
##      1714      1727      1731      1733      1734      1741      1743 
## 0.7006499 0.6415627 0.3539186 0.6616913 0.7694767 0.6370176 0.5162460 
##      1747      1749      1751      1753      1754      1755      1756 
## 0.6103959 0.6103959 0.5948124 0.3519707 0.3733979 0.5513087 0.5766318 
##      1757      1759      1760      1762      1763      1764      1767 
## 0.6285765 0.6506531 0.3331407 0.6285765 0.6207848 0.5454649 0.5610484 
##      1769      1770      1776      1780      1783      1785      1792 
## 0.5740345 0.5681908 0.5084543 0.5941631 0.6331217 0.6201355 0.5552046 
##      1795      1796      1799      1802      1805      1808      1812 
## 0.6084479 0.6201355 0.4818326 0.5935138 0.5688401 0.5065064 0.4714436 
##      1818      1820      1823      1824      1825      1826      1828 
## 0.6084479 0.5441663 0.5948124 0.7564905 0.6448093 0.3798910 0.5240377 
##      1829      1830      1831      1841      1844      1846      1847 
## 0.4681971 0.5584511 0.6311738 0.6201355 0.6240314 0.5811769 0.6805213 
##      1849      1854      1856      1860      1862      1868      1871 
## 0.6071493 0.6071493 0.6103959 0.6039028 0.6850665 0.5811769 0.6071493 
##      1879      1882      1883      1884      1887      1888      1891 
## 0.5785797 0.6201355 0.5811769 0.5318294 0.3617104 0.5188432 0.5454649 
##      1899      1909      1911      1918      1919      1921      1926 
## 0.5610484 0.3967731 0.6201355 0.4506657 0.6227327 0.5694894 0.5552046 
##      1927      1930      1935      1937      1939      1944      1947 
## 0.5305308 0.5948124 0.5863714 0.5552046 0.6500037 0.5104022 0.6201355 
##      1948      1949      1950      1951      1952      1953      1955 
## 0.5259856 0.5831249 0.4370302 0.6162397 0.5578018 0.6597434 0.6058507 
##      1958      1965      1968      1970      1977      1985      1988 
## 0.6331217 0.5941631 0.7097402 0.6071493 0.6474065 0.6844171 0.5110515 
##      1990      1991      1992      1993      1996      2000      2003 
## 0.5629963 0.6344203 0.7402578 0.5487115 0.5448156 0.7824629 0.6077986 
##      2005      2007      2010      2015      2018      2019      2022 
## 0.7149347 0.5746838 0.6019548 0.6175383 0.5941631 0.6201355 0.5941631 
##      2025      2027      2030      2031      2036      2037      2049 
## 0.5584511 0.6142917 0.6357189 0.5065064 0.5909166 0.5928645 0.5707880 
##      2055      2060      2064      2067      2071      2075      2076 
## 0.6019548 0.5376732 0.6461079 0.6370176 0.6331217 0.5188432 0.5428677 
##      2077      2078      2084      2085      2087      2093      2096 
## 0.4428740 0.5584511 0.4798847 0.5935138 0.5785797 0.5201419 0.4714436 
##      2101      2105      2110      2111      2112      2117      2118 
## 0.6331217 0.5811769 0.5850728 0.5941631 0.5681908 0.3162587 0.5584511 
##      2120      2121      2122      2128      2141      2142      2143 
## 0.5526073 0.5350760 0.5993576 0.5402704 0.5454649 0.5435170 0.5779304 
##      2144      2145      2150      2151      2155      2156      2157 
## 0.6805213 0.6065000 0.6331217 0.5941631 0.5831249 0.4967667 0.5876700 
##      2158      2159      2162      2164      2167      2169      2173 
## 0.5850728 0.5753332 0.5948124 0.5681908 0.6201355 0.5941631 0.5461142 
##      2174      2179      2185      2192      2193      2196      2202 
## 0.5318294 0.6071493 0.6461079 0.6266286 0.5740345 0.6201355 0.3383352 
##      2205      2215      2216      2217      2227      2238      2241 
## 0.6597434 0.5591004 0.6493544 0.6201355 0.6513024 0.7499974 0.6590941 
##      2243      2254      2259      2260      2261      2263      2264 
## 0.6746775 0.5500101 0.6629899 0.7110388 0.6065000 0.6623406 0.5597497 
##      2271      2273      2279      2280      2287      2294      2296 
## 0.6980526 0.6870144 0.5909166 0.6428613 0.5175446 0.3078177 0.5733852 
##      2298      2300      2301      2302      2305      2307      2309 
## 0.6097466 0.6103959 0.4870271 0.6039028 0.6922089 0.5402704 0.7285702 
##      2311      2312      2316      2319      2326      2331      2333 
## 0.4019675 0.5759825 0.4883257 0.6396148 0.6688337 0.6623406 0.5013119 
##      2335      2339      2353      2357      2360      2373      2393 
## 0.5876700 0.6370176 0.5668921 0.5194925 0.5850728 0.4039155 0.5714373 
##      2403      2407      2409      2412      2416      2417      2422 
## 0.5000133 0.3870334 0.3214532 0.7097402 0.3746965 0.3526200 0.4740409 
##      2425      2426      2427      2430      2431      2434      2437 
## 0.5714373 0.6233821 0.5422184 0.5227391 0.6461079 0.6298752 0.5681908 
##      2440      2442      2445      2450      2455      2462      2468 
## 0.6915596 0.6039028 0.7097402 0.5792290 0.4617040 0.3714500 0.5311801 
##      2469      2474      2481      2486      2487      2489      2496 
## 0.5480622 0.6123438 0.4123565 0.6824692 0.5805276 0.6590941 0.5636456 
##      2503      2504      2517      2520      2521      2526      2527 
## 0.5844235 0.7305181 0.5798783 0.6194862 0.6714310 0.6538996 0.5506594 
##      2535      2537      2541      2542      2543      2548      2552 
## 0.4032662 0.6006562 0.5818263 0.6655872 0.6857158 0.5915659 0.6564968 
##      2553      2561      2563      2565      2571      2572      2576 
## 0.5350760 0.3850855 0.5883193 0.4707943 0.5837742 0.6688337 0.6538996 
##      2581      2582      2583      2587      2590      2594      2597 
## 0.5441663 0.4701450 0.6065000 0.5675414 0.5571525 0.6383162 0.7064937 
##      2598      2599      2600      2601      2602      2603      2604 
## 0.6383162 0.6948061 0.5629963 0.4402768 0.5194925 0.4617040 0.5013119 
##      2605      2606      2607      2609      2610      2611      2612 
## 0.5623470 0.5902673 0.6662365 0.5902673 0.4831312 0.5474129 0.5707880 
##      2613      2615      2617      2618      2621      2624      2642 
## 0.5578018 0.5649442 0.6298752 0.6065000 0.5578018 0.5071557 0.3649569 
##      2644      2646      2647      2658      2664      2666      2668 
## 0.6077986 0.3539186 0.5922152 0.4831312 0.5305308 0.6513024 0.6266286 
##      2675      2677      2686      2691      2692      2694      2696 
## 0.6461079 0.6103959 0.7740219 0.4078113 0.3318421 0.6032535 0.7136361 
##      2697      2700      2702      2704      2710      2714      2720 
## 0.4805340 0.6967540 0.6136424 0.7071430 0.5642949 0.7512960 0.8084353 
##      2721      2722      2726      2728      2734      2735      2738 
## 0.7727232 0.6759761 0.6363682 0.6513024 0.6162397 0.6902609 0.6850665 
##      2739      2740      2741      2742      2743      2744      2745 
## 0.5026105 0.4136551 0.5753332 0.5987083 0.7006499 0.5513087 0.4623533 
##      2746      2747      2749      2750      2751      2752      2755 
## 0.6766254 0.5324787 0.6980526 0.6720803 0.6603927 0.6675351 0.5935138 
##      2758      2763      2764      2770      2782      2788      2791 
## 0.6376669 0.7954491 0.5603990 0.6655872 0.5396211 0.6259793 0.7181812 
##      2792      2795      2799      2803      2805      2807      2810 
## 0.6039028 0.6545489 0.5110515 0.5941631 0.6039028 0.5681908 0.5668921 
##      2814      2817      2822      2828      2830      2833      2836 
## 0.6616913 0.6136424 0.5941631 0.6519517 0.5954618 0.5714373 0.6077986 
##      2839      2844      2848      2849      2852      2855      2856 
## 0.6188369 0.5616977 0.3831376 0.5052077 0.7538933 0.6610420 0.6467572 
##      2858      2862      2865      2868      2871      2876      2877 
## 0.5194925 0.6720803 0.5954618 0.6175383 0.5980590 0.5006626 0.6428613 
##      2884      2888      2893      2894      2902      2911      2913 
## 0.6039028 0.6850665 0.6090973 0.6240314 0.5513087 0.5941631 0.4110579 
##      2915      2922      2923      2924      2931      2935      2936 
## 0.6487051 0.6590941 0.5974097 0.5584511 0.4707943 0.6071493 0.5896180 
##      2937      2938      2940      2948      2951      2954      2956 
## 0.5967604 0.6233821 0.6207848 0.6675351 0.4000196 0.6233821 0.5097529 
##      2966      2971      2976      2981      3000      3005      3016 
## 0.4370302 0.5578018 0.5655935 0.4448220 0.5078050 0.6065000 0.6175383 
##      3019      3022      3023      3026      3029      3031      3033 
## 0.5987083 0.7986956 0.6461079 0.4779367 0.5532566 0.6363682 0.7272716 
##      3034      3041      3044      3049      3054      3058      3060 
## 0.6272779 0.6331217 0.6233821 0.6655872 0.6207848 0.6720803 0.5441663 
##      3062      3063      3065      3067      3068      3071      3074 
## 0.6850665 0.5376732 0.5155967 0.5194925 0.5039091 0.6201355 0.7240250 
##      3078      3081      3082      3083      3086      3104      3107 
## 0.6013055 0.6461079 0.6389655 0.6201355 0.4344330 0.6026042 0.6603927 
##      3110      3115      3123      3126      3128      3130      3131 
## 0.5740345 0.5727359 0.5961111 0.6350696 0.5980590 0.5539059 0.5513087 
##      3133      3140      3141      3142      3147      3152      3156 
## 0.5681908 0.6071493 0.5000133 0.3779431 0.6077986 0.6162397 0.4909229 
##      3157      3162      3167      3169      3171      3179      3181 
## 0.6259793 0.6915596 0.5162460 0.6052014 0.6461079 0.6240314 0.5584511 
##      3184      3186      3187      3192      3193      3195      3196 
## 0.6461079 0.4233947 0.4207975 0.6935075 0.6694830 0.6649379 0.3435297 
##      3197      3200      3204      3210      3214      3217      3218 
## 0.6233821 0.6474065 0.6733789 0.6331217 0.5058570 0.5331280 0.6564968 
##      3219      3220      3221      3240      3241      3247      3250 
## 0.6019548 0.6733789 0.5402704 0.6026042 0.5798783 0.6519517 0.3526200 
##      3252      3255      3256      3262      3265      3266      3267 
## 0.6753268 0.6513024 0.6538996 0.6779241 0.6526010 0.6746775 0.6305245 
##      3269      3270      3278      3282      3283      3284      3288 
## 0.4318358 0.6292258 0.4149537 0.7162333 0.6610420 0.6214341 0.5987083 
##      3289      3290      3291      3295      3297      3298      3301 
## 0.7837615 0.6590941 0.6071493 0.5454649 0.6188369 0.5785797 0.6123438 
##      3302      3305      3313      3316      3317      3318      3319 
## 0.6831185 0.7220771 0.5915659 0.6435107 0.7012992 0.6500037 0.6532503 
##      3320      3321      3322      3323      3324      3325      3326 
## 0.6246807 0.6259793 0.6564968 0.6441600 0.6110452 0.6474065 0.6753268 
##      3327      3328      3329      3330      3331      3332      3333 
## 0.6824692 0.6616913 0.4993640 0.6480558 0.6603927 0.6584448 0.6922089 
##      3334      3344      3345      3346      3347      3349      3351 
## 0.6129931 0.3331407 0.5785797 0.6227327 0.6311738 0.5168953 0.6363682 
##      3352      3353      3354      3355      3362      3366      3371 
## 0.6194862 0.6175383 0.4480685 0.7038964 0.6298752 0.6720803 0.5935138 
##      3373      3374      3376      3379      3384      3385      3392 
## 0.6311738 0.6052014 0.6045521 0.5454649 0.6389655 0.6272779 0.3454776 
##      3395      3396      3405      3406      3408      3412      3414 
## 0.5454649 0.6461079 0.6649379 0.7564905 0.4233947 0.6214341 0.5753332 
##      3417      3420      3421      3422      3424      3428      3435 
## 0.5909166 0.6116945 0.5974097 0.6422120 0.5941631 0.3441790 0.6798720 
##      3437      3438      3446      3447      3450      3453      3456 
## 0.5766318 0.4617040 0.6019548 0.6285765 0.5928645 0.5376732 0.5792290 
##      3457      3458      3460      3461      3462      3463      3465 
## 0.7525946 0.4571588 0.6318231 0.6039028 0.6052014 0.5974097 0.6162397 
##      3468      3474      3475      3480      3481      3484      3485 
## 0.6701323 0.6681844 0.6136424 0.6623406 0.5279336 0.5681908 0.6461079 
##      3486      3487      3488      3489      3490      3491      3492 
## 0.6701323 0.4857285 0.7077923 0.7551919 0.6805213 0.7733725 0.6292258 
##      3493      3494      3496      3504      3505      3507      3509 
## 0.7499974 0.6610420 0.7110388 0.5922152 0.5006626 0.5214405 0.6584448 
##      3511      3512      3517      3521      3523      3525      3526 
## 0.6097466 0.5980590 0.6331217 0.6103959 0.6396148 0.5091036 0.5824756 
##      3528      3533      3536      3539      3540      3541      3542 
## 0.6084479 0.5980590 0.5467635 0.6201355 0.5552046 0.5123501 0.6720803 
##      3543      3544      3546      3548      3552      3553      3557 
## 0.5844235 0.5727359 0.5584511 0.6850665 0.5980590 0.5129995 0.6071493 
##      3562      3564      3567      3572      3574      3577      3578 
## 0.6616913 0.5506594 0.7285702 0.6045521 0.5993576 0.7811643 0.7986956 
##      3579      3580      3583      3587      3589      3591      3593 
## 0.5772811 0.5909166 0.5948124 0.6103959 0.6077986 0.6058507 0.5636456 
##      3601      3605      3607      3621      3622      3623      3624 
## 0.5941631 0.4344330 0.6850665 0.6253300 0.5694894 0.4980653 0.5941631 
##      3628      3629      3630      3632      3633      3635      3641 
## 0.5584511 0.6513024 0.5837742 0.6331217 0.5162460 0.3143108 0.5675414 
##      3645      3649      3656      3668      3671      3674      3675 
## 0.6422120 0.5233884 0.4792354 0.6129931 0.6461079 0.5779304 0.6292258 
##      3678      3681      3682      3683      3696      3699      3700 
## 0.4896243 0.6577955 0.6935075 0.6857158 0.6026042 0.5915659 0.5980590 
##      3702      3704      3706      3707      3708      3717      3722 
## 0.6954554 0.5363746 0.6422120 0.7474002 0.6506531 0.6506531 0.6876637 
##      3724      3727      3729      3731      3735      3746      3754 
## 0.5117008 0.6201355 0.5850728 0.6909102 0.6298752 0.5642949 0.6649379 
##      3755      3759      3760      3763      3766      3768      3769 
## 0.6571461 0.5811769 0.7240250 0.3279463 0.5513087 0.5545553 0.6266286 
##      3772      3774      3780      3784      3785      3786      3787 
## 0.6285765 0.6052014 0.4214468 0.5233884 0.6279272 0.6058507 0.6883130 
##      3789      3790      3798      3799      3800      3801      3802 
## 0.6980526 0.6519517 0.6772747 0.4928709 0.5922152 0.4344330 0.4584575 
##      3804      3806      3809      3810      3811      3813      3814 
## 0.5935138 0.4922215 0.6136424 0.6506531 0.6026042 0.7486988 0.5552046 
##      3816      3817      3818      3830      3832      3838      3839 
## 0.6370176 0.6571461 0.4441727 0.6616913 0.6461079 0.4383289 0.5552046 
##      3855      3859      3862      3864      3867      3868      3872 
## 0.5857221 0.5831249 0.5415691 0.5474129 0.6480558 0.5292322 0.6649379 
##      3873      3875      3877      3882      3886      3889      3891 
## 0.6675351 0.3805403 0.5922152 0.7246743 0.5026105 0.6766254 0.6870144 
##      3892      3893      3894      3897      3906      3907      3909 
## 0.5902673 0.3844362 0.5837742 0.5279336 0.6298752 0.6246807 0.7227264 
##      3910      3912      3913      3914      3916      3919      3920 
## 0.5279336 0.5629963 0.6272779 0.5733852 0.5272843 0.6006562 0.6233821 
##      3922      3924      3925      3926      3933      3935      3941 
## 0.6279272 0.6402641 0.5526073 0.6259793 0.7136361 0.6220834 0.6474065 
##      3943      3944      3949      3951      3953      3954      3960 
## 0.5707880 0.5707880 0.4078113 0.5701387 0.6305245 0.5902673 0.5902673 
##      3964      3966      3968      3969      3970      3973      3974 
## 0.6616913 0.4870271 0.5584511 0.3948251 0.5214405 0.7324660 0.7720739 
##      3975      3977      3990      3999      4003      4006      4025 
## 0.6324724 0.3701514 0.6409134 0.6538996 0.5987083 0.4922215 0.6149410 
##      4028      4030      4032      4036      4037      4046      4047 
## 0.5519580 0.4772874 0.5896180 0.5357253 0.5078050 0.5779304 0.6071493 
##      4048      4051      4053      4056      4058      4061      4062 
## 0.4707943 0.5552046 0.4169017 0.6331217 0.6220834 0.6876637 0.6740282 
##      4065      4067      4068      4069      4070      4074      4082 
## 0.6344203 0.6272779 0.6357189 0.6493544 0.6915596 0.6129931 0.6629899 
##      4087      4091      4093      4094      4095      4101      4102 
## 0.6272779 0.6642886 0.6493544 0.6376669 0.6233821 0.5818263 0.6058507 
##      4106      4108      4111      4112      4113      4115      4116 
## 0.6720803 0.5941631 0.6246807 0.5681908 0.5591004 0.5688401 0.5954618 
##      4122      4126      4127      4132      4134      4140      4141 
## 0.6597434 0.6590941 0.4837805 0.4688464 0.6720803 0.5714373 0.5565032 
##      4143      4144      4148      4149      4153      4157      4158 
## 0.5454649 0.7435043 0.6461079 0.5688401 0.5941631 0.5552046 0.5941631 
##      4159      4160      4161      4162      4164      4165      4166 
## 0.5324787 0.5753332 0.6071493 0.6331217 0.5941631 0.6201355 0.4409261 
##      4167      4168      4169      4170      4180      4239      4242 
## 0.6201355 0.5681908 0.5941631 0.5941631 0.5500101 0.5915659 0.6181876 
##      4243      4249      4260      4261      4262      4386      4473 
## 0.5311801 0.5045584 0.7590877 0.3246997 0.4883257 0.4487178 0.6603927 
##      4628      4629      4739      4754      4811      5056      5165 
## 0.6207848 0.6402641 0.6266286 0.4818326 0.5649442 0.5370239 0.5117008 
##      5195      5201      5263      5264      5265      5339      5458 
## 0.6181876 0.5883193 0.6240314 0.5941631 0.6259793 0.6162397 0.3182066 
##      5528      5632      5685      5856      5858      5912      6051 
## 0.4896243 0.6065000 0.5714373 0.5214405 0.5727359 0.6065000 0.5584511 
##      6104      6301      6700      6948      7082      7129      7252 
## 0.5441663 0.5539059 0.5707880 0.6006562 0.6071493 0.6162397 0.7000006
reg8 <- lm(PCTFLOAN ~ ADM_RATE, data=data2)
summary(reg8)
## 
## Call:
## lm(formula = PCTFLOAN ~ ADM_RATE, data = data2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.62435 -0.11274  0.03085  0.15665  0.44315 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.51186    0.01603  31.923  < 2e-16 ***
## ADM_RATE     0.11249    0.02219   5.069 4.32e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2168 on 2193 degrees of freedom
##   (5508 observations deleted due to missingness)
## Multiple R-squared:  0.01158,    Adjusted R-squared:  0.01113 
## F-statistic:  25.7 on 1 and 2193 DF,  p-value: 4.324e-07
coefficients(reg8)
## (Intercept)    ADM_RATE 
##   0.5118554   0.1124929
confint(reg8, level=0.95)
##                  2.5 %    97.5 %
## (Intercept) 0.48041193 0.5432989
## ADM_RATE    0.06897642 0.1560094
lm.beta(reg8)
##  ADM_RATE 
## 0.1076242
fitted(reg8)
##         1         2         4         5         6         9        10 
## 0.5709817 0.6082506 0.6041334 0.5717691 0.5692831 0.6020410 0.6057533 
##        11        13        23        24        25        27        31 
## 0.5719154 0.5717916 0.6243483 0.5775400 0.6243483 0.6055170 0.5852570 
##        33        35        37        38        40        42        47 
## 0.5928391 0.5809148 0.5776300 0.5954377 0.5882156 0.5657058 0.5788337 
##        51        52        53        54        57        58        65 
## 0.6056183 0.5700930 0.6243483 0.5782375 0.5615098 0.5672244 0.5591812 
##        76        77        78        83        85        96        99 
## 0.6232684 0.6243483 0.6243483 0.6067207 0.5957976 0.6020297 0.5766176 
##       103       104       108       116       123       129       135 
## 0.6171263 0.6152477 0.6029634 0.5891718 0.5756727 0.5785412 0.5809486 
##       138       139       141       142       145       147       148 
## 0.5816460 0.5553677 0.5932890 0.6088918 0.5810836 0.6178912 0.5759426 
##       157       158       159       162       172       175       176 
## 0.6233584 0.5824785 0.6050221 0.5903530 0.5912867 0.6118841 0.5813873 
##       187       189       192       194       200       208       211 
## 0.5911517 0.5921979 0.5751777 0.6085881 0.5345340 0.6028622 0.6039084 
##       215       216       217       224       225       227       228 
## 0.5870682 0.5966751 0.6233584 0.6014785 0.5835022 0.5217885 0.5804424 
##       229       230       231       232       233       234       235 
## 0.5466045 0.5552214 0.5912754 0.5936603 0.6068557 0.5702055 0.5916804 
##       236       237       238       239       240       241       242 
## 0.5594849 0.5786762 0.5618810 0.5909492 0.5517454 0.5805548 0.5713192 
##       243       244       245       246       247       248       249 
## 0.5935815 0.5298768 0.5572688 0.5539503 0.5327341 0.5774275 0.5493043 
##       251       252       258       259       264       275       276 
## 0.5527353 0.5745365 0.5393262 0.5868882 0.6102867 0.5647721 0.6243483 
##       277       278       284       288       293       308       319 
## 0.6086893 0.5742890 0.5239709 0.5611273 0.6001511 0.6028847 0.5701043 
##       320       321       331       337       344       351       353 
## 0.5724666 0.5861457 0.5867982 0.6243483 0.5278857 0.5760439 0.5979687 
##       360       361       362       365       367       369       370 
## 0.6181387 0.6173963 0.6128741 0.5584950 0.5864720 0.5642321 0.5776300 
##       378       387       393       400       408       411       423 
## 0.5575725 0.5972150 0.5711504 0.6102305 0.5625447 0.5975075 0.5999374 
##       426       435       438       439       440       441       442 
## 0.6181612 0.6220985 0.6243483 0.6243483 0.6243483 0.5992737 0.5591474 
##       446       448       449       455       456       461       462 
## 0.5866407 0.5467282 0.6243483 0.5652221 0.5736140 0.5517454 0.5265020 
##       464       465       472       489       490       491       492 
## 0.5900717 0.5255683 0.5940765 0.5506430 0.5638834 0.6188137 0.5537815 
##       493       495       499       501       507       511       514 
## 0.5860670 0.5794074 0.5971363 0.5791824 0.5673707 0.5438034 0.6243483 
##       520       525       527       531       532       536       537 
## 0.5763814 0.5972938 0.6018723 0.5771013 0.6243483 0.6027384 0.5321266 
##       541       545       547       557       559       560       565 
## 0.6048871 0.6243483 0.6243483 0.6194549 0.6011298 0.5814660 0.5939415 
##       568       571       573       574       576       577       578 
## 0.5853020 0.6034359 0.5939640 0.6157989 0.6065295 0.6179587 0.5319917 
##       579       583       585       596       598       605       606 
## 0.5762014 0.5528816 0.6023897 0.5979013 0.6140215 0.6044033 0.5850996 
##       608       613       620       622       623       629       636 
## 0.5906680 0.5915904 0.6198936 0.6243483 0.6162263 0.6214348 0.5801611 
##       637       640       643       646       647       653       660 
## 0.5798461 0.5541528 0.5680569 0.5828385 0.5923216 0.5929966 0.5906455 
##       664       671       673       674       675       677       678 
## 0.6028172 0.6098030 0.5859995 0.5761451 0.6018160 0.5551202 0.5923329 
##       681       683       684       686       692       693       694 
## 0.5490231 0.5387525 0.5568863 0.5189425 0.5610598 0.5881594 0.5691706 
##       696       698       699       702       703       704       705 
## 0.5756389 0.5634222 0.5949989 0.5853358 0.5611161 0.5313729 0.5663132 
##       708       709       714       715       717       718       724 
## 0.6243483 0.6140552 0.5743565 0.5637259 0.5835247 0.5960789 0.5515542 
##       726       727       730       734       736       737       738 
## 0.5515992 0.5676632 0.5815110 0.5936828 0.5714204 0.5940427 0.5669207 
##       739       741       742       743       744       745       746 
## 0.5861345 0.5657170 0.5980137 0.6243483 0.6243483 0.6243483 0.6243483 
##       747       749       751       754       755       758       774 
## 0.5811173 0.5712292 0.5349615 0.5622635 0.5741652 0.5631634 0.6002186 
##       775       777       787       796       799       805       806 
## 0.5749302 0.5666170 0.5667295 0.5548052 0.5932665 0.5799924 0.5566164 
##       807       811       820       822       824       832       835 
## 0.5667632 0.6190274 0.6077219 0.5763026 0.5930303 0.6243483 0.5716567 
##       836       838       839       846       849       853       855 
## 0.6073619 0.5807461 0.5612848 0.5702167 0.5834909 0.5411036 0.5687318 
##       857       862       863       868       869       870       874 
## 0.5587312 0.5987674 0.5880356 0.5650533 0.5639509 0.5883844 0.5702280 
##       878       883       885       887       888       891       894 
## 0.6071032 0.5802849 0.5971363 0.6018498 0.6157426 0.5596087 0.5739740 
##       896       901       902       904       906       907       908 
## 0.6205686 0.5671119 0.5420260 0.5390675 0.5494056 0.5901955 0.5976200 
##       909       910       911       912       918       919       921 
## 0.5828385 0.5787212 0.5745365 0.5662907 0.5719829 0.5740078 0.5760889 
##       923       924       925       929       930       931       932 
## 0.6243483 0.5869107 0.6063832 0.5998586 0.5363901 0.5765951 0.5493493 
##       933       935       936       937       940       941       943 
## 0.6131215 0.5867195 0.5991837 0.5897230 0.5726016 0.6007923 0.5796549 
##       944       945       947       949       950       952       953 
## 0.5535340 0.6202198 0.5727591 0.5665382 0.5684281 0.6081719 0.5921079 
##       954       956       962       965       967       968       969 
## 0.6005223 0.5814098 0.6133690 0.5916129 0.5681019 0.6161926 0.5984750 
##       972       973       974       975       979       981       987 
## 0.5877656 0.6163613 0.6232684 0.5966863 0.5850546 0.6239209 0.5896443 
##       988       989       994       997      1011      1013      1021 
## 0.5721629 0.6030872 0.5850883 0.5841884 0.5455583 0.5217098 0.6114454 
##      1022      1027      1031      1033      1034      1036      1039 
## 0.5724329 0.5904655 0.5678319 0.5880244 0.5843909 0.5868544 0.6177000 
##      1040      1041      1046      1049      1050      1052      1053 
## 0.6243483 0.5744915 0.6162938 0.5956401 0.5986662 0.5782712 0.5798349 
##      1055      1057      1059      1067      1070      1072      1075 
## 0.5727478 0.5687768 0.5949652 0.5941102 0.6057983 0.5886206 0.5739515 
##      1080      1081      1082      1085      1087      1091      1094 
## 0.5814998 0.5653796 0.5751214 0.5831084 0.5761339 0.6000161 0.5806448 
##      1096      1097      1098      1099      1100      1105      1108 
## 0.5611948 0.6108492 0.5824222 0.5895430 0.5929291 0.6214685 0.5791712 
##      1109      1111      1112      1113      1114      1117      1122 
## 0.5732878 0.5691031 0.6170700 0.5266032 0.5766626 0.5956514 0.6118954 
##      1127      1130      1131      1132      1135      1137      1138 
## 0.5392250 0.5735015 0.5991949 0.5801049 0.5687318 0.5676969 0.5811286 
##      1141      1145      1150      1151      1152      1153      1156 
## 0.5538265 0.5883506 0.6035709 0.6096793 0.6243483 0.6243483 0.6133465 
##      1157      1160      1163      1164      1167      1169      1170 
## 0.6243483 0.5974513 0.5901955 0.5896443 0.5736253 0.5792162 0.5911967 
##      1171      1172      1177      1180      1181      1182      1183 
## 0.5888681 0.5498555 0.5755264 0.5844359 0.6051683 0.5897230 0.5726016 
##      1184      1187      1189      1191      1193      1194      1195 
## 0.6019847 0.5843796 0.6166538 0.6210973 0.6140777 0.5911517 0.6243483 
##      1196      1197      1198      1199      1200      1201      1202 
## 0.5866407 0.5912417 0.5921079 0.6047071 0.5875182 0.5943465 0.5974513 
##      1203      1204      1205      1206      1207      1208      1209 
## 0.5982275 0.6022097 0.5835809 0.6000386 0.5689568 0.6010173 0.5977325 
##      1210      1211      1218      1219      1220      1228      1229 
## 0.6174525 0.5568526 0.5954152 0.5753464 0.6187799 0.5356364 0.5737715 
##      1231      1232      1235      1237      1238      1239      1240 
## 0.5789912 0.5934240 0.5779900 0.6208161 0.5865620 0.6243483 0.6056070 
##      1243      1244      1245      1246      1249      1250      1251 
## 0.5846496 0.6108829 0.5973388 0.6045046 0.5905780 0.5118554 0.5784737 
##      1252      1253      1257      1258      1259      1260      1263 
## 0.5812523 0.5882269 0.5893630 0.5911517 0.5740640 0.5946840 0.6141227 
##      1264      1265      1266      1268      1270      1272      1273 
## 0.5939640 0.5897680 0.5994649 0.5565826 0.5875969 0.5679219 0.6228859 
##      1274      1286      1287      1289      1295      1296      1297 
## 0.5433647 0.6096230 0.5580563 0.6029184 0.6188699 0.5919054 0.5547152 
##      1299      1300      1301      1304      1305      1310      1312 
## 0.6206023 0.5757739 0.5757851 0.5992849 0.5994087 0.6243483 0.6199274 
##      1313      1316      1322      1323      1324      1328      1330 
## 0.5388537 0.6079806 0.5905330 0.5893068 0.6005336 0.5788900 0.5900717 
##      1332      1333      1334      1339      1340      1348      1350 
## 0.6218510 0.6214798 0.5670894 0.6243483 0.5676857 0.5979013 0.6107254 
##      1351      1352      1355      1362      1365      1366      1368 
## 0.5721179 0.5809036 0.5772138 0.6243483 0.6146964 0.5712629 0.6186449 
##      1369      1370      1374      1375      1376      1380      1382 
## 0.5810048 0.5648058 0.5783275 0.6235384 0.5894643 0.6237521 0.6009386 
##      1384      1388      1389      1390      1393      1395      1396 
## 0.5652896 0.6107704 0.5617685 0.6082394 0.6193199 0.5525441 0.5891381 
##      1400      1401      1404      1405      1407      1412      1413 
## 0.6056745 0.5497205 0.5672807 0.5936603 0.5923666 0.5864157 0.5949539 
##      1416      1427      1428      1429      1430      1431      1434 
## 0.6116929 0.5726016 0.5655033 0.5801611 0.5930866 0.5655595 0.6123003 
##      1435      1439      1440      1441      1443      1448      1459 
## 0.5949427 0.5773488 0.6068332 0.6018048 0.6139090 0.6243483 0.5632759 
##      1462      1463      1465      1466      1476      1484      1486 
## 0.6167888 0.6047971 0.5964838 0.6168338 0.5857295 0.5575163 0.5612961 
##      1492      1493      1495      1499      1501      1502      1503 
## 0.5732203 0.5980587 0.5981037 0.5805436 0.5850096 0.6133803 0.5965288 
##      1504      1505      1506      1509      1510      1511      1521 
## 0.5608686 0.6112654 0.5987225 0.5939528 0.5750539 0.5935253 0.5952802 
##      1524      1525      1526      1528      1530      1531      1534 
## 0.6060457 0.5722079 0.5351415 0.5746265 0.5432972 0.5860895 0.5918379 
##      1535      1537      1538      1540      1542      1546      1547 
## 0.5404511 0.5286281 0.5493493 0.5434097 0.5927941 0.6069682 0.5957864 
##      1549      1550      1552      1555      1556      1559      1560 
## 0.6047408 0.6003086 0.6082394 0.6213448 0.6001961 0.6062932 0.5954152 
##      1561      1571      1572      1573      1577      1578      1582 
## 0.6165863 0.5816460 0.5737940 0.5911629 0.5623872 0.5603624 0.5776750 
##      1584      1588      1591      1592      1594      1598      1599 
## 0.5970013 0.6026260 0.5299443 0.6125028 0.5789349 0.5789124 0.5657733 
##      1600      1601      1605      1606      1607      1609      1614 
## 0.5727816 0.5807798 0.5852570 0.5870794 0.5995324 0.5674944 0.5733778 
##      1615      1617      1619      1622      1623      1624      1628 
## 0.6005786 0.6096793 0.5784625 0.5819498 0.5744690 0.5974963 0.5878669 
##      1629      1631      1632      1633      1634      1636      1637 
## 0.5274244 0.5991162 0.6070469 0.6033122 0.5414523 0.5949989 0.5827822 
##      1638      1640      1641      1642      1647      1648      1649 
## 0.5685631 0.5821297 0.5637259 0.5572801 0.5500018 0.5557727 0.5506767 
##      1650      1651      1653      1658      1659      1661      1663 
## 0.5514754 0.6010736 0.5651433 0.6136390 0.5726353 0.6095893 0.5890931 
##      1664      1666      1667      1668      1669      1672      1673 
## 0.5438934 0.5713304 0.5671794 0.5898130 0.5941440 0.5856170 0.5931990 
##      1674      1676      1680      1681      1685      1690      1692 
## 0.5818935 0.6112654 0.5868207 0.5185600 0.5606099 0.5977100 0.5922766 
##      1694      1698      1699      1701      1702      1703      1704 
## 0.5816123 0.5809148 0.5914667 0.6063607 0.5939078 0.5207199 0.5811511 
##      1709      1713      1714      1717      1720      1724      1725 
## 0.5993412 0.5733890 0.5889018 0.6134928 0.5446359 0.6176550 0.5908929 
##      1726      1727      1731      1733      1734      1738      1741 
## 0.5976650 0.5931541 0.5481006 0.6006911 0.5881706 0.5972488 0.5912417 
##      1743      1744      1745      1746      1747      1749      1750 
## 0.5705317 0.6124128 0.5593387 0.5920066 0.5915792 0.5982725 0.5984300 
##      1751      1753      1754      1755      1756      1757      1758 
## 0.6062482 0.5312492 0.5457270 0.6048196 0.6020185 0.5957301 0.5901842 
##      1759      1760      1761      1762      1763      1764      1767 
## 0.6103092 0.5335891 0.5611048 0.5808136 0.5814773 0.5802399 0.5928278 
##      1769      1770      1776      1780      1783      1785      1786 
## 0.5533428 0.5850771 0.5941327 0.5897793 0.6010511 0.5631634 0.6169013 
##      1791      1792      1795      1796      1797      1799      1801 
## 0.6238084 0.5895430 0.5893293 0.6000724 0.5922091 0.5924453 0.5922091 
##      1802      1805      1808      1809      1812      1818      1820 
## 0.5892955 0.6023335 0.5989362 0.6164288 0.5902067 0.6143252 0.5764489 
##      1823      1824      1825      1826      1828      1829      1830 
## 0.5777650 0.5663245 0.5575163 0.5481231 0.5862020 0.5967876 0.5823547 
##      1831      1841      1844      1846      1847      1849      1853 
## 0.6003198 0.5929516 0.5900042 0.5872257 0.5809598 0.5913317 0.5761339 
##      1854      1856      1860      1862      1868      1871      1879 
## 0.6018048 0.5953702 0.5868207 0.5629835 0.5988462 0.6064170 0.5883731 
##      1882      1883      1884      1887      1888      1889      1891 
## 0.6170700 0.5992399 0.6192074 0.5374701 0.5841659 0.5717467 0.6213335 
##      1898      1899      1909      1911      1917      1918      1919 
## 0.5805548 0.5901392 0.5527466 0.5867532 0.6243483 0.5628710 0.5928053 
##      1921      1923      1925      1926      1927      1930      1935 
## 0.5843121 0.6243483 0.6134590 0.5982275 0.5833897 0.6065632 0.6144490 
##      1937      1939      1944      1947      1948      1949      1950 
## 0.5900830 0.5868544 0.6043021 0.6043133 0.6004548 0.5953702 0.5695418 
##      1951      1952      1953      1955      1958      1962      1965 
## 0.5438034 0.5863032 0.6092968 0.5874619 0.5871582 0.5933003 0.5827710 
##      1968      1969      1970      1977      1985      1988      1990 
## 0.6000949 0.5925016 0.5737603 0.6157314 0.5911292 0.5761789 0.6032222 
##      1991      1992      1993      1996      2000      2003      2005 
## 0.6171600 0.5302255 0.5827710 0.5917479 0.5555589 0.5869332 0.5571901 
##      2007      2010      2011      2014      2015      2017      2018 
## 0.5685744 0.5703292 0.5815560 0.5732203 0.6243483 0.5595524 0.5799474 
##      2019      2020      2022      2023      2025      2027      2030 
## 0.5995436 0.5980475 0.6243483 0.6184312 0.6243483 0.5913092 0.5767863 
##      2031      2036      2037      2041      2049      2050      2053 
## 0.5955614 0.5844471 0.6137853 0.5806786 0.5793174 0.6243483 0.6243483 
##      2055      2059      2060      2064      2067      2071      2072 
## 0.5713417 0.6243483 0.5929066 0.5977550 0.5796099 0.6198486 0.6243483 
##      2073      2075      2076      2077      2078      2084      2085 
## 0.5611048 0.5992287 0.5841434 0.6084306 0.5971026 0.5956401 0.5980025 
##      2087      2088      2089      2093      2094      2096      2101 
## 0.5212036 0.5868095 0.6243483 0.5984075 0.5853470 0.5805661 0.6168451 
##      2105      2110      2111      2112      2117      2118      2120 
## 0.5814323 0.5721516 0.6072269 0.6075081 0.5311255 0.5929178 0.5864832 
##      2121      2122      2128      2136      2141      2142      2143 
## 0.5825347 0.5976875 0.5765726 0.5857745 0.6139427 0.6061807 0.6161589 
##      2144      2145      2150      2151      2155      2156      2157 
## 0.6243483 0.5834122 0.5808586 0.5763139 0.5980362 0.5936040 0.6011185 
##      2158      2159      2162      2164      2167      2169      2173 
## 0.5620498 0.5902067 0.6064732 0.6047858 0.5795537 0.6001624 0.5997574 
##      2174      2177      2179      2185      2192      2193      2196 
## 0.5904767 0.5713079 0.5705092 0.5577075 0.6096005 0.6062145 0.5858083 
##      2199      2201      2202      2205      2209      2211      2213 
## 0.6137290 0.5826022 0.5247921 0.6066869 0.6243483 0.6195449 0.6065857 
##      2215      2216      2217      2218      2227      2228      2229 
## 0.6018723 0.6002636 0.5906905 0.5964501 0.5822310 0.5974513 0.5493493 
##      2231      2232      2238      2241      2243      2254      2255 
## 0.5973500 0.5429035 0.5831759 0.5837721 0.6039984 0.5907917 0.6118504 
##      2259      2260      2261      2263      2264      2268      2269 
## 0.6019735 0.6065295 0.6026934 0.5884181 0.5608686 0.5467620 0.5118554 
##      2271      2272      2273      2279      2280      2282      2283 
## 0.5980137 0.6195899 0.5910054 0.5953139 0.5870344 0.5868544 0.5637597 
##      2287      2294      2295      2296      2298      2300      2301 
## 0.5831647 0.5202249 0.6078906 0.5718366 0.5916241 0.5797786 0.5799136 
##      2302      2305      2307      2309      2311      2312      2313 
## 0.5824447 0.5758639 0.5968326 0.5766401 0.5611048 0.5846946 0.6243483 
##      2316      2319      2326      2328      2331      2333      2335 
## 0.5669432 0.5957526 0.5827935 0.6243483 0.5567288 0.5527916 0.5629047 
##      2339      2344      2352      2353      2357      2360      2362 
## 0.5901505 0.6243483 0.5959776 0.5933228 0.5876756 0.5899705 0.5718479 
##      2363      2365      2366      2368      2369      2372      2373 
## 0.5831872 0.5904092 0.5378188 0.5922091 0.6214685 0.5620385 0.5385950 
##      2376      2377      2378      2393      2397      2398      2402 
## 0.6243483 0.6243483 0.5323066 0.6021085 0.5975750 0.6243483 0.6099830 
##      2403      2407      2408      2409      2412      2416      2417 
## 0.5817585 0.5413736 0.5710154 0.5196737 0.5959664 0.5287969 0.5278182 
##      2420      2421      2422      2425      2426      2427      2430 
## 0.5404511 0.5835022 0.5432409 0.5515992 0.6179025 0.5546702 0.5508567 
##      2431      2434      2435      2436      2437      2440      2442 
## 0.5538265 0.5443771 0.6152814 0.5937278 0.5566501 0.5536240 0.5892393 
##      2443      2444      2445      2446      2448      2450      2452 
## 0.5736140 0.6243483 0.5825122 0.6000049 0.5587312 0.6043358 0.5616673 
##      2454      2455      2462      2463      2466      2467      2468 
## 0.5749864 0.5659870 0.5414973 0.6126041 0.6025585 0.5653233 0.5811623 
##      2469      2474      2477      2479      2481      2482      2485 
## 0.6173850 0.6093868 0.5783500 0.6173175 0.5814435 0.5213386 0.6050671 
##      2486      2487      2488      2489      2494      2496      2497 
## 0.5953364 0.5860445 0.6089706 0.6052470 0.6243483 0.5867082 0.5622747 
##      2498      2499      2500      2501      2503      2504      2505 
## 0.5949427 0.5512279 0.6243483 0.5551764 0.5945377 0.5814885 0.6243483 
##      2507      2508      2509      2510      2511      2514      2517 
## 0.5927266 0.5906005 0.6243483 0.6165863 0.5443771 0.6193536 0.5966751 
##      2518      2520      2521      2524      2525      2526      2527 
## 0.5571563 0.6115466 0.6189599 0.5911517 0.5841771 0.5551989 0.5859883 
##      2535      2537      2541      2542      2543      2544      2548 
## 0.5517342 0.5859433 0.5838846 0.5630509 0.6236284 0.6243483 0.6074631 
##      2549      2551      2552      2553      2555      2557      2558 
## 0.6225822 0.5458170 0.5656158 0.5714654 0.6243483 0.5912642 0.6243483 
##      2560      2561      2563      2565      2566      2569      2571 
## 0.6187237 0.5540403 0.5891943 0.5765051 0.5528141 0.5735128 0.5910842 
##      2572      2573      2574      2575      2576      2577      2578 
## 0.5985200 0.5906005 0.5654470 0.5976763 0.6027722 0.6243483 0.5716342 
##      2580      2581      2582      2583      2586      2587      2590 
## 0.6093530 0.5859433 0.5538603 0.5914217 0.5816798 0.5882494 0.5821860 
##      2594      2595      2596      2597      2598      2599      2600 
## 0.5728716 0.6026035 0.5885643 0.5943577 0.5643334 0.5750652 0.5746715 
##      2601      2602      2603      2604      2605      2606      2607 
## 0.5614198 0.5768876 0.5583600 0.5693731 0.5749639 0.5669207 0.5810948 
##      2608      2609      2610      2611      2612      2613      2614 
## 0.5669320 0.5717242 0.5783725 0.5590237 0.5679669 0.5662682 0.5878781 
##      2615      2617      2618      2620      2621      2624      2625 
## 0.5577750 0.5819948 0.5656945 0.6031097 0.5710829 0.5717354 0.6243483 
##      2626      2630      2631      2632      2636      2640      2642 
## 0.6243483 0.6243483 0.5453558 0.5770451 0.5581125 0.6035709 0.5383363 
##      2643      2644      2645      2646      2647      2648      2651 
## 0.6016698 0.5982162 0.5930528 0.5489668 0.5755152 0.6011185 0.6150789 
##      2653      2654      2655      2657      2658      2659      2660 
## 0.6243483 0.6243483 0.6243483 0.6055958 0.6038746 0.6243483 0.6243483 
##      2664      2666      2668      2669      2672      2675      2677 
## 0.5823435 0.5551202 0.5897343 0.6151127 0.5604636 0.6121204 0.5884181 
##      2679      2681      2686      2691      2692      2694      2696 
## 0.6177338 0.5522404 0.5791374 0.5362326 0.5246909 0.5987899 0.5669770 
##      2697      2700      2702      2704      2705      2710      2713 
## 0.5725229 0.5684619 0.5873607 0.5940990 0.5818035 0.6020635 0.6053145 
##      2714      2716      2718      2720      2721      2722      2726 
## 0.5593837 0.5815560 0.5858758 0.5841321 0.5592149 0.5817023 0.6243483 
##      2727      2728      2734      2735      2738      2739      2740 
## 0.5807798 0.5747840 0.5636697 0.5645584 0.5759764 0.5941327 0.5439159 
##      2741      2742      2743      2744      2745      2746      2747 
## 0.5839521 0.5801724 0.5604749 0.5604524 0.5699018 0.5717691 0.5777200 
##      2749      2750      2751      2752      2755      2758      2763 
## 0.5826247 0.5942677 0.5649858 0.5636809 0.6001061 0.5544790 0.5951339 
##      2764      2767      2770      2775      2780      2782      2788 
## 0.5791824 0.5786200 0.5761226 0.5957751 0.5505642 0.5925916 0.5962926 
##      2791      2792      2795      2799      2803      2805      2807 
## 0.5795312 0.5603511 0.5805098 0.5842559 0.6003311 0.5767413 0.6085993 
##      2810      2814      2817      2819      2821      2822      2823 
## 0.6049321 0.5528591 0.6134028 0.5949989 0.6243483 0.6195224 0.5575613 
##      2828      2830      2833      2834      2836      2839      2842 
## 0.5392362 0.5934915 0.5962251 0.5838171 0.5748852 0.5718929 0.6042121 
##      2843      2844      2848      2849      2852      2855      2856 
## 0.6243483 0.5936828 0.5549515 0.5956514 0.5542878 0.5969901 0.5776750 
##      2858      2862      2865      2867      2868      2871      2876 
## 0.5971026 0.5854258 0.5872144 0.5612286 0.6065857 0.6115691 0.5782375 
##      2877      2878      2884      2887      2888      2890      2891 
## 0.5846271 0.5743227 0.5928166 0.6243483 0.6005561 0.5868544 0.6070469 
##      2893      2894      2900      2902      2903      2904      2911 
## 0.5962926 0.5816910 0.5991837 0.6051233 0.6122666 0.6212210 0.6067769 
##      2913      2914      2915      2922      2923      2924      2927 
## 0.5400461 0.6224472 0.5898805 0.5844696 0.5925578 0.5899930 0.5760214 
##      2931      2935      2936      2937      2938      2940      2948 
## 0.5859208 0.5949764 0.5945940 0.5973275 0.6104217 0.5978450 0.6125366 
##      2951      2954      2956      2966      2971      2974      2975 
## 0.5486631 0.5642434 0.5890143 0.5714317 0.5954039 0.6243483 0.5954377 
##      2976      2979      2981      2982      2984      2988      3000 
## 0.5965738 0.6243483 0.6177338 0.6021647 0.6018498 0.5857295 0.5995099 
##      3004      3005      3016      3018      3019      3022      3023 
## 0.5730291 0.6184200 0.5855495 0.6243483 0.6026147 0.5540853 0.6191399 
##      3025      3026      3029      3030      3031      3033      3034 
## 0.6146514 0.5783275 0.5941440 0.5942902 0.6055620 0.5601824 0.5823885 
##      3041      3044      3049      3053      3054      3058      3060 
## 0.6134590 0.6211873 0.5716229 0.5983287 0.5962364 0.5863595 0.5838621 
##      3062      3063      3065      3067      3068      3071      3074 
## 0.5787887 0.5961689 0.5798911 0.5880919 0.6033459 0.6015798 0.5984862 
##      3076      3078      3081      3082      3083      3086      3103 
## 0.5711729 0.5878444 0.6003536 0.6028397 0.6077669 0.5571451 0.6243483 
##      3104      3107      3109      3110      3112      3114      3115 
## 0.5710492 0.5840534 0.5876644 0.5993299 0.6079581 0.5867982 0.6173400 
##      3118      3123      3125      3126      3128      3129      3130 
## 0.6243483 0.5756052 0.6141227 0.5927491 0.5791712 0.5687093 0.5993299 
##      3131      3132      3133      3140      3141      3142      3147 
## 0.5961126 0.6044933 0.6023560 0.5898468 0.5826472 0.5554239 0.5988912 
##      3151      3152      3156      3157      3162      3164      3167 
## 0.5711842 0.5539053 0.6033234 0.6116816 0.5771238 0.5681806 0.5925916 
##      3169      3171      3179      3181      3183      3184      3185 
## 0.6014560 0.5959889 0.6091505 0.5780013 0.6177338 0.6106354 0.6111979 
##      3186      3187      3192      3193      3195      3196      3197 
## 0.5573813 0.5464132 0.5965401 0.6127278 0.6138865 0.5395287 0.5707230 
##      3199      3200      3204      3205      3207      3210      3211 
## 0.5707005 0.5958989 0.6161476 0.6194549 0.5175363 0.5970576 0.5659533 
##      3214      3217      3218      3219      3220      3221      3237 
## 0.5973613 0.5940427 0.6034921 0.5818035 0.6235609 0.5915229 0.5761339 
##      3238      3239      3240      3241      3242      3247      3248 
## 0.6018498 0.5556489 0.5992287 0.5917929 0.5629610 0.5977775 0.6173175 
##      3250      3252      3253      3255      3256      3260      3261 
## 0.5396299 0.5942677 0.5852233 0.5972825 0.6184200 0.5605086 0.5952914 
##      3262      3263      3265      3266      3267      3269      3270 
## 0.6154051 0.5875294 0.6014785 0.6175313 0.5998586 0.5453221 0.5787437 
##      3275      3278      3282      3283      3284      3288      3289 
## 0.5912192 0.5504067 0.5424085 0.6169126 0.6076094 0.5930978 0.5723316 
##      3290      3291      3294      3295      3296      3297      3298 
## 0.6138865 0.5953027 0.6022322 0.6018273 0.5783275 0.5891493 0.5922429 
##      3300      3301      3302      3303      3305      3306      3309 
## 0.5777988 0.6088243 0.5950777 0.5712517 0.6176438 0.6243483 0.5720166 
##      3313      3316      3317      3318      3319      3320      3321 
## 0.6093868 0.6032334 0.5874057 0.6061245 0.5974738 0.6076094 0.6112429 
##      3322      3323      3324      3325      3326      3327      3328 
## 0.6030534 0.6115916 0.6041896 0.6072157 0.6115466 0.6058882 0.6085768 
##      3329      3330      3331      3332      3333      3334      3336 
## 0.5684281 0.5971700 0.5996224 0.6011073 0.5959776 0.6056183 0.6115916 
##      3339      3343      3344      3345      3346      3347      3349 
## 0.6222222 0.5594287 0.5235209 0.5837834 0.5900830 0.6218735 0.5769663 
##      3351      3352      3353      3354      3355      3358      3359 
## 0.5854483 0.5956851 0.6020522 0.5716117 0.5985537 0.5843684 0.6078344 
##      3362      3366      3369      3371      3373      3374      3375 
## 0.5914329 0.5394837 0.6102417 0.5975750 0.5769663 0.5891606 0.6070807 
##      3376      3379      3380      3381      3383      3384      3385 
## 0.5927603 0.5987674 0.5896218 0.6098367 0.6036946 0.6053708 0.5860670 
##      3386      3388      3391      3392      3393      3394      3395 
## 0.6243483 0.6148652 0.5998249 0.5310017 0.5386625 0.5962251 0.5812973 
##      3396      3404      3405      3406      3408      3411      3412 
## 0.5900267 0.6054045 0.6165188 0.6206698 0.5673482 0.5587087 0.6058545 
##      3414      3415      3417      3420      3421      3422      3424 
## 0.5720166 0.5558739 0.6172163 0.5849871 0.6003086 0.5470432 0.5630285 
##      3428      3429      3430      3434      3435      3437      3438 
## 0.5216873 0.5963151 0.6031434 0.5827935 0.5854820 0.5982612 0.5485169 
##      3439      3440      3446      3447      3450      3451      3453 
## 0.5995324 0.5917141 0.5923104 0.5778438 0.6029859 0.5828834 0.5996224 
##      3456      3457      3458      3460      3461      3462      3463 
## 0.5968326 0.5610936 0.5698118 0.5691143 0.5492256 0.6007811 0.5720166 
##      3465      3468      3469      3474      3475      3480      3481 
## 0.5799924 0.5783500 0.5891493 0.5768538 0.5703517 0.5756952 0.5787437 
##      3484      3485      3486      3487      3488      3489      3490 
## 0.5722866 0.5854933 0.5762464 0.5852008 0.5833222 0.5719154 0.5766401 
##      3491      3492      3493      3494      3496      3502      3504 
## 0.5919054 0.5834009 0.6069569 0.5645246 0.5856845 0.5681469 0.5919279 
##      3505      3507      3509      3511      3512      3517      3521 
## 0.5989137 0.5808023 0.6177113 0.6065745 0.5944590 0.5932553 0.6051008 
##      3523      3525      3526      3528      3533      3536      3539 
## 0.5759201 0.6108717 0.6153602 0.6212435 0.6117716 0.5805211 0.6122778 
##      3540      3541      3542      3543      3544      3546      3548 
## 0.5722979 0.6049096 0.5764489 0.5663245 0.5820510 0.5677757 0.6243483 
##      3550      3552      3553      3557      3562      3564      3567 
## 0.6243483 0.5640746 0.5743790 0.6150564 0.6057308 0.6169126 0.5633209 
##      3572      3574      3577      3578      3579      3580      3583 
## 0.5752677 0.5756164 0.5605311 0.5705205 0.6120304 0.5955164 0.5915342 
##      3587      3589      3591      3593      3601      3605      3607 
## 0.5546702 0.5651771 0.5929178 0.5820623 0.5707342 0.5793399 0.6229197 
##      3609      3611      3621      3622      3623      3624      3628 
## 0.6243483 0.5846383 0.5868544 0.5987899 0.5960339 0.5943577 0.6180600 
##      3629      3630      3632      3633      3635      3641      3645 
## 0.5772926 0.5940652 0.5927828 0.5890031 0.5265807 0.5686306 0.6045946 
##      3649      3654      3656      3659      3660      3668      3671 
## 0.5730291 0.6243483 0.5741315 0.5867645 0.5597662 0.6078006 0.6070469 
##      3674      3675      3678      3681      3682      3683      3696 
## 0.5638384 0.5545577 0.6076206 0.5748402 0.5653458 0.5656720 0.5757514 
##      3699      3700      3702      3703      3704      3706      3707 
## 0.5520491 0.5763814 0.6065407 0.5745815 0.5827147 0.6042346 0.5790137 
##      3708      3711      3712      3715      3717      3722      3724 
## 0.6167101 0.6174750 0.6166876 0.6098817 0.6005111 0.5643896 0.5674269 
##      3727      3729      3731      3732      3735      3746      3748 
## 0.6179587 0.6017485 0.5809261 0.5681019 0.5811961 0.5854033 0.5894418 
##      3754      3755      3759      3760      3763      3766      3768 
## 0.5675619 0.5825010 0.6130653 0.5558739 0.5288419 0.6000049 0.6007136 
##      3769      3772      3774      3780      3783      3784      3785 
## 0.5947290 0.6170700 0.5787437 0.5708017 0.5494618 0.5664370 0.5776750 
##      3786      3787      3789      3790      3798      3799      3800 
## 0.5938628 0.5677082 0.6169238 0.5709592 0.6058657 0.5917591 0.5809261 
##      3801      3802      3803      3804      3806      3809      3810 
## 0.5564701 0.5815335 0.6242246 0.6058770 0.5668307 0.5747052 0.6097243 
##      3811      3813      3814      3816      3817      3818      3830 
## 0.5972488 0.5702617 0.5862470 0.5546702 0.6078231 0.5663245 0.6218060 
##      3832      3836      3838      3839      3850      3855      3859 
## 0.5876981 0.5990374 0.5647271 0.5510705 0.6144827 0.5805098 0.6219072 
##      3862      3864      3865      3866      3867      3868      3870 
## 0.6034472 0.6195786 0.5874619 0.6000386 0.6149439 0.5840421 0.6243483 
##      3871      3872      3873      3874      3875      3877      3879 
## 0.5887443 0.6192412 0.6233809 0.6036496 0.5311705 0.5858083 0.6023672 
##      3881      3882      3883      3885      3886      3888      3889 
## 0.5856283 0.6172950 0.6226947 0.6054383 0.5944702 0.6136053 0.5789462 
##      3891      3892      3893      3894      3897      3906      3907 
## 0.6220872 0.5656495 0.5490006 0.6016473 0.5747165 0.5925353 0.5798461 
##      3909      3910      3912      3913      3914      3916      3919 
## 0.5943240 0.5868319 0.5650308 0.5445459 0.5753802 0.5857970 0.5369638 
##      3920      3922      3924      3925      3926      3933      3935 
## 0.5938853 0.5869444 0.6192299 0.5981600 0.6063045 0.5857295 0.6039759 
##      3938      3941      3943      3944      3947      3949      3951 
## 0.5231047 0.6006236 0.5797336 0.6029859 0.5713417 0.5476282 0.5898355 
##      3953      3954      3960      3964      3966      3968      3969 
## 0.6047633 0.5648058 0.6170813 0.5892730 0.5935590 0.5966188 0.5444784 
##      3970      3973      3974      3975      3977      3980      3990 
## 0.5618023 0.6019172 0.5387300 0.6120191 0.5337465 0.6142577 0.6091168 
##      3997      3999      4002      4003      4006      4011      4013 
## 0.6080594 0.5955389 0.6213335 0.6231109 0.5877994 0.5951789 0.6150227 
##      4014      4020      4025      4028      4030      4032      4036 
## 0.6166313 0.5960001 0.6199836 0.5962364 0.6010511 0.6117716 0.6056745 
##      4037      4046      4047      4048      4051      4053      4054 
## 0.5943690 0.5768651 0.6041896 0.5739628 0.6069907 0.5579888 0.5959551 
##      4056      4058      4059      4061      4062      4065      4067 
## 0.5597549 0.5896330 0.5868544 0.5816573 0.5549852 0.5802174 0.5543327 
##      4068      4069      4070      4074      4077      4082      4087 
## 0.5773488 0.5866745 0.5642321 0.5979462 0.5914217 0.5482469 0.6224247 
##      4091      4093      4094      4095      4101      4102      4106 
## 0.5584725 0.5932553 0.5815110 0.5991387 0.6083631 0.5823097 0.5851896 
##      4108      4109      4111      4112      4113      4115      4116 
## 0.5665832 0.5898243 0.6052020 0.6027947 0.5924566 0.5966863 0.5975975 
##      4121      4122      4124      4125      4126      4127      4131 
## 0.6180600 0.5733890 0.5939190 0.5972825 0.5981825 0.5868994 0.5783162 
##      4132      4134      4140      4141      4143      4144      4148 
## 0.5890818 0.5515317 0.5832097 0.5877319 0.6037734 0.5651771 0.6240784 
##      4149      4153      4157      4158      4159      4160      4161 
## 0.5896330 0.6038634 0.6060007 0.6101180 0.5976763 0.5842109 0.6022322 
##      4162      4163      4164      4165      4166      4167      4168 
## 0.6086218 0.6243483 0.6139990 0.6114904 0.5759089 0.6125928 0.6180487 
##      4169      4170      4180      4191      4193      4195      4198 
## 0.6125816 0.6124353 0.6217160 0.6064057 0.5685744 0.6243483 0.5600699 
##      4199      4202      4204      4208      4209      4217      4218 
## 0.5946052 0.6152027 0.5897343 0.6161701 0.6078906 0.6094318 0.6223797 
##      4219      4220      4221      4222      4223      4224      4225 
## 0.6196461 0.5954714 0.5832997 0.5723316 0.5632084 0.5371551 0.5863932 
##      4226      4227      4228      4233      4234      4235      4236 
## 0.5959214 0.5951114 0.5807798 0.6243483 0.6118504 0.6128853 0.5979800 
##      4239      4240      4241      4242      4243      4244      4245 
## 0.6136278 0.6004998 0.5410023 0.6002074 0.6047971 0.5664482 0.5567176 
##      4246      4248      4249      4252      4254      4256      4258 
## 0.5973838 0.5947065 0.5435447 0.5434547 0.5618473 0.5752002 0.6173513 
##      4260      4261      4262      4263      4265      4267      4268 
## 0.6210523 0.5175813 0.5785525 0.5868544 0.5977325 0.6213673 0.6207598 
##      4272      4284      4298      4311      4319      4321      4330 
## 0.5696093 0.6035371 0.6243483 0.6167438 0.6088131 0.6055958 0.5837271 
##      4335      4338      4341      4343      4347      4352      4358 
## 0.5778550 0.6012760 0.5738053 0.6174975 0.6207148 0.5819273 0.6078006 
##      4363      4370      4371      4376      4382      4385      4386 
## 0.5681019 0.6180375 0.6117829 0.6010173 0.5883506 0.5941665 0.5792049 
##      4412      4429      4437      4440      4446      4462      4466 
## 0.6057308 0.5849758 0.5853470 0.5781025 0.6011860 0.6025585 0.6150789 
##      4470      4471      4472      4473      4485      4494      4500 
## 0.6184987 0.6218510 0.6153602 0.5813760 0.5847846 0.5954264 0.6243483 
##      4503      4505      4507      4509      4516      4540      4544 
## 0.5917816 0.5668757 0.6161364 0.5634109 0.5978450 0.6192299 0.6243483 
##      4552      4556      4565      4584      4601      4606      4613 
## 0.5923891 0.5833559 0.5551989 0.5935928 0.5810836 0.6016135 0.6111529 
##      4616      4617      4619      4627      4628      4629      4635 
## 0.6161701 0.5969901 0.5986325 0.5980475 0.6008936 0.6069344 0.5646821 
##      4636      4641      4643      4645      4672      4678      4680 
## 0.6084418 0.6243483 0.5681019 0.5896330 0.6184537 0.5718479 0.6216148 
##      4700      4707      4712      4717      4718      4719      4731 
## 0.5409461 0.5782375 0.6243483 0.6084643 0.5817585 0.6243483 0.5962251 
##      4739      4754      4757      4792      4795      4805      4807 
## 0.5415086 0.5607448 0.5993524 0.6243483 0.6018498 0.5868544 0.5714092 
##      4811      4813      4819      4820      4847      4851      4860 
## 0.5993749 0.6033909 0.6011635 0.6243483 0.6129528 0.5945152 0.5898805 
##      4875      4877      4888      4889      4890      4891      4892 
## 0.5868544 0.6057083 0.6159901 0.6135828 0.6007136 0.6129416 0.6227622 
##      4897      4902      4905      4906      4909      4910      4912 
## 0.5991049 0.6117379 0.5986662 0.5782262 0.5906455 0.6146289 0.5868544 
##      4914      4934      4941      4945      4947      4949      4950 
## 0.6243483 0.5962251 0.5743565 0.5476507 0.5607673 0.5906005 0.5618473 
##      4951      4953      4954      4958      4959      4960      4962 
## 0.5922091 0.6034584 0.6223910 0.6029409 0.5564251 0.6243483 0.6243483 
##      4964      4966      4967      4969      4970      4971      4972 
## 0.6243483 0.5415761 0.6130990 0.6223347 0.6198036 0.6198486 0.6243483 
##      4988      4989      4991      4993      4997      4998      5003 
## 0.5962251 0.6163163 0.5978788 0.6064507 0.5780238 0.6243483 0.6038971 
##      5009      5016      5036      5043      5047      5056      5072 
## 0.6082731 0.6100617 0.6004661 0.5449396 0.6201299 0.5981712 0.5945490 
##      5086      5088      5090      5102      5114      5126      5129 
## 0.5892055 0.6200736 0.6206361 0.5809598 0.6159564 0.5925241 0.6028622 
##      5130      5131      5132      5133      5135      5139      5146 
## 0.6107479 0.5942902 0.6020072 0.5755039 0.5981037 0.6243483 0.6243483 
##      5152      5165      5170      5176      5186      5188      5190 
## 0.5671794 0.6118504 0.5489668 0.6243483 0.5663920 0.6243483 0.6179812 
##      5195      5199      5201      5204      5215      5223      5224 
## 0.5311930 0.6243483 0.5780913 0.5877994 0.5974738 0.6199836 0.6066532 
##      5225      5226      5256      5263      5264      5265      5266 
## 0.6205686 0.6173850 0.5978788 0.5859095 0.5837609 0.5758076 0.6136953 
##      5267      5271      5272      5280      5281      5288      5293 
## 0.6154051 0.6220085 0.6026035 0.5464695 0.5269970 0.6243483 0.6243483 
##      5297      5308      5313      5315      5318      5327      5339 
## 0.6243483 0.5899480 0.6211310 0.6163951 0.6043358 0.5958539 0.6243483 
##      5348      5364      5366      5369      5381      5433      5434 
## 0.5821635 0.6173175 0.5681019 0.5982837 0.6026485 0.5486294 0.5118554 
##      5437      5443      5451      5454      5455      5456      5458 
## 0.6037509 0.6243483 0.5732653 0.5933115 0.6058770 0.6055058 0.5253546 
##      5466      5472      5473      5474      5477      5482      5495 
## 0.5793512 0.5770788 0.6119404 0.5594287 0.6004098 0.6228297 0.6243483 
##      5508      5519      5520      5524      5528      5532      5533 
## 0.5509805 0.5929178 0.5773375 0.5721179 0.5848408 0.6013210 0.5843459 
##      5537      5558      5572      5585      5600      5610      5616 
## 0.6180150 0.6224585 0.6042121 0.5709592 0.6125028 0.6243483 0.5986325 
##      5627      5632      5634      5638      5646      5663      5664 
## 0.6143027 0.5874282 0.5962251 0.5946277 0.6243483 0.6059782 0.5892168 
##      5685      5689      5700      5705      5712      5718      5734 
## 0.5700143 0.6104892 0.5841771 0.6143477 0.6055958 0.5904092 0.6149777 
##      5735      5736      5737      5755      5823      5829      5830 
## 0.6107142 0.6226609 0.5888793 0.5734565 0.5618473 0.6190612 0.6189599 
##      5831      5832      5833      5834      5835      5836      5856 
## 0.6193874 0.6225597 0.6024235 0.6113217 0.5886543 0.5899818 0.5516104 
##      5858      5890      5898      5903      5904      5905      5910 
## 0.6005673 0.6243483 0.5552777 0.6243483 0.5663920 0.6156976 0.6041559 
##      5912      5919      5945      5946      5947      5948      5949 
## 0.5388312 0.6111192 0.6182062 0.6188137 0.5952352 0.6110854 0.6065070 
##      5950      5951      5977      5978      5998      6026      6028 
## 0.6183862 0.5827260 0.6231784 0.6199049 0.6170475 0.5935703 0.6243483 
##      6029      6030      6051      6061      6062      6067      6068 
## 0.6243483 0.6195899 0.5500243 0.6034697 0.6006236 0.6211085 0.5935140 
##      6069      6070      6071      6072      6073      6104      6105 
## 0.6167213 0.5997011 0.6051683 0.6216710 0.5881594 0.5910392 0.5793512 
##      6106      6107      6181      6183      6186      6195      6197 
## 0.6098367 0.5681019 0.5949989 0.6237746 0.6243483 0.6050671 0.6076769 
##      6220      6266      6267      6268      6269      6270      6271 
## 0.5619710 0.6205798 0.6133690 0.6220760 0.6108942 0.5868544 0.6189374 
##      6301      6305      6309      6310      6311      6312      6317 
## 0.5541415 0.6243483 0.6243483 0.6113667 0.5600699 0.6085881 0.6085093 
##      6332      6336      6375      6384      6391      6393      6400 
## 0.5703517 0.6082731 0.6144265 0.5484831 0.5761339 0.6163163 0.5306080 
##      6401      6419      6421      6491      6507      6508      6509 
## 0.5431060 0.6243483 0.6158664 0.5986887 0.5969338 0.5852458 0.5845483 
##      6510      6512      6513      6514      6515      6516      6518 
## 0.5957301 0.6182625 0.6243483 0.6218060 0.6217947 0.6162376 0.6100055 
##      6519      6520      6521      6526      6527      6547      6548 
## 0.6213448 0.6210635 0.5499343 0.6243483 0.6243483 0.6243483 0.6243483 
##      6549      6572      6579      6583      6584      6591      6671 
## 0.6243483 0.6025810 0.6130315 0.5785525 0.5916916 0.5493493 0.6243483 
##      6682      6700      6701      6702      6711      6712      6713 
## 0.6141227 0.6102867 0.6100617 0.6072044 0.5761339 0.6118504 0.6034022 
##      6717      6748      6750      6783      6784      6786      6787 
## 0.6227172 0.6243483 0.6065857 0.6201186 0.6122553 0.6186562 0.6139877 
##      6834      6837      6845      6846      6847      6848      6881 
## 0.6243483 0.6243483 0.5732203 0.5868544 0.6104555 0.6082731 0.6198486 
##      6887      6889      6918      6932      6936      6937      6940 
## 0.6243483 0.6243483 0.5243534 0.6118504 0.6065182 0.6209061 0.5888231 
##      6941      6943      6944      6945      6946      6948      6949 
## 0.6202311 0.6160689 0.6032109 0.6040209 0.6222672 0.5771913 0.5852233 
##      6952      6997      7002      7007      7014      7018      7040 
## 0.6018498 0.5834459 0.5834459 0.6243483 0.6107142 0.5804986 0.6243483 
##      7042      7057      7058      7082      7083      7086      7104 
## 0.6243483 0.6199949 0.6194549 0.5979575 0.5797786 0.5967988 0.5955277 
##      7105      7106      7107      7108      7109      7110      7111 
## 0.6092518 0.6041446 0.5895768 0.5966863 0.5966751 0.5931316 0.6170925 
##      7112      7113      7114      7115      7116      7117      7118 
## 0.6243483 0.5906005 0.5993524 0.5973500 0.5922091 0.6114791 0.5912642 
##      7119      7120      7121      7122      7123      7124      7125 
## 0.6079244 0.5906005 0.6243483 0.6090380 0.5894418 0.6039646 0.6243483 
##      7126      7127      7128      7129      7140      7154      7179 
## 0.6073057 0.6088356 0.5868544 0.5900155 0.5803749 0.6118504 0.5868544 
##      7195      7224      7225      7252 
## 0.5868544 0.6243483 0.6243483 0.6042121
reg9 <- lm(PCTPELL ~ SAT_AVG, data=data2)
summary(reg9)
## 
## Call:
## lm(formula = PCTPELL ~ SAT_AVG, data = data2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.35515 -0.06343 -0.01101  0.05314  0.51893 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.187e+00  2.255e-02   52.66   <2e-16 ***
## SAT_AVG     -7.729e-04  2.113e-05  -36.59   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1016 on 1300 degrees of freedom
##   (6401 observations deleted due to missingness)
## Multiple R-squared:  0.5073, Adjusted R-squared:  0.5069 
## F-statistic:  1339 on 1 and 1300 DF,  p-value: < 2.2e-16
coefficients(reg9)
##   (Intercept)       SAT_AVG 
##  1.1873341490 -0.0007729444
confint(reg9, level=0.95)
##                     2.5 %        97.5 %
## (Intercept)  1.1430998883  1.2315684098
## SAT_AVG     -0.0008143909 -0.0007314978
lm.beta(reg9)
##    SAT_AVG 
## -0.7122496
fitted(reg9)
##            1            2            4            5            6 
##  0.548109167  0.331684747  0.245114979  0.529558502  0.271395087 
##            9           10           11           13           24 
##  0.407433294  0.248206757  0.274486865  0.459220566  0.394293240 
##           27           33           35           37           38 
##  0.382699075  0.422119237  0.371877854  0.403568572  0.360283688 
##           40           42           47           51           52 
##  0.391974407  0.470041787  0.286853975  0.377288464  0.324728248 
##           53           54           57           58           65 
##  0.468495898  0.560476277  0.375742576  0.431394569  0.372650798 
##           83          116          123          129          135 
##  0.302312862  0.357964855  0.423665126  0.377288464  0.330138859 
##          138          139          141          142          145 
##  0.294583418  0.502505450  0.346370690  0.406660350  0.422119237 
##          147          148          157          158          159 
##  0.376515520  0.425983959  0.313134083  0.422892181  0.225791370 
##          172          175          176          187          189 
##  0.327820025  0.367240188  0.468495898  0.427529847  0.422892181 
##          211          216          224          227          228 
##  0.385790852  0.320090582  0.432940458 -0.006864881  0.330138859 
##          229          233          234          235          237 
##  0.233520814  0.504051339  0.357191911  0.417481571  0.483954785 
##          238          240          241          242          243 
##  0.398157962  0.372650798  0.514099615  0.480863008  0.463085288 
##          244          245          246          247          248 
##  0.119125049  0.239704369  0.284535142  0.159318156  0.315452916 
##          249          251          252          275          277 
##  0.172458210  0.218834871  0.299221084  0.252071479  0.385017908 
##          278          284          308          331          344 
##  0.420573348  0.090526108  0.378061409  0.406660350  0.027917615 
##          351          353          367          369          378 
##  0.503278394  0.425211014  0.489365396  0.403568572  0.465404121 
##          387          393          408          411          423 
##  0.334776525  0.245887924  0.418254515  0.296902251  0.490138340 
##          441          442          446          448          455 
##  0.466950009  0.182506487  0.406660350  0.494776006  0.401249739 
##          456          461          464          465          472 
##  0.271395087  0.233520814  0.310042305  0.063473056  0.329365914 
##          489          490          493          495          499 
##  0.325501192  0.226564315  0.422119237  0.296902251  0.407433294 
##          501          507          511          520          525 
##  0.385017908  0.175549987  0.136129825  0.395839129  0.330138859 
##          527          531          536          537          541 
##  0.426756903  0.437578124  0.297675196  0.120670938  0.212651316 
##          559          560          568          573          574 
##  0.279124531  0.367240188  0.449172289  0.371877854  0.345597746 
##          576          583          585          596          598 
##  0.254390312  0.156999323  0.315452916  0.235839647  0.398930906 
##          605          606          613          620          623 
##  0.437578124  0.435259291  0.388882630  0.330911803  0.436805180 
##          629          636          637          643          653 
##  0.422119237  0.492457173  0.402795628  0.224245482  0.414389793 
##          664          671          673          675          678 
##  0.365694299  0.526466725  0.334003580  0.438351068  0.466950009 
##          684          686          692          693          696 
##  0.429075736  0.033328226  0.496321895  0.264438588  0.528012614 
##          698          699          702          703          704 
##  0.219607816  0.313907027  0.531104391  0.184825320  0.094390830 
##          705          714          715          717          718 
##  0.333230636  0.443761679  0.462312343  0.566659831  0.429848680 
##          726          727          730          734          736 
##  0.460766455  0.271395087  0.434486347  0.296129307  0.549655056 
##          738          739          741          742          746 
##  0.454582900  0.369559021  0.369559021  0.365694299  0.470041787 
##          747          749          754          755          758 
##  0.278351587  0.345597746  0.300766973  0.238158480  0.203375984 
##          796          805          806          807          811 
##  0.159318156  0.311588194  0.476998286  0.303858750  0.359510744 
##          835          836          839          846          849 
##  0.289172808  0.476998286  0.441442846  0.341733024  0.492457173 
##          853          855          857          862          868 
##  0.520283170  0.453037011  0.364148410  0.470814731  0.511007838 
##          869          870          874          878          883 
##  0.570524553  0.409752127  0.478544175  0.522602003  0.272940976 
##          885          888          891          894          896 
##  0.425983959  0.476225342  0.468495898  0.432940458  0.279124531 
##          901          902          904          906          907 
##  0.445307568  0.131492159  0.512553726  0.105212051  0.437578124 
##          908          909          910          911          912 
##  0.312361138  0.337868302  0.371877854  0.222699593  0.523374947 
##          918          919          924          925          929 
##  0.355646022  0.387336741  0.255936200  0.411298016  0.306950528 
##          930          931          933          935          936 
##  0.599896439  0.439124013  0.433713402  0.351781300  0.532650280 
##          937          940          941          944          945 
##  0.452264067  0.410525072  0.310815250  0.437578124  0.436805180 
##          947          949          950          952          953 
##  0.400476795  0.453037011  0.422119237  0.446853456  0.463858232 
##          954          968          969          972          973 
##  0.360283688  0.417481571  0.381926130  0.370331965  0.355646022 
##          974          979          981          987          989 
##  0.473906509  0.374196687  0.382699075  0.364148410  0.406660350 
##          994          997         1011         1013         1022 
##  0.422892181  0.289172808  0.514872560  0.024052894  0.390428518 
##         1031         1033         1034         1039         1040 
##  0.406660350  0.345597746  0.373423742  0.484727730  0.468495898 
##         1041         1046         1049         1050         1052 
##  0.371104909  0.391201463  0.317771749  0.391201463  0.162409933 
##         1053         1057         1059         1067         1080 
##  0.221926649  0.208786595  0.329365914  0.352554245  0.360283688 
##         1081         1082         1085         1091         1094 
##  0.409752127  0.317771749  0.250525590  0.437578124  0.377288464 
##         1096         1098         1099         1108         1109 
##  0.468495898  0.378834353  0.388882630  0.317771749  0.395066184 
##         1111         1113         1114         1117         1122 
##  0.391201463  0.058062445  0.499413672  0.333230636  0.395839129 
##         1130         1131         1132         1135         1137 
##  0.407433294  0.375742576  0.391974407  0.364921355  0.408206238 
##         1138         1150         1151         1156         1157 
##  0.351781300  0.371877854  0.360283688  0.352554245  0.366467243 
##         1160         1163         1164         1167         1169 
##  0.330138859  0.437578124  0.174004099  0.377288464  0.363375466 
##         1170         1171         1177         1181         1182 
##  0.383472019  0.255936200  0.249752646  0.303085806  0.390428518 
##         1183         1184         1187         1189         1191 
##  0.330138859  0.329365914  0.336322413  0.438351068  0.388109685 
##         1193         1194         1196         1197         1198 
##  0.412843905  0.406660350  0.400476795  0.441442846  0.413616849 
##         1199         1200         1201         1202         1203 
##  0.481635952  0.465404121  0.459220566  0.261346811  0.479317119 
##         1204         1205         1218         1219         1220 
##  0.446080512  0.458447622  0.414389793  0.386563796  0.351781300 
##         1228         1229         1231         1232         1235 
##  0.066564833  0.445307568  0.441442846  0.446080512  0.176322932 
##         1237         1238         1239         1240         1243 
##  0.429075736  0.417481571  0.458447622  0.303085806  0.458447622 
##         1244         1245         1246         1249         1252 
##  0.272168032  0.354100134  0.294583418  0.315452916  0.410525072 
##         1253         1257         1258         1259         1260 
##  0.378061409  0.336322413  0.391974407  0.301539917  0.259800922 
##         1264         1265         1266         1268         1270 
##  0.337095358  0.229656092  0.459993510  0.400476795  0.411298016 
##         1272         1273         1274         1286         1287 
##  0.462312343  0.439896957  0.106757940  0.302312862  0.422119237 
##         1289         1295         1296         1300         1301 
##  0.287626919  0.346370690  0.293037529  0.364148410  0.391201463 
##         1304         1305         1312         1316         1322 
##  0.375742576  0.334776525  0.375742576  0.317771749  0.453037011 
##         1323         1324         1330         1332         1333 
##  0.481635952  0.337095358  0.368786076  0.321636471  0.438351068 
##         1334         1340         1348         1352         1355 
##  0.414389793  0.440669901  0.407433294  0.391974407  0.529558502 
##         1365         1366         1369         1374         1375 
##  0.302312862  0.355646022  0.368786076  0.391201463  0.410525072 
##         1376         1382         1384         1388         1389 
##  0.406660350  0.406660350  0.412843905  0.408979183  0.431394569 
##         1390         1395         1396         1400         1401 
##  0.385790852  0.408206238  0.310042305  0.321636471  0.317771749 
##         1404         1405         1407         1412         1413 
##  0.384244963  0.442215790  0.211105428  0.385017908  0.408206238 
##         1416         1427         1428         1429         1430 
##  0.335549469  0.406660350  0.504824283  0.398157962  0.304631695 
##         1431         1435         1440         1441         1443 
##  0.440669901  0.303085806  0.391974407  0.364921355  0.378834353 
##         1448         1459         1462         1463         1465 
##  0.440669901  0.439896957  0.428302792  0.236612591  0.437578124 
##         1466         1476         1484         1486         1492 
##  0.378061409  0.330138859  0.502505450  0.516418448  0.424438070 
##         1493         1495         1499         1501         1502 
##  0.289945752  0.375742576  0.422119237  0.334003580  0.310042305 
##         1503         1504         1505         1506         1509 
##  0.391201463  0.351008356  0.390428518  0.391201463  0.393520296 
##         1511         1524         1525         1526         1528 
##  0.406660350  0.391201463  0.483954785  0.564340998  0.360283688 
##         1530         1531         1538         1540         1542 
##  0.150042824  0.384244963  0.414389793  0.156999323  0.452264067 
##         1547         1549         1550         1552         1556 
##  0.492457173  0.354100134  0.395839129  0.357964855  0.441442846 
##         1559         1571         1572         1573         1577 
##  0.415935682  0.476225342  0.517191393  0.356418967  0.527239669 
##         1578         1582         1591         1598         1599 
##  0.507143116  0.439896957  0.075067221  0.249752646  0.170912321 
##         1600         1601         1605         1606         1609 
##  0.286853975  0.536515002  0.511780782  0.377288464  0.377288464 
##         1615         1617         1619         1622         1624 
##  0.269076254  0.164728766  0.351008356  0.422119237  0.341733024 
##         1628         1629         1634         1636         1637 
##  0.501732505  0.075067221  0.204148929  0.511007838  0.452264067 
##         1640         1641         1647         1649         1650 
##  0.402795628  0.223472537  0.120670938  0.182506487  0.129173326 
##         1651         1661         1663         1666         1667 
##  0.421346292  0.454582900  0.524920836  0.477771230  0.225791370 
##         1668         1673         1674         1676         1681 
##  0.342505968  0.411298016  0.405887405  0.289945752  0.027144671 
##         1690         1692         1694         1698         1699 
##  0.434486347  0.347916579  0.302312862  0.246660868  0.375742576 
##         1701         1702         1703         1704         1714 
##  0.357191911  0.354873078  0.027917615  0.333230636  0.502505450 
##         1727         1731         1733         1734         1741 
##  0.432167513  0.089753164  0.456128789  0.584437552  0.426756903 
##         1743         1747         1749         1751         1753 
##  0.282989253  0.395066184  0.395066184  0.376515520  0.087434331 
##         1754         1755         1756         1757         1759 
##  0.112941495  0.324728248  0.354873078  0.416708626  0.442988734 
##         1760         1762         1763         1764         1767 
##  0.065018944  0.416708626  0.407433294  0.317771749  0.336322413 
##         1769         1770         1776         1780         1783 
##  0.351781300  0.344824801  0.273713921  0.375742576  0.422119237 
##         1785         1792         1795         1796         1799 
##  0.406660350  0.329365914  0.392747351  0.406660350  0.242023202 
##         1802         1805         1808         1812         1818 
##  0.374969631  0.345597746  0.271395087  0.229656092  0.392747351 
##         1820         1823         1824         1825         1826 
##  0.316225860  0.376515520  0.568978664  0.436032235  0.120670938 
##         1828         1829         1830         1831         1841 
##  0.292264585  0.225791370  0.333230636  0.419800404  0.406660350 
##         1844         1846         1847         1849         1854 
##  0.411298016  0.360283688  0.478544175  0.391201463  0.391201463 
##         1856         1860         1862         1868         1871 
##  0.395066184  0.387336741  0.483954785  0.360283688  0.391201463 
##         1879         1882         1883         1884         1887 
##  0.357191911  0.406660350  0.360283688  0.301539917  0.099028496 
##         1888         1891         1899         1909         1911 
##  0.286081030  0.317771749  0.336322413  0.140767491  0.406660350 
##         1918         1919         1921         1926         1927 
##  0.204921873  0.409752127  0.346370690  0.329365914  0.299994029 
##         1930         1935         1937         1939         1944 
##  0.376515520  0.366467243  0.329365914  0.442215790  0.276032754 
##         1947         1948         1949         1950         1951 
##  0.406660350  0.294583418  0.362602521  0.188690041  0.402022684 
##         1952         1953         1955         1958         1965 
##  0.332457692  0.453809955  0.389655574  0.422119237  0.375742576 
##         1968         1970         1977         1985         1988 
##  0.513326671  0.391201463  0.439124013  0.483181841  0.276805698 
##         1990         1991         1992         1993         1996 
##  0.338641246  0.423665126  0.549655056  0.321636471  0.316998804 
##         2000         2003         2005         2007         2010 
##  0.599896439  0.391974407  0.519510226  0.352554245  0.385017908 
##         2015         2018         2019         2022         2025 
##  0.403568572  0.375742576  0.406660350  0.375742576  0.333230636 
##         2027         2030         2031         2036         2037 
##  0.399703851  0.425211014  0.271395087  0.371877854  0.374196687 
##         2049         2055         2060         2064         2067 
##  0.347916579  0.385017908  0.308496417  0.437578124  0.426756903 
##         2071         2075         2076         2077         2078 
##  0.422119237  0.286081030  0.314679971  0.195646541  0.333230636 
##         2084         2085         2087         2093         2096 
##  0.239704369  0.374969631  0.357191911  0.287626919  0.229656092 
##         2101         2105         2110         2111         2112 
##  0.422119237  0.360283688  0.364921355  0.375742576  0.344824801 
##         2117         2118         2120         2121         2122 
##  0.044922391  0.333230636  0.326274137  0.305404639  0.381926130 
##         2128         2141         2142         2143         2144 
##  0.311588194  0.317771749  0.315452916  0.356418967  0.478544175 
##         2145         2150         2151         2155         2156 
##  0.390428518  0.422119237  0.375742576  0.362602521  0.259800922 
##         2157         2158         2159         2162         2164 
##  0.368013132  0.364921355  0.353327189  0.376515520  0.344824801 
##         2167         2169         2173         2174         2179 
##  0.406660350  0.375742576  0.318544693  0.301539917  0.391201463 
##         2185         2192         2193         2196         2202 
##  0.437578124  0.414389793  0.351781300  0.406660350  0.071202499 
##         2205         2215         2216         2217         2227 
##  0.453809955  0.334003580  0.441442846  0.406660350  0.443761679 
##         2238         2241         2243         2254         2259 
##  0.561249221  0.453037011  0.471587676  0.323182359  0.457674677 
##         2260         2261         2263         2264         2271 
##  0.514872560  0.390428518  0.456901733  0.334776525  0.499413672 
##         2273         2279         2280         2287         2294 
##  0.486273618  0.371877854  0.433713402  0.284535142  0.034874115 
##         2296         2298         2300         2301         2302 
##  0.351008356  0.394293240  0.395066184  0.248206757  0.387336741 
##         2305         2307         2309         2311         2312 
##  0.492457173  0.311588194  0.535742057  0.146951046  0.354100134 
##         2316         2319         2326         2331         2333 
##  0.249752646  0.429848680  0.464631176  0.456901733  0.265211533 
##         2335         2339         2353         2357         2360 
##  0.368013132  0.426756903  0.343278913  0.286853975  0.364921355 
##         2373         2393         2403         2407         2409 
##  0.149269879  0.348689523  0.263665644  0.129173326  0.051105946 
##         2412         2416         2417         2422         2425 
##  0.513326671  0.114487383  0.088207275  0.232747870  0.348689523 
##         2426         2427         2430         2431         2434 
##  0.410525072  0.313907027  0.290718696  0.437578124  0.418254515 
##         2437         2440         2442         2445         2450 
##  0.344824801  0.491684229  0.387336741  0.513326671  0.357964855 
##         2455         2462         2468         2469         2474 
##  0.218061927  0.110622661  0.300766973  0.320863526  0.397385017 
##         2481         2486         2487         2489         2496 
##  0.159318156  0.480863008  0.359510744  0.453037011  0.339414191 
##         2503         2504         2517         2520         2521 
##  0.364148410  0.538060890  0.358737800  0.405887405  0.467722954 
##         2526         2527         2535         2537         2541 
##  0.446853456  0.323955304  0.148496935  0.383472019  0.361056633 
##         2542         2543         2548         2552         2553 
##  0.460766455  0.484727730  0.372650798  0.449945234  0.305404639 
##         2561         2563         2565         2571         2572 
##  0.126854493  0.368786076  0.228883148  0.363375466  0.464631176 
##         2576         2581         2582         2583         2587 
##  0.446853456  0.316225860  0.228110204  0.390428518  0.344051857 
##         2590         2594         2597         2598         2599 
##  0.331684747  0.428302792  0.509461949  0.428302792  0.495548951 
##         2600         2601         2602         2603         2604 
##  0.338641246  0.192554763  0.286853975  0.218061927  0.265211533 
##         2605         2606         2607         2609         2610 
##  0.337868302  0.371104909  0.461539399  0.371104909  0.243569091 
##         2611         2612         2613         2615         2617 
##  0.320090582  0.347916579  0.332457692  0.340960079  0.418254515 
##         2618         2621         2624         2642         2644 
##  0.390428518  0.332457692  0.272168032  0.102893218  0.391974407 
##         2646         2647         2658         2664         2666 
##  0.089753164  0.373423742  0.243569091  0.299994029  0.443761679 
##         2668         2675         2677         2686         2691 
##  0.414389793  0.437578124  0.395066184  0.589848162  0.153907545 
##         2692         2694         2696         2697         2700 
##  0.063473056  0.386563796  0.517964337  0.240477313  0.497867784 
##         2702         2704         2710         2714         2720 
##  0.398930906  0.510234893  0.340187135  0.562795110  0.630814213 
##         2721         2722         2726         2728         2734 
##  0.588302273  0.473133564  0.425983959  0.443761679  0.402022684 
##         2735         2738         2739         2740         2741 
##  0.490138340  0.483954785  0.266757421  0.160864045  0.353327189 
##         2742         2743         2744         2745         2746 
##  0.381153186  0.502505450  0.324728248  0.218834871  0.473906509 
##         2747         2749         2750         2751         2752 
##  0.302312862  0.499413672  0.468495898  0.454582900  0.463085288 
##         2755         2758         2763         2764         2770 
##  0.374969631  0.427529847  0.615355326  0.335549469  0.460766455 
##         2782         2788         2791         2792         2795 
##  0.310815250  0.413616849  0.523374947  0.387336741  0.447626401 
##         2799         2803         2805         2807         2810 
##  0.276805698  0.375742576  0.387336741  0.344824801  0.343278913 
##         2814         2817         2822         2828         2830 
##  0.456128789  0.398930906  0.375742576  0.444534623  0.377288464 
##         2833         2836         2839         2844         2848 
##  0.348689523  0.391974407  0.405114461  0.337095358  0.124535660 
##         2849         2852         2855         2856         2858 
##  0.269849199  0.565886887  0.455355844  0.438351068  0.286853975 
##         2862         2865         2868         2871         2876 
##  0.468495898  0.377288464  0.403568572  0.380380242  0.264438588 
##         2877         2884         2888         2893         2894 
##  0.433713402  0.387336741  0.483954785  0.393520296  0.411298016 
##         2902         2911         2913         2915         2922 
##  0.324728248  0.375742576  0.157772267  0.440669901  0.453037011 
##         2923         2924         2931         2935         2936 
##  0.379607297  0.333230636  0.228883148  0.391201463  0.370331965 
##         2937         2938         2940         2948         2951 
##  0.378834353  0.410525072  0.407433294  0.463085288  0.144632213 
##         2954         2956         2966         2971         2976 
##  0.410525072  0.275259809  0.188690041  0.332457692  0.341733024 
##         2981         3000         3005         3016         3019 
##  0.197965374  0.272940976  0.390428518  0.403568572  0.381153186 
##         3022         3023         3026         3029         3031 
##  0.619220048  0.437578124  0.237385536  0.327047081  0.425983959 
##         3033         3034         3041         3044         3049 
##  0.534196168  0.415162738  0.422119237  0.410525072  0.460766455 
##         3054         3058         3060         3062         3063 
##  0.407433294  0.468495898  0.316225860  0.483954785  0.308496417 
##         3065         3067         3068         3071         3074 
##  0.282216308  0.286853975  0.268303310  0.406660350  0.530331447 
##         3078         3081         3082         3083         3086 
##  0.384244963  0.437578124  0.429075736  0.406660350  0.185598264 
##         3104         3107         3110         3115         3123 
##  0.385790852  0.454582900  0.351781300  0.350235412  0.378061409 
##         3126         3128         3130         3131         3133 
##  0.424438070  0.380380242  0.327820025  0.324728248  0.344824801 
##         3140         3141         3142         3147         3152 
##  0.391201463  0.263665644  0.118352105  0.391974407  0.402022684 
##         3156         3157         3162         3167         3169 
##  0.252844423  0.413616849  0.491684229  0.282989253  0.388882630 
##         3171         3179         3181         3184         3186 
##  0.437578124  0.411298016  0.333230636  0.437578124  0.172458210 
##         3187         3192         3193         3195         3196 
##  0.169366433  0.494003062  0.465404121  0.459993510  0.077386054 
##         3197         3200         3204         3210         3214 
##  0.410525072  0.439124013  0.470041787  0.422119237  0.270622143 
##         3217         3218         3219         3220         3221 
##  0.303085806  0.449945234  0.385017908  0.470041787  0.311588194 
##         3240         3241         3247         3250         3252 
##  0.385790852  0.358737800  0.444534623  0.088207275  0.472360620 
##         3255         3256         3262         3265         3266 
##  0.443761679  0.446853456  0.475452397  0.445307568  0.471587676 
##         3267         3269         3270         3278         3282 
##  0.419027459  0.182506487  0.417481571  0.162409933  0.521056114 
##         3283         3284         3288         3289         3290 
##  0.455355844  0.408206238  0.381153186  0.601442327  0.453037011 
##         3291         3295         3297         3298         3301 
##  0.391201463  0.317771749  0.405114461  0.357191911  0.397385017 
##         3302         3305         3313         3316         3317 
##  0.481635952  0.528012614  0.372650798  0.434486347  0.503278394 
##         3318         3319         3320         3321         3322 
##  0.442215790  0.446080512  0.412070960  0.413616849  0.449945234 
##         3323         3324         3325         3326         3327 
##  0.435259291  0.395839129  0.439124013  0.472360620  0.480863008 
##         3328         3329         3330         3331         3332 
##  0.456128789  0.262892700  0.439896957  0.454582900  0.452264067 
##         3333         3334         3344         3345         3346 
##  0.492457173  0.398157962  0.065018944  0.357191911  0.409752127 
##         3347         3349         3351         3352         3353 
##  0.419800404  0.283762197  0.425983959  0.405887405  0.403568572 
##         3354         3355         3362         3366         3371 
##  0.201830095  0.506370172  0.418254515  0.468495898  0.374969631 
##         3373         3374         3376         3379         3384 
##  0.419800404  0.388882630  0.388109685  0.317771749  0.429075736 
##         3385         3392         3395         3396         3405 
##  0.415162738  0.079704887  0.317771749  0.437578124  0.459993510 
##         3406         3408         3412         3414         3417 
##  0.568978664  0.172458210  0.408206238  0.353327189  0.371877854 
##         3420         3421         3422         3424         3428 
##  0.396612073  0.379607297  0.432940458  0.375742576  0.078158999 
##         3435         3437         3438         3446         3447 
##  0.477771230  0.354873078  0.218061927  0.385017908  0.416708626 
##         3450         3453         3456         3457         3458 
##  0.374196687  0.308496417  0.357964855  0.564340998  0.212651316 
##         3460         3461         3462         3463         3465 
##  0.420573348  0.387336741  0.388882630  0.379607297  0.402022684 
##         3468         3474         3475         3480         3481 
##  0.466177065  0.463858232  0.398930906  0.456901733  0.296902251 
##         3484         3485         3486         3487         3488 
##  0.344824801  0.437578124  0.466177065  0.246660868  0.511007838 
##         3489         3490         3491         3492         3493 
##  0.567432776  0.478544175  0.589075218  0.417481571  0.561249221 
##         3494         3496         3504         3505         3507 
##  0.455355844  0.514872560  0.373423742  0.264438588  0.289172808 
##         3509         3511         3512         3517         3521 
##  0.452264067  0.394293240  0.380380242  0.422119237  0.395066184 
##         3523         3525         3526         3528         3533 
##  0.429848680  0.274486865  0.361829577  0.392747351  0.380380242 
##         3536         3539         3540         3541         3542 
##  0.319317638  0.406660350  0.329365914  0.278351587  0.468495898 
##         3543         3544         3546         3548         3552 
##  0.364148410  0.350235412  0.333230636  0.483954785  0.380380242 
##         3553         3557         3562         3564         3567 
##  0.279124531  0.391201463  0.456128789  0.323955304  0.535742057 
##         3572         3574         3577         3578         3579 
##  0.388109685  0.381926130  0.598350550  0.619220048  0.355646022 
##         3580         3583         3587         3589         3591 
##  0.371877854  0.376515520  0.395066184  0.391974407  0.389655574 
##         3593         3601         3605         3607         3621 
##  0.339414191  0.375742576  0.185598264  0.483954785  0.412843905 
##         3622         3623         3624         3628         3629 
##  0.346370690  0.261346811  0.375742576  0.333230636  0.443761679 
##         3630         3632         3633         3635         3641 
##  0.363375466  0.422119237  0.282989253  0.042603558  0.344051857 
##         3645         3649         3656         3668         3671 
##  0.432940458  0.291491641  0.238931425  0.398157962  0.437578124 
##         3674         3675         3678         3681         3682 
##  0.356418967  0.417481571  0.251298534  0.451491122  0.494003062 
##         3683         3696         3699         3700         3702 
##  0.484727730  0.385790852  0.372650798  0.380380242  0.496321895 
##         3704         3706         3707         3708         3717 
##  0.306950528  0.432940458  0.558157443  0.442988734  0.442988734 
##         3722         3724         3727         3729         3731 
##  0.487046563  0.277578642  0.406660350  0.364921355  0.490911285 
##         3735         3746         3754         3755         3759 
##  0.418254515  0.340187135  0.459993510  0.450718178  0.360283688 
##         3760         3763         3766         3768         3769 
##  0.530331447  0.058835390  0.324728248  0.328592970  0.414389793 
##         3772         3774         3780         3784         3785 
##  0.416708626  0.388882630  0.170139377  0.291491641  0.415935682 
##         3786         3787         3789         3790         3798 
##  0.389655574  0.487819507  0.499413672  0.444534623  0.474679453 
##         3799         3800         3801         3802         3804 
##  0.255163256  0.373423742  0.185598264  0.214197205  0.374969631 
##         3806         3809         3810         3811         3813 
##  0.254390312  0.398930906  0.442988734  0.385790852  0.559703332 
##         3814         3816         3817         3818         3830 
##  0.329365914  0.426756903  0.450718178  0.197192429  0.456128789 
##         3832         3838         3839         3855         3859 
##  0.437578124  0.190235930  0.329365914  0.365694299  0.362602521 
##         3862         3864         3867         3868         3872 
##  0.313134083  0.320090582  0.439896957  0.298448140  0.459993510 
##         3873         3875         3877         3882         3886 
##  0.463085288  0.121443882  0.373423742  0.531104391  0.266757421 
##         3889         3891         3892         3893         3894 
##  0.473906509  0.486273618  0.371104909  0.126081549  0.363375466 
##         3897         3906         3907         3909         3910 
##  0.296902251  0.418254515  0.412070960  0.528785558  0.296902251 
##         3912         3913         3914         3916         3919 
##  0.338641246  0.415162738  0.351008356  0.296129307  0.383472019 
##         3920         3922         3924         3925         3926 
##  0.410525072  0.415935682  0.430621625  0.326274137  0.413616849 
##         3933         3935         3941         3943         3944 
##  0.517964337  0.408979183  0.439124013  0.347916579  0.347916579 
##         3949         3951         3953         3954         3960 
##  0.153907545  0.347143634  0.419027459  0.371104909  0.371104909 
##         3964         3966         3968         3969         3970 
##  0.456128789  0.248206757  0.333230636  0.138448658  0.289172808 
##         3973         3974         3975         3977         3990 
##  0.540379723  0.587529329  0.421346292  0.109076773  0.431394569 
##         3999         4003         4006         4025         4028 
##  0.446853456  0.381153186  0.254390312  0.400476795  0.325501192 
##         4030         4032         4036         4037         4046 
##  0.236612591  0.370331965  0.306177583  0.272940976  0.356418967 
##         4047         4048         4051         4053         4056 
##  0.391201463  0.228883148  0.329365914  0.164728766  0.422119237 
##         4058         4061         4062         4065         4067 
##  0.408979183  0.487046563  0.470814731  0.423665126  0.415162738 
##         4068         4069         4070         4074         4082 
##  0.425211014  0.441442846  0.491684229  0.398157962  0.457674677 
##         4087         4091         4093         4094         4095 
##  0.415162738  0.459220566  0.441442846  0.427529847  0.410525072 
##         4101         4102         4106         4108         4111 
##  0.361056633  0.389655574  0.468495898  0.375742576  0.412070960 
##         4112         4113         4115         4116         4122 
##  0.344824801  0.334003580  0.345597746  0.377288464  0.453809955 
##         4126         4127         4132         4134         4140 
##  0.453037011  0.244342035  0.226564315  0.468495898  0.348689523 
##         4141         4143         4144         4148         4149 
##  0.330911803  0.317771749  0.553519777  0.437578124  0.345597746 
##         4153         4157         4158         4159         4160 
##  0.375742576  0.329365914  0.375742576  0.302312862  0.353327189 
##         4161         4162         4164         4165         4166 
##  0.391201463  0.422119237  0.375742576  0.406660350  0.193327708 
##         4167         4168         4169         4170         4180 
##  0.406660350  0.344824801  0.375742576  0.375742576  0.323182359 
##         4239         4242         4243         4249         4260 
##  0.372650798  0.404341517  0.300766973  0.269076254  0.572070442 
##         4261         4262         4386         4473         4628 
##  0.054970668  0.249752646  0.202603040  0.454582900  0.407433294 
##         4629         4739         4754         4811         5056 
##  0.430621625  0.414389793  0.242023202  0.340960079  0.307723472 
##         5165         5195         5201         5263         5264 
##  0.277578642  0.404341517  0.368786076  0.411298016  0.375742576 
##         5265         5339         5458         5528         5632 
##  0.413616849  0.402022684  0.047241224  0.251298534  0.390428518 
##         5685         5856         5858         5912         6051 
##  0.348689523  0.289172808  0.350235412  0.390428518  0.333230636 
##         6104         6301         6700         6948         7082 
##  0.316225860  0.327820025  0.347916579  0.383472019  0.391201463 
##         7129         7252 
##  0.402022684  0.501732505
reg10 <- lm(PCTPELL ~ ADM_RATE, data=data2)
summary(reg10)
## 
## Call:
## lm(formula = PCTPELL ~ ADM_RATE, data = data2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.51384 -0.15179 -0.03645  0.12828  0.62865 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.27636    0.01451   19.05   <2e-16 ***
## ADM_RATE     0.23748    0.02008   11.83   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1961 on 2193 degrees of freedom
##   (5508 observations deleted due to missingness)
## Multiple R-squared:  0.05997,    Adjusted R-squared:  0.05954 
## F-statistic: 139.9 on 1 and 2193 DF,  p-value: < 2.2e-16
coefficients(reg10)
## (Intercept)    ADM_RATE 
##   0.2763592   0.2374819
confint(reg10, level=0.95)
##                 2.5 %    97.5 %
## (Intercept) 0.2479088 0.3048095
## ADM_RATE    0.1981078 0.2768560
lm.beta(reg10)
##  ADM_RATE 
## 0.2448835
fitted(reg10)
##         1         2         4         5         6         9        10 
## 0.4011797 0.4798574 0.4711656 0.4028420 0.3975937 0.4667484 0.4745853 
##        11        13        23        24        25        27        31 
## 0.4031508 0.4028895 0.5138411 0.4150249 0.5138411 0.4740866 0.4313161 
##        33        35        37        38        40        42        47 
## 0.4473224 0.4221493 0.4152148 0.4528082 0.4375619 0.3900418 0.4177559 
##        51        52        53        54        57        58        65 
## 0.4743003 0.3993036 0.5138411 0.4164972 0.3811837 0.3932478 0.3762678 
##        76        77        78        83        85        96        99 
## 0.5115613 0.5138411 0.5138411 0.4766277 0.4535682 0.4667247 0.4130775 
##       103       104       108       116       123       129       135 
## 0.4985947 0.4946288 0.4686958 0.4395805 0.4110827 0.4171384 0.4222206 
##       138       139       141       142       145       147       148 
## 0.4236929 0.3682172 0.4482723 0.4812111 0.4225055 0.5002096 0.4116526 
##       157       158       159       162       172       175       176 
## 0.5117512 0.4254503 0.4730417 0.4420740 0.4440451 0.4875281 0.4231467 
##       187       189       192       194       200       208       211 
## 0.4437602 0.4459687 0.4100377 0.4805699 0.3242355 0.4684820 0.4706906 
##       215       216       217       224       225       227       228 
## 0.4351396 0.4554205 0.5117512 0.4655610 0.4276114 0.2973288 0.4211519 
##       229       230       231       232       233       234       235 
## 0.3497173 0.3679084 0.4440214 0.4490560 0.4769126 0.3995410 0.4448763 
##       236       237       238       239       240       241       242 
## 0.3769090 0.4174234 0.3819674 0.4433327 0.3605703 0.4213894 0.4018921 
##       243       244       245       246       247       248       249 
## 0.4488898 0.3144038 0.3722306 0.3652249 0.3204358 0.4147874 0.3554169 
##       251       252       258       259       264       275       276 
## 0.3626601 0.4086841 0.3343522 0.4347596 0.4841558 0.3880707 0.5138411 
##       277       278       284       288       293       308       319 
## 0.4807836 0.4081616 0.3019360 0.3803762 0.4627587 0.4685295 0.3993273 
##       320       321       331       337       344       351       353 
## 0.4043144 0.4331922 0.4345696 0.5138411 0.3102003 0.4118663 0.4581516 
##       360       361       362       365       367       369       370 
## 0.5007321 0.4991647 0.4896179 0.3748192 0.4338809 0.3869307 0.4152148 
##       378       387       393       400       408       411       423 
## 0.3728718 0.4565604 0.4015359 0.4840371 0.3833685 0.4571779 0.4623075 
##       426       435       438       439       440       441       442 
## 0.5007796 0.5090914 0.5138411 0.5138411 0.5138411 0.4609064 0.3761966 
##       446       448       449       455       456       461       462 
## 0.4342371 0.3499786 0.5138411 0.3890206 0.4067367 0.3605703 0.3072793 
##       464       465       472       489       490       491       492 
## 0.4414803 0.3053082 0.4499347 0.3582429 0.3861946 0.5021570 0.3648687 
##       493       495       499       501       507       511       514 
## 0.4330260 0.4189671 0.4563942 0.4184921 0.3935565 0.3438040 0.5138411 
##       520       525       527       531       532       536       537 
## 0.4125788 0.4567267 0.4663922 0.4140987 0.5138411 0.4682208 0.3191534 
##       541       545       547       557       559       560       565 
## 0.4727567 0.5138411 0.5138411 0.5035106 0.4648248 0.4233130 0.4496497 
##       568       571       573       574       576       577       578 
## 0.4314111 0.4696932 0.4496972 0.4957925 0.4762239 0.5003521 0.3188684 
##       579       583       585       596       598       605       606 
## 0.4121988 0.3629688 0.4674846 0.4580091 0.4920402 0.4717355 0.4309836 
##       608       613       620       622       623       629       636 
## 0.4427390 0.4446863 0.5044368 0.5138411 0.4966949 0.5076903 0.4205582 
##       637       640       643       646       647       653       660 
## 0.4198932 0.3656524 0.3950051 0.4262103 0.4462300 0.4476549 0.4426915 
##       664       671       673       674       675       677       678 
## 0.4683870 0.4831347 0.4328835 0.4120801 0.4662735 0.3676947 0.4462537 
##       681       683       684       686       692       693       694 
## 0.3548232 0.3331411 0.3714232 0.2913205 0.3802338 0.4374431 0.3973562 
##       696       698       699       702       703       704       705 
## 0.4110114 0.3852209 0.4518820 0.4314824 0.3803525 0.3175623 0.3913242 
##       708       709       714       715       717       718       724 
## 0.5138411 0.4921115 0.4083041 0.3858621 0.4276589 0.4541619 0.3601665 
##       726       727       730       734       736       737       738 
## 0.3602615 0.3941739 0.4234080 0.4491035 0.4021058 0.4498635 0.3926066 
##       739       741       742       743       744       745       746 
## 0.4331685 0.3900655 0.4582466 0.5138411 0.5138411 0.5138411 0.5138411 
##       747       749       751       754       755       758       774 
## 0.4225768 0.4017021 0.3251380 0.3827748 0.4079004 0.3846747 0.4629012 
##       775       777       787       796       799       805       806 
## 0.4095153 0.3919654 0.3922028 0.3670298 0.4482248 0.4202020 0.3708532 
##       807       811       820       822       824       832       835 
## 0.3922741 0.5026082 0.4787413 0.4124126 0.4477261 0.5138411 0.4026046 
##       836       838       839       846       849       853       855 
## 0.4779813 0.4217931 0.3807087 0.3995648 0.4275876 0.3381045 0.3964300 
##       857       862       863       868       869       870       874 
## 0.3753179 0.4598377 0.4371819 0.3886644 0.3863370 0.4379181 0.3995885 
##       878       883       885       887       888       891       894 
## 0.4774351 0.4208194 0.4563942 0.4663447 0.4956737 0.3771702 0.4074967 
##       896       901       902       904       906       907       908 
## 0.5058617 0.3930103 0.3400518 0.3338060 0.3556306 0.4417416 0.4574154 
##       909       910       911       912       918       919       921 
## 0.4262103 0.4175184 0.4086841 0.3912767 0.4032932 0.4075679 0.4119613 
##       923       924       925       929       930       931       932 
## 0.5138411 0.4348071 0.4759152 0.4621413 0.3281540 0.4130300 0.3555119 
##       933       935       936       937       940       941       943 
## 0.4901404 0.4344034 0.4607164 0.4407441 0.4045994 0.4641124 0.4194895 
##       944       945       947       949       950       952       953 
## 0.3643462 0.5051255 0.4049319 0.3917991 0.3957888 0.4796912 0.4457788 
##       954       956       962       965       967       968       969 
## 0.4635424 0.4231942 0.4906628 0.4447338 0.3951001 0.4966236 0.4592202 
##       972       973       974       975       979       981       987 
## 0.4366120 0.4969799 0.5115613 0.4554443 0.4308886 0.5129386 0.4405779 
##       988       989       994       997      1011      1013      1021 
## 0.4036732 0.4689570 0.4309599 0.4290600 0.3475087 0.2971626 0.4866019 
##      1022      1027      1031      1033      1034      1036      1039 
## 0.4042432 0.4423115 0.3945302 0.4371582 0.4294875 0.4346884 0.4998059 
##      1040      1041      1046      1049      1050      1052      1053 
## 0.5138411 0.4085891 0.4968374 0.4532357 0.4596240 0.4165685 0.4198695 
##      1055      1057      1059      1067      1070      1072      1075 
## 0.4049081 0.3965250 0.4518108 0.4500059 0.4746803 0.4384168 0.4074492 
##      1080      1081      1082      1085      1087      1091      1094 
## 0.4233842 0.3893531 0.4099190 0.4267802 0.4120563 0.4624737 0.4215794 
##      1096      1097      1098      1099      1100      1105      1108 
## 0.3805187 0.4853433 0.4253316 0.4403642 0.4475124 0.5077615 0.4184683 
##      1109      1111      1112      1113      1114      1117      1122 
## 0.4060480 0.3972137 0.4984760 0.3074930 0.4131725 0.4532594 0.4875518 
##      1127      1130      1131      1132      1135      1137      1138 
## 0.3341385 0.4064993 0.4607401 0.4204394 0.3964300 0.3942452 0.4226005 
##      1141      1145      1150      1151      1152      1153      1156 
## 0.3649637 0.4378469 0.4699782 0.4828734 0.5138411 0.5138411 0.4906153 
##      1157      1160      1163      1164      1167      1169      1170 
## 0.5138411 0.4570592 0.4417416 0.4405779 0.4067605 0.4185633 0.4438552 
##      1171      1172      1177      1180      1181      1182      1183 
## 0.4389393 0.3565806 0.4107739 0.4295825 0.4733504 0.4407441 0.4045994 
##      1184      1187      1189      1191      1193      1194      1195 
## 0.4666297 0.4294638 0.4975973 0.5069779 0.4921590 0.4437602 0.5138411 
##      1196      1197      1198      1199      1200      1201      1202 
## 0.4342371 0.4439502 0.4457788 0.4723767 0.4360895 0.4505047 0.4570592 
##      1203      1204      1205      1206      1207      1208      1209 
## 0.4586978 0.4671046 0.4277776 0.4625212 0.3969050 0.4645873 0.4576529 
##      1210      1211      1218      1219      1220      1228      1229 
## 0.4992834 0.3713519 0.4527607 0.4103940 0.5020857 0.3265628 0.4070692 
##      1231      1232      1235      1237      1238      1239      1240 
## 0.4180884 0.4485573 0.4159748 0.5063841 0.4340709 0.5138411 0.4742766 
##      1243      1244      1245      1246      1249      1250      1251 
## 0.4300337 0.4854145 0.4568217 0.4719493 0.4425490 0.2763592 0.4169960 
##      1252      1253      1257      1258      1259      1260      1263 
## 0.4228618 0.4375856 0.4399842 0.4437602 0.4076867 0.4512171 0.4922540 
##      1264      1265      1266      1268      1270      1272      1273 
## 0.4496972 0.4408391 0.4613101 0.3707820 0.4362557 0.3947202 0.5107538 
##      1274      1286      1287      1289      1295      1296      1297 
## 0.3428778 0.4827547 0.3738930 0.4686008 0.5022757 0.4453513 0.3668398 
##      1299      1300      1301      1304      1305      1310      1312 
## 0.5059329 0.4112964 0.4113201 0.4609301 0.4611913 0.5138411 0.5045080 
##      1313      1316      1322      1323      1324      1328      1330 
## 0.3333548 0.4792875 0.4424540 0.4398655 0.4635662 0.4178746 0.4414803 
##      1332      1333      1334      1339      1340      1348      1350 
## 0.5085690 0.5077853 0.3929628 0.5138411 0.3942214 0.4580091 0.4850820 
##      1351      1352      1355      1362      1365      1366      1368 
## 0.4035782 0.4221256 0.4143362 0.5138411 0.4934651 0.4017734 0.5018007 
##      1369      1370      1374      1375      1376      1380      1382 
## 0.4223393 0.3881419 0.4166872 0.5121312 0.4401979 0.5125824 0.4644211 
##      1384      1388      1389      1390      1393      1395      1396 
## 0.3891631 0.4851770 0.3817299 0.4798337 0.5032256 0.3622564 0.4395092 
##      1400      1401      1404      1405      1407      1412      1413 
## 0.4744191 0.3562956 0.3933665 0.4490560 0.4463250 0.4337622 0.4517871 
##      1416      1427      1428      1429      1430      1431      1434 
## 0.4871244 0.4045994 0.3896143 0.4205582 0.4478449 0.3897330 0.4884068 
##      1435      1439      1440      1441      1443      1448      1459 
## 0.4517633 0.4146211 0.4768651 0.4662497 0.4918028 0.5138411 0.3849121 
##      1462      1463      1465      1466      1476      1484      1486 
## 0.4978823 0.4725667 0.4550168 0.4979773 0.4323135 0.3727531 0.3807325 
##      1492      1493      1495      1499      1501      1502      1503 
## 0.4059055 0.4583416 0.4584365 0.4213656 0.4307937 0.4906866 0.4551118 
##      1504      1505      1506      1509      1510      1511      1521 
## 0.3798300 0.4862219 0.4597427 0.4496735 0.4097765 0.4487710 0.4524758 
##      1524      1525      1526      1528      1530      1531      1534 
## 0.4752028 0.4037682 0.3255179 0.4088741 0.3427354 0.4330735 0.4452088 
##      1535      1537      1538      1540      1542      1546      1547 
## 0.3367271 0.3117677 0.3555119 0.3429728 0.4472274 0.4771501 0.4535444 
##      1549      1550      1552      1555      1556      1559      1560 
## 0.4724480 0.4630912 0.4798337 0.5075003 0.4628537 0.4757252 0.4527607 
##      1561      1571      1572      1573      1577      1578      1582 
## 0.4974548 0.4236929 0.4071167 0.4437839 0.3830360 0.3787614 0.4153098 
##      1584      1588      1591      1592      1594      1598      1599 
## 0.4561092 0.4679833 0.3145463 0.4888342 0.4179696 0.4179221 0.3901842 
##      1600      1601      1605      1606      1607      1609      1614 
## 0.4049794 0.4218643 0.4313161 0.4351633 0.4614526 0.3938177 0.4062380 
##      1615      1617      1619      1622      1623      1624      1628 
## 0.4636612 0.4828734 0.4169722 0.4243341 0.4085416 0.4571541 0.4368257 
##      1629      1631      1632      1633      1634      1636      1637 
## 0.3092267 0.4605739 0.4773164 0.4694320 0.3388407 0.4518820 0.4260915 
##      1638      1640      1641      1642      1647      1648      1649 
## 0.3960738 0.4247141 0.3858621 0.3722544 0.3568893 0.3690721 0.3583142 
##      1650      1651      1653      1658      1659      1661      1663 
## 0.3600003 0.4647061 0.3888543 0.4912328 0.4046706 0.4826835 0.4394142 
##      1664      1666      1667      1668      1669      1672      1673 
## 0.3439940 0.4019159 0.3931528 0.4409341 0.4500772 0.4320761 0.4480823 
##      1674      1676      1680      1681      1685      1690      1692 
## 0.4242154 0.4862219 0.4346171 0.2905131 0.3792838 0.4576054 0.4461350 
##      1694      1698      1699      1701      1702      1703      1704 
## 0.4236217 0.4221493 0.4444251 0.4758677 0.4495785 0.2950727 0.4226480 
##      1709      1713      1714      1717      1720      1724      1725 
## 0.4610489 0.4062618 0.4390105 0.4909241 0.3455614 0.4997109 0.4432140 
##      1726      1727      1731      1733      1734      1738      1741 
## 0.4575104 0.4479873 0.3528758 0.4638986 0.4374669 0.4566317 0.4439502 
##      1743      1744      1745      1746      1747      1749      1750 
## 0.4002297 0.4886442 0.3766003 0.4455650 0.4446626 0.4587928 0.4591252 
##      1751      1753      1754      1755      1756      1757      1758 
## 0.4756302 0.3173010 0.3478650 0.4726142 0.4667009 0.4534257 0.4417178 
##      1759      1760      1761      1762      1763      1764      1767 
## 0.4842033 0.3222407 0.3803287 0.4219356 0.4233367 0.4207244 0.4472986 
##      1769      1770      1776      1780      1783      1785      1786 
## 0.3639425 0.4309361 0.4500534 0.4408629 0.4646586 0.3846747 0.4981198 
##      1791      1792      1795      1796      1797      1799      1801 
## 0.5127012 0.4403642 0.4399130 0.4625925 0.4459925 0.4464912 0.4459925 
##      1802      1805      1808      1809      1812      1818      1820 
## 0.4398417 0.4673659 0.4601939 0.4971224 0.4417653 0.4926814 0.4127213 
##      1823      1824      1825      1826      1828      1829      1830 
## 0.4154998 0.3913479 0.3727531 0.3529233 0.4333110 0.4556580 0.4251891 
##      1831      1841      1844      1846      1847      1849      1853 
## 0.4631149 0.4475599 0.4413379 0.4354720 0.4222443 0.4441401 0.4120563 
##      1854      1856      1860      1862      1868      1871      1879 
## 0.4662497 0.4526657 0.4346171 0.3842947 0.4600039 0.4759865 0.4378944 
##      1882      1883      1884      1887      1888      1889      1891 
## 0.4984760 0.4608351 0.5029882 0.3304338 0.4290125 0.4027945 0.5074766 
##      1898      1899      1909      1911      1917      1918      1919 
## 0.4213894 0.4416228 0.3626838 0.4344746 0.5138411 0.3840572 0.4472512 
##      1921      1923      1925      1926      1927      1930      1935 
## 0.4293213 0.5138411 0.4908528 0.4586978 0.4273739 0.4762952 0.4929427 
##      1937      1939      1944      1947      1948      1949      1950 
## 0.4415041 0.4346884 0.4715218 0.4715456 0.4633999 0.4526657 0.3981399 
##      1951      1952      1953      1955      1958      1962      1965 
## 0.3438040 0.4335247 0.4820660 0.4359708 0.4353296 0.4482961 0.4260678 
##      1968      1969      1970      1977      1985      1988      1990 
## 0.4626400 0.4466099 0.4070455 0.4956500 0.4437127 0.4121513 0.4692420 
##      1991      1992      1993      1996      2000      2003      2005 
## 0.4986660 0.3151400 0.4260678 0.4450188 0.3686209 0.4348546 0.3720644 
##      2007      2010      2011      2014      2015      2017      2018 
## 0.3960975 0.3998023 0.4235030 0.4059055 0.5138411 0.3770515 0.4201070 
##      2019      2020      2022      2023      2025      2027      2030 
## 0.4614763 0.4583178 0.5138411 0.5013495 0.5138411 0.4440926 0.4134337 
##      2031      2036      2037      2041      2049      2050      2053 
## 0.4530695 0.4296062 0.4915415 0.4216506 0.4187771 0.5138411 0.5138411 
##      2055      2059      2060      2064      2067      2071      2072 
## 0.4019396 0.5138411 0.4474649 0.4577004 0.4193945 0.5043418 0.5138411 
##      2073      2075      2076      2077      2078      2084      2085 
## 0.3803287 0.4608114 0.4289650 0.4802374 0.4563230 0.4532357 0.4582228 
##      2087      2088      2089      2093      2094      2096      2101 
## 0.2960939 0.4345934 0.5138411 0.4590778 0.4315061 0.4214131 0.4980010 
##      2105      2110      2111      2112      2117      2118      2120 
## 0.4232417 0.4036495 0.4776963 0.4782900 0.3170398 0.4474886 0.4339047 
##      2121      2122      2128      2136      2141      2142      2143 
## 0.4255691 0.4575579 0.4129825 0.4324085 0.4918740 0.4754878 0.4965524 
##      2144      2145      2150      2151      2155      2156      2157 
## 0.5138411 0.4274214 0.4220306 0.4124363 0.4582941 0.4489373 0.4648011 
##      2158      2159      2162      2164      2167      2169      2173 
## 0.3823236 0.4417653 0.4761052 0.4725430 0.4192758 0.4627825 0.4619275 
##      2174      2177      2179      2185      2192      2193      2196 
## 0.4423353 0.4018684 0.4001822 0.3731568 0.4827072 0.4755590 0.4324798 
##      2199      2201      2202      2205      2209      2211      2213 
## 0.4914228 0.4257115 0.3036696 0.4765564 0.5138411 0.5037006 0.4763427 
##      2215      2216      2217      2218      2227      2228      2229 
## 0.4663922 0.4629962 0.4427865 0.4549456 0.4249279 0.4570592 0.3555119 
##      2231      2232      2238      2241      2243      2254      2255 
## 0.4568454 0.3419042 0.4269227 0.4281814 0.4708806 0.4430002 0.4874568 
##      2259      2260      2261      2263      2264      2268      2269 
## 0.4666059 0.4762239 0.4681258 0.4379894 0.3798300 0.3500498 0.2763592 
##      2271      2272      2273      2279      2280      2282      2283 
## 0.4582466 0.5037956 0.4434514 0.4525470 0.4350683 0.4346884 0.3859333 
##      2287      2294      2295      2296      2298      2300      2301 
## 0.4268990 0.2940278 0.4790975 0.4029845 0.4447576 0.4197507 0.4200357 
##      2302      2305      2307      2309      2311      2312      2313 
## 0.4253791 0.4114864 0.4557530 0.4131250 0.3803287 0.4301287 0.5138411 
##      2316      2319      2326      2328      2331      2333      2335 
## 0.3926541 0.4534732 0.4261153 0.5138411 0.3710907 0.3627788 0.3841285 
##      2339      2344      2352      2353      2357      2360      2362 
## 0.4416466 0.5138411 0.4539481 0.4483436 0.4364220 0.4412666 0.4030083 
##      2363      2365      2366      2368      2369      2372      2373 
## 0.4269464 0.4421928 0.3311700 0.4459925 0.5077615 0.3822998 0.3328086 
##      2376      2377      2378      2393      2397      2398      2402 
## 0.5138411 0.5138411 0.3195334 0.4668909 0.4573204 0.5138411 0.4835146 
##      2403      2407      2408      2409      2412      2416      2417 
## 0.4239304 0.3386744 0.4012509 0.2928642 0.4539244 0.3121239 0.3100578 
##      2420      2421      2422      2425      2426      2427      2430 
## 0.3367271 0.4276114 0.3426166 0.3602615 0.5002334 0.3667448 0.3586941 
##      2431      2434      2435      2436      2437      2440      2442 
## 0.3649637 0.3450152 0.4947000 0.4491985 0.3709245 0.3645362 0.4397230 
##      2443      2444      2445      2446      2448      2450      2452 
## 0.4067367 0.5138411 0.4255216 0.4624500 0.3753179 0.4715930 0.3815162 
##      2454      2455      2462      2463      2466      2467      2468 
## 0.4096340 0.3906355 0.3389356 0.4890480 0.4678408 0.3892343 0.4226718 
##      2469      2474      2477      2479      2481      2482      2485 
## 0.4991409 0.4822560 0.4167347 0.4989985 0.4232655 0.2963789 0.4731367 
##      2486      2487      2488      2489      2494      2496      2497 
## 0.4525945 0.4329785 0.4813773 0.4735167 0.5138411 0.4343796 0.3827986 
##      2498      2499      2500      2501      2503      2504      2505 
## 0.4517633 0.3594778 0.5138411 0.3678135 0.4509084 0.4233605 0.5138411 
##      2507      2508      2509      2510      2511      2514      2517 
## 0.4470849 0.4425965 0.5138411 0.4974548 0.3450152 0.5032969 0.4554205 
##      2518      2520      2521      2524      2525      2526      2527 
## 0.3719931 0.4868156 0.5024657 0.4437602 0.4290363 0.3678609 0.4328597 
##      2535      2537      2541      2542      2543      2544      2548 
## 0.3605465 0.4327648 0.4284188 0.3844372 0.5123212 0.5138411 0.4781950 
##      2549      2551      2552      2553      2555      2557      2558 
## 0.5101126 0.3480550 0.3898518 0.4022008 0.5138411 0.4439976 0.5138411 
##      2560      2561      2563      2565      2566      2569      2571 
## 0.5019670 0.3654149 0.4396280 0.4128400 0.3628263 0.4065230 0.4436177 
##      2572      2573      2574      2575      2576      2577      2578 
## 0.4593152 0.4425965 0.3894955 0.4575341 0.4682920 0.5138411 0.4025571 
##      2580      2581      2582      2583      2586      2587      2590 
## 0.4821847 0.4327648 0.3650349 0.4443301 0.4237642 0.4376331 0.4248329 
##      2594      2595      2596      2597      2598      2599      2600 
## 0.4051694 0.4679358 0.4382981 0.4505284 0.3871445 0.4098003 0.4089691 
##      2601      2602      2603      2604      2605      2606      2607 
## 0.3809937 0.4136475 0.3745342 0.3977837 0.4095865 0.3926066 0.4225293 
##      2608      2609      2610      2611      2612      2613      2614 
## 0.3926303 0.4027470 0.4167822 0.3759353 0.3948151 0.3912292 0.4368494 
##      2615      2617      2618      2620      2621      2624      2625 
## 0.3732993 0.4244291 0.3900180 0.4690045 0.4013934 0.4027708 0.5138411 
##      2626      2630      2631      2632      2636      2640      2642 
## 0.5138411 0.5138411 0.3470813 0.4139799 0.3740117 0.4699782 0.3322624 
##      2643      2644      2645      2646      2647      2648      2651 
## 0.4659647 0.4586740 0.4477736 0.3547044 0.4107502 0.4648011 0.4942726 
##      2653      2654      2655      2657      2658      2659      2660 
## 0.5138411 0.5138411 0.5138411 0.4742528 0.4706194 0.5138411 0.5138411 
##      2664      2666      2668      2669      2672      2675      2677 
## 0.4251653 0.3676947 0.4407679 0.4943438 0.3789751 0.4880268 0.4379894 
##      2679      2681      2686      2691      2692      2694      2696 
## 0.4998771 0.3616152 0.4183971 0.3278215 0.3034559 0.4598852 0.3927253 
##      2697      2700      2702      2704      2705      2710      2713 
## 0.4044332 0.3958601 0.4357570 0.4499822 0.4240254 0.4667959 0.4736591 
##      2714      2716      2718      2720      2721      2722      2726 
## 0.3766953 0.4235030 0.4326223 0.4289413 0.3763391 0.4238117 0.5138411 
##      2727      2728      2734      2735      2738      2739      2740 
## 0.4218643 0.4092065 0.3857433 0.3876194 0.4117239 0.4500534 0.3440415 
##      2741      2742      2743      2744      2745      2746      2747 
## 0.4285613 0.4205819 0.3789988 0.3789514 0.3988998 0.4028420 0.4154048 
##      2749      2750      2751      2752      2755      2758      2763 
## 0.4257590 0.4503384 0.3885219 0.3857671 0.4626637 0.3663411 0.4521670 
##      2764      2767      2770      2775      2780      2782      2788 
## 0.4184921 0.4173047 0.4120326 0.4535207 0.3580767 0.4467999 0.4546131 
##      2791      2792      2795      2799      2803      2805      2807 
## 0.4192283 0.3787376 0.4212944 0.4292025 0.4631387 0.4133387 0.4805936 
##      2810      2814      2817      2819      2821      2822      2823 
## 0.4728517 0.3629213 0.4907341 0.4518820 0.5138411 0.5036531 0.3728481 
##      2828      2830      2833      2834      2836      2839      2842 
## 0.3341623 0.4486998 0.4544706 0.4282763 0.4094203 0.4031033 0.4713318 
##      2843      2844      2848      2849      2852      2855      2856 
## 0.5138411 0.4491035 0.3673385 0.4532594 0.3659373 0.4560855 0.4153098 
##      2858      2862      2865      2867      2868      2871      2876 
## 0.4563230 0.4316723 0.4354483 0.3805900 0.4763427 0.4868631 0.4164972 
##      2877      2878      2884      2887      2888      2890      2891 
## 0.4299862 0.4082329 0.4472749 0.5138411 0.4636137 0.4346884 0.4773164 
##      2893      2894      2900      2902      2903      2904      2911 
## 0.4546131 0.4237879 0.4607164 0.4732554 0.4883355 0.5072391 0.4767464 
##      2913      2914      2915      2922      2923      2924      2927 
## 0.3358721 0.5098276 0.4410766 0.4296537 0.4467287 0.4413141 0.4118188 
##      2931      2935      2936      2937      2938      2940      2948 
## 0.4327173 0.4518346 0.4510271 0.4567979 0.4844408 0.4578903 0.4889055 
##      2951      2954      2956      2966      2971      2974      2975 
## 0.3540632 0.3869545 0.4392480 0.4021296 0.4527370 0.5138411 0.4528082 
##      2976      2979      2981      2982      2984      2988      3000 
## 0.4552068 0.5138411 0.4998771 0.4670096 0.4663447 0.4323135 0.4614051 
##      3004      3005      3016      3018      3019      3022      3023 
## 0.4055018 0.5013258 0.4319336 0.5138411 0.4679596 0.3655099 0.5028457 
##      3025      3026      3029      3030      3031      3033      3034 
## 0.4933701 0.4166872 0.4500772 0.4503859 0.4741816 0.3783814 0.4252603 
##      3041      3044      3049      3053      3054      3058      3060 
## 0.4908528 0.5071678 0.4025333 0.4589115 0.4544943 0.4336434 0.4283713 
##      3062      3063      3065      3067      3068      3071      3074 
## 0.4176609 0.4543519 0.4199882 0.4373007 0.4695032 0.4657747 0.4592440 
##      3076      3078      3081      3082      3083      3086      3103 
## 0.4015834 0.4367782 0.4631862 0.4684345 0.4788362 0.3719694 0.5138411 
##      3104      3107      3109      3110      3112      3114      3115 
## 0.4013221 0.4287751 0.4363982 0.4610251 0.4792400 0.4345696 0.4990460 
##      3118      3123      3125      3126      3128      3129      3130 
## 0.5138411 0.4109402 0.4922540 0.4471324 0.4184683 0.3963825 0.4610251 
##      3131      3132      3133      3140      3141      3142      3147 
## 0.4542331 0.4719255 0.4674134 0.4410054 0.4258065 0.3683359 0.4600989 
##      3151      3152      3156      3157      3162      3164      3167 
## 0.4016071 0.3651299 0.4694557 0.4871006 0.4141462 0.3952664 0.4467999 
##      3169      3171      3179      3181      3183      3184      3185 
## 0.4655135 0.4539719 0.4817573 0.4159985 0.4998771 0.4848920 0.4860794 
##      3186      3187      3192      3193      3195      3196      3197 
## 0.3724681 0.3493136 0.4551356 0.4893092 0.4917553 0.3347797 0.4006335 
##      3199      3200      3204      3205      3207      3210      3211 
## 0.4005860 0.4537819 0.4965286 0.5035106 0.2883520 0.4562280 0.3905642 
##      3214      3217      3218      3219      3220      3221      3237 
## 0.4568692 0.4498635 0.4698119 0.4240254 0.5121787 0.4445439 0.4120563 
##      3238      3239      3240      3241      3242      3247      3248 
## 0.4663447 0.3688109 0.4608114 0.4451138 0.3842472 0.4577479 0.4989985 
##      3250      3252      3253      3255      3256      3260      3261 
## 0.3349934 0.4503384 0.4312449 0.4567029 0.5013258 0.3790701 0.4524995 
##      3262      3263      3265      3266      3267      3269      3270 
## 0.4949613 0.4361132 0.4655610 0.4994497 0.4621413 0.3470100 0.4175659 
##      3275      3278      3282      3283      3284      3288      3289 
## 0.4439027 0.3577442 0.3408593 0.4981435 0.4785038 0.4478686 0.4040294 
##      3290      3291      3294      3295      3296      3297      3298 
## 0.4917553 0.4525232 0.4671521 0.4662972 0.4166872 0.4395330 0.4460637 
##      3300      3301      3302      3303      3305      3306      3309 
## 0.4155711 0.4810686 0.4520483 0.4017496 0.4996872 0.5138411 0.4033645 
##      3313      3316      3317      3318      3319      3320      3321 
## 0.4822560 0.4692657 0.4358520 0.4753690 0.4571067 0.4785038 0.4861744 
##      3322      3323      3324      3325      3326      3327      3328 
## 0.4688858 0.4869106 0.4712843 0.4776726 0.4868156 0.4748703 0.4805461 
##      3329      3330      3331      3332      3333      3334      3336 
## 0.3957888 0.4564654 0.4616426 0.4647773 0.4539481 0.4743003 0.4869106 
##      3339      3343      3344      3345      3346      3347      3349 
## 0.5093527 0.3767903 0.3009860 0.4282051 0.4415041 0.5086165 0.4138137 
##      3351      3352      3353      3354      3355      3358      3359 
## 0.4317198 0.4533307 0.4667722 0.4025096 0.4593865 0.4294400 0.4789787 
##      3362      3366      3369      3371      3373      3374      3375 
## 0.4443539 0.3346847 0.4840608 0.4573204 0.4138137 0.4395567 0.4773876 
##      3376      3379      3380      3381      3383      3384      3385 
## 0.4471562 0.4598377 0.4405304 0.4832059 0.4702394 0.4737779 0.4330260 
##      3386      3388      3391      3392      3393      3394      3395 
## 0.5138411 0.4938214 0.4620700 0.3167786 0.3329511 0.4544706 0.4229568 
##      3396      3404      3405      3406      3408      3411      3412 
## 0.4413853 0.4738491 0.4973123 0.5060754 0.3935090 0.3752704 0.4747991 
##      3414      3415      3417      3420      3421      3422      3424 
## 0.4033645 0.3692858 0.4987847 0.4307462 0.4630912 0.3506435 0.3843897 
##      3428      3429      3430      3434      3435      3437      3438 
## 0.2971151 0.4546606 0.4690757 0.4261153 0.4317911 0.4587690 0.3537545 
##      3439      3440      3446      3447      3450      3451      3453 
## 0.4614526 0.4449476 0.4462062 0.4156661 0.4687433 0.4263052 0.4616426 
##      3456      3457      3458      3460      3461      3462      3463 
## 0.4557530 0.3803050 0.3987098 0.3972375 0.3552507 0.4640886 0.4033645 
##      3465      3468      3469      3474      3475      3480      3481 
## 0.4202020 0.4167347 0.4395330 0.4135762 0.3998498 0.4111302 0.4175659 
##      3484      3485      3486      3487      3488      3489      3490 
## 0.4039344 0.4318148 0.4122938 0.4311974 0.4272314 0.4031508 0.4131250 
##      3491      3492      3493      3494      3496      3502      3504 
## 0.4453513 0.4273977 0.4771264 0.3875482 0.4322185 0.3951951 0.4453988 
##      3505      3507      3509      3511      3512      3517      3521 
## 0.4601464 0.4219118 0.4998296 0.4763189 0.4507421 0.4482011 0.4732079 
##      3523      3525      3526      3528      3533      3536      3539 
## 0.4116051 0.4853907 0.4948663 0.5072866 0.4872906 0.4213181 0.4883593 
##      3540      3541      3542      3543      3544      3546      3548 
## 0.4039582 0.4728042 0.4127213 0.3913479 0.4245479 0.3944114 0.5138411 
##      3550      3552      3553      3557      3562      3564      3567 
## 0.5138411 0.3865983 0.4083516 0.4942251 0.4745378 0.4981435 0.3850071 
##      3572      3574      3577      3578      3579      3580      3583 
## 0.4102277 0.4109639 0.3791176 0.4002060 0.4878368 0.4529745 0.4445676 
##      3587      3589      3591      3593      3601      3605      3607 
## 0.3667448 0.3889256 0.4474886 0.4245716 0.4006572 0.4188246 0.5108251 
##      3609      3611      3621      3622      3623      3624      3628 
## 0.5138411 0.4300100 0.4346884 0.4598852 0.4540669 0.4505284 0.5005658 
##      3629      3630      3632      3633      3635      3641      3645 
## 0.4145024 0.4499109 0.4472037 0.4392243 0.3074455 0.3962163 0.4721393 
##      3649      3654      3656      3659      3660      3668      3671 
## 0.4055018 0.5138411 0.4078292 0.4344984 0.3775027 0.4789075 0.4773164 
##      3674      3675      3678      3681      3682      3683      3696 
## 0.3860996 0.3665073 0.4785275 0.4093253 0.3892818 0.3899705 0.4112489 
##      3699      3700      3702      3703      3704      3706      3707 
## 0.3612115 0.4125788 0.4762477 0.4087791 0.4259490 0.4713793 0.4181359 
##      3708      3711      3712      3715      3717      3722      3724 
## 0.4977161 0.4993309 0.4976686 0.4833009 0.4635187 0.3872632 0.3936752 
##      3727      3729      3731      3732      3735      3746      3748 
## 0.5003521 0.4661310 0.4221731 0.3951001 0.4227430 0.4316248 0.4401504 
##      3754      3755      3759      3760      3763      3766      3768 
## 0.3939602 0.4254978 0.4900216 0.3692858 0.3122189 0.4624500 0.4639461 
##      3769      3772      3774      3780      3783      3784      3785 
## 0.4513121 0.4984760 0.4175659 0.4007997 0.3557494 0.3915854 0.4153098 
##      3786      3787      3789      3790      3798      3799      3800 
## 0.4494835 0.3942689 0.4981673 0.4011322 0.4748228 0.4450426 0.4221731 
##      3801      3802      3803      3804      3806      3809      3810 
## 0.3705445 0.4234555 0.5135798 0.4748465 0.3924166 0.4090403 0.4829684 
##      3811      3813      3814      3816      3817      3818      3830 
## 0.4566317 0.3996598 0.4334060 0.3667448 0.4789550 0.3913479 0.5084740 
##      3832      3836      3838      3839      3850      3855      3859 
## 0.4364695 0.4604076 0.3879757 0.3591454 0.4930139 0.4212944 0.5086877 
##      3862      3864      3865      3866      3867      3868      3870 
## 0.4697169 0.5037718 0.4359708 0.4625212 0.4939876 0.4287513 0.5138411 
##      3871      3872      3873      3874      3875      3877      3879 
## 0.4386781 0.5030594 0.5117987 0.4701444 0.3171348 0.4324798 0.4674371 
##      3881      3882      3883      3885      3886      3888      3889 
## 0.4320998 0.4989510 0.5103501 0.4739204 0.4507659 0.4911616 0.4179934 
##      3891      3892      3893      3894      3897      3906      3907 
## 0.5090677 0.3899230 0.3547757 0.4659172 0.4090641 0.4466812 0.4198932 
##      3909      3910      3912      3913      3914      3916      3919 
## 0.4504572 0.4346409 0.3886169 0.3453714 0.4104652 0.4324560 0.3293651 
##      3920      3922      3924      3925      3926      3933      3935 
## 0.4495310 0.4348783 0.5030357 0.4585553 0.4757490 0.4323135 0.4708331 
##      3938      3941      3943      3944      3947      3949      3951 
## 0.3001074 0.4637561 0.4196558 0.4687433 0.4019396 0.3518784 0.4409816 
##      3953      3954      3960      3964      3966      3968      3969 
## 0.4724955 0.3881419 0.4984997 0.4397942 0.4488423 0.4553018 0.3452289 
##      3970      3973      3974      3975      3977      3980      3990 
## 0.3818011 0.4664872 0.3330936 0.4878131 0.3225731 0.4925390 0.4816860 
##      3997      3999      4002      4003      4006      4011      4013 
## 0.4794537 0.4530220 0.5074766 0.5112288 0.4366832 0.4522620 0.4941538 
##      4014      4020      4025      4028      4030      4032      4036 
## 0.4975498 0.4539956 0.5046268 0.4544943 0.4646586 0.4872906 0.4744191 
##      4037      4046      4047      4048      4051      4053      4054 
## 0.4505521 0.4136000 0.4712843 0.4074729 0.4771976 0.3737505 0.4539006 
##      4056      4058      4059      4061      4062      4065      4067 
## 0.3774790 0.4405542 0.4346884 0.4237167 0.3674097 0.4206769 0.3660323 
##      4068      4069      4070      4074      4077      4082      4087 
## 0.4146211 0.4343084 0.3869307 0.4581041 0.4443301 0.3531846 0.5097801 
##      4091      4093      4094      4095      4101      4102      4106 
## 0.3747717 0.4482011 0.4234080 0.4606214 0.4800949 0.4250941 0.4311736 
##      4108      4109      4111      4112      4113      4115      4116 
## 0.3918941 0.4409579 0.4734217 0.4683395 0.4465150 0.4554443 0.4573679 
##      4121      4122      4124      4125      4126      4127      4131 
## 0.5005658 0.4062618 0.4496022 0.4567029 0.4586028 0.4347834 0.4166635 
##      4132      4134      4140      4141      4143      4144      4148 
## 0.4393905 0.3601190 0.4269939 0.4365407 0.4704056 0.3889256 0.5132711 
##      4149      4153      4157      4158      4159      4160      4161 
## 0.4405542 0.4705956 0.4751078 0.4837996 0.4575341 0.4291075 0.4671521 
##      4162      4163      4164      4165      4166      4167      4168 
## 0.4806411 0.5138411 0.4919927 0.4866969 0.4115814 0.4890242 0.5005421 
##      4169      4170      4180      4191      4193      4195      4198 
## 0.4890005 0.4886917 0.5082840 0.4759627 0.3960975 0.5138411 0.3781439 
##      4199      4202      4204      4208      4209      4217      4218 
## 0.4510509 0.4945338 0.4407679 0.4965761 0.4790975 0.4823510 0.5096851 
##      4219      4220      4221      4222      4223      4224      4225 
## 0.5039143 0.4528795 0.4271839 0.4040294 0.3847697 0.3297688 0.4337147 
##      4226      4227      4228      4233      4234      4235      4236 
## 0.4538294 0.4521195 0.4218643 0.5138411 0.4874568 0.4896417 0.4581753 
##      4239      4240      4241      4242      4243      4244      4245 
## 0.4912091 0.4634949 0.3378907 0.4628775 0.4725667 0.3916091 0.3710670 
##      4246      4248      4249      4252      4254      4256      4258 
## 0.4569167 0.4512646 0.3432578 0.3430678 0.3818961 0.4100852 0.4990697 
##      4260      4261      4262      4263      4265      4267      4268 
## 0.5068829 0.2884470 0.4171622 0.4346884 0.4576529 0.5075478 0.5062654 
##      4272      4284      4298      4311      4319      4321      4330 
## 0.3982824 0.4699069 0.5138411 0.4977873 0.4810448 0.4742528 0.4280864 
##      4335      4338      4341      4343      4347      4352      4358 
## 0.4156898 0.4651335 0.4071405 0.4993784 0.5061704 0.4242866 0.4789075 
##      4363      4370      4371      4376      4382      4385      4386 
## 0.3951001 0.5005183 0.4873144 0.4645873 0.4378469 0.4501247 0.4185396 
##      4412      4429      4437      4440      4446      4462      4466 
## 0.4745378 0.4307224 0.4315061 0.4162123 0.4649436 0.4678408 0.4942726 
##      4470      4471      4472      4473      4485      4494      4500 
## 0.5014920 0.5085690 0.4948663 0.4231230 0.4303187 0.4527845 0.5138411 
##      4503      4505      4507      4509      4516      4540      4544 
## 0.4450901 0.3925116 0.4965049 0.3851971 0.4578903 0.5030357 0.5138411 
##      4552      4556      4565      4584      4601      4606      4613 
## 0.4463725 0.4273027 0.3678609 0.4489135 0.4225055 0.4658460 0.4859845 
##      4616      4617      4619      4627      4628      4629      4635 
## 0.4965761 0.4560855 0.4595527 0.4583178 0.4643261 0.4770789 0.3878807 
##      4636      4641      4643      4645      4672      4678      4680 
## 0.4802611 0.5138411 0.3951001 0.4405542 0.5013970 0.4030083 0.5080703 
##      4700      4707      4712      4717      4718      4719      4731 
## 0.3377720 0.4164972 0.5138411 0.4803086 0.4239304 0.5138411 0.4544706 
##      4739      4754      4757      4792      4795      4805      4807 
## 0.3389594 0.3795688 0.4610726 0.5138411 0.4663447 0.4346884 0.4020821 
##      4811      4813      4819      4820      4847      4851      4860 
## 0.4611201 0.4695982 0.4648961 0.5138411 0.4897842 0.4508609 0.4410766 
##      4875      4877      4888      4889      4890      4891      4892 
## 0.4346884 0.4744903 0.4961962 0.4911141 0.4639461 0.4897604 0.5104926 
##      4897      4902      4905      4906      4909      4910      4912 
## 0.4605501 0.4872194 0.4596240 0.4164735 0.4426915 0.4933226 0.4346884 
##      4914      4934      4941      4945      4947      4949      4950 
## 0.5138411 0.4544706 0.4083041 0.3519259 0.3796163 0.4425965 0.3818961 
##      4951      4953      4954      4958      4959      4960      4962 
## 0.4459925 0.4697407 0.5097089 0.4686483 0.3704495 0.5138411 0.5138411 
##      4964      4966      4967      4969      4970      4971      4972 
## 0.5138411 0.3391019 0.4900929 0.5095902 0.5042468 0.5043418 0.5138411 
##      4988      4989      4991      4993      4997      4998      5003 
## 0.4544706 0.4968849 0.4579616 0.4760577 0.4160460 0.5138411 0.4706669 
##      5009      5016      5036      5043      5047      5056      5072 
## 0.4799049 0.4836809 0.4634237 0.3462026 0.5049355 0.4585790 0.4509321 
##      5086      5088      5090      5102      5114      5126      5129 
## 0.4396517 0.5048168 0.5060042 0.4222443 0.4961249 0.4466574 0.4684820 
##      5130      5131      5132      5133      5135      5139      5146 
## 0.4851295 0.4503859 0.4666772 0.4107264 0.4584365 0.5138411 0.5138411 
##      5152      5165      5170      5176      5186      5188      5190 
## 0.3931528 0.4874568 0.3547044 0.5138411 0.3914904 0.5138411 0.5003996 
##      5195      5199      5201      5204      5215      5223      5224 
## 0.3171823 0.5138411 0.4161885 0.4366832 0.4571067 0.5046268 0.4764852 
##      5225      5226      5256      5263      5264      5265      5266 
## 0.5058617 0.4991409 0.4579616 0.4326935 0.4281576 0.4113676 0.4913515 
##      5267      5271      5272      5280      5281      5288      5293 
## 0.4949613 0.5089015 0.4679358 0.3494324 0.3083242 0.5138411 0.5138411 
##      5297      5308      5313      5315      5318      5327      5339 
## 0.5138411 0.4412191 0.5070491 0.4970511 0.4715930 0.4536869 0.5138411 
##      5348      5364      5366      5369      5381      5433      5434 
## 0.4247854 0.4989985 0.3951001 0.4588165 0.4680308 0.3539920 0.2763592 
##      5437      5443      5451      5454      5455      5456      5458 
## 0.4703581 0.5138411 0.4060005 0.4483198 0.4748465 0.4740629 0.3048570 
##      5466      5472      5473      5474      5477      5482      5495 
## 0.4188483 0.4140512 0.4876468 0.3767903 0.4633049 0.5106351 0.5138411 
##      5508      5519      5520      5524      5528      5532      5533 
## 0.3589554 0.4474886 0.4145974 0.4035782 0.4304374 0.4652285 0.4293925 
##      5537      5558      5572      5585      5600      5610      5616 
## 0.5004708 0.5098514 0.4713318 0.4011322 0.4888342 0.5138411 0.4595527 
##      5627      5632      5634      5638      5646      5663      5664 
## 0.4926339 0.4358995 0.4544706 0.4510984 0.5138411 0.4750603 0.4396755 
##      5685      5689      5700      5705      5712      5718      5734 
## 0.3991373 0.4845833 0.4290363 0.4927289 0.4742528 0.4421928 0.4940588 
##      5735      5736      5737      5755      5823      5829      5830 
## 0.4850583 0.5102789 0.4389630 0.4064043 0.3818961 0.5026794 0.5024657 
##      5831      5832      5833      5834      5835      5836      5856 
## 0.5033681 0.5100651 0.4675559 0.4863407 0.4384881 0.4412904 0.3602853 
##      5858      5890      5898      5903      5904      5905      5910 
## 0.4636374 0.5138411 0.3680272 0.5138411 0.3914904 0.4955787 0.4712131 
##      5912      5919      5945      5946      5947      5948      5949 
## 0.3333073 0.4859132 0.5008746 0.5021570 0.4523808 0.4858420 0.4761764 
##      5950      5951      5977      5978      5998      6026      6028 
## 0.5012545 0.4259728 0.5113713 0.5044605 0.4984285 0.4488660 0.5138411 
##      6029      6030      6051      6061      6062      6067      6068 
## 0.5138411 0.5037956 0.3569368 0.4697644 0.4637561 0.5070016 0.4487473 
##      6069      6070      6071      6072      6073      6104      6105 
## 0.4977398 0.4618088 0.4733504 0.5081890 0.4374431 0.4435227 0.4188483 
##      6106      6107      6181      6183      6186      6195      6197 
## 0.4832059 0.3951001 0.4518820 0.5126299 0.5138411 0.4731367 0.4786463 
##      6220      6266      6267      6268      6269      6270      6271 
## 0.3821574 0.5058854 0.4906628 0.5090439 0.4854382 0.4346884 0.5024182 
##      6301      6305      6309      6310      6311      6312      6317 
## 0.3656286 0.5138411 0.5138411 0.4864357 0.3781439 0.4805699 0.4804036 
##      6332      6336      6375      6384      6391      6393      6400 
## 0.3998498 0.4799049 0.4928952 0.3536833 0.4120563 0.4968849 0.3159474 
##      6401      6419      6421      6491      6507      6508      6509 
## 0.3423316 0.5138411 0.4959349 0.4596715 0.4559667 0.4312924 0.4298200 
##      6510      6512      6513      6514      6515      6516      6518 
## 0.4534257 0.5009933 0.5138411 0.5084740 0.5084502 0.4967186 0.4835621 
##      6519      6520      6521      6526      6527      6547      6548 
## 0.5075003 0.5069066 0.3567468 0.5138411 0.5138411 0.5138411 0.5138411 
##      6549      6572      6579      6583      6584      6591      6671 
## 0.5138411 0.4678883 0.4899504 0.4171622 0.4449001 0.3555119 0.5138411 
##      6682      6700      6701      6702      6711      6712      6713 
## 0.4922540 0.4841558 0.4836809 0.4776488 0.4120563 0.4874568 0.4696219 
##      6717      6748      6750      6783      6784      6786      6787 
## 0.5103976 0.5138411 0.4763427 0.5049118 0.4883118 0.5018245 0.4919690 
##      6834      6837      6845      6846      6847      6848      6881 
## 0.5138411 0.5138411 0.4059055 0.4346884 0.4845121 0.4799049 0.5043418 
##      6887      6889      6918      6932      6936      6937      6940 
## 0.5138411 0.5138411 0.3027434 0.4874568 0.4762002 0.5065741 0.4388443 
##      6941      6943      6944      6945      6946      6948      6949 
## 0.5051492 0.4963624 0.4692182 0.4709281 0.5094477 0.4142887 0.4312449 
##      6952      6997      7002      7007      7014      7018      7040 
## 0.4663447 0.4274927 0.4274927 0.5138411 0.4850583 0.4212706 0.5138411 
##      7042      7057      7058      7082      7083      7086      7104 
## 0.5138411 0.5046505 0.5035106 0.4581278 0.4197507 0.4556818 0.4529982 
##      7105      7106      7107      7108      7109      7110      7111 
## 0.4819710 0.4711893 0.4404354 0.4554443 0.4554205 0.4479398 0.4985235 
##      7112      7113      7114      7115      7116      7117      7118 
## 0.5138411 0.4425965 0.4610726 0.4568454 0.4459925 0.4866731 0.4439976 
##      7119      7120      7121      7122      7123      7124      7125 
## 0.4791687 0.4425965 0.5138411 0.4815198 0.4401504 0.4708094 0.5138411 
##      7126      7127      7128      7129      7140      7154      7179 
## 0.4778626 0.4810923 0.4346884 0.4413616 0.4210094 0.4874568 0.4346884 
##      7195      7224      7225      7252 
## 0.4346884 0.5138411 0.5138411 0.4713318
describe(data2$SAT_AVG)
describe(data2$ADM_RATE)
describe(data2$UGDS)
sample_means50000 <- rep(NA, 50000)
for(i in 1:50000){
   samp <- sample(data2$SAT_AVG, 50)
   sample_means50000[i] <- mean(samp)
   }

#install.packages("gridExtra")
library(gridExtra)

describe(data2$SAT_AVG)
pnorm(1400, mean=1059, sd=210, lower.tail=FALSE)
## [1] 0.05220823
pnorm(800, mean=1059, sd=210, lower.tail=TRUE)
## [1] 0.1087257
pnorm(1400, mean=1055, sd=210, lower.tail=FALSE)
## [1] 0.05020625
pnorm(800, mean=1055, sd=210, lower.tail=TRUE)
## [1] 0.1123193
pnorm(1400, mean=1000, sd=200, lower.tail=FALSE)
## [1] 0.02275013
pnorm(800, mean=1000, sd=200, lower.tail=TRUE)
## [1] 0.1586553

Including Plots

library(corrplot)
## corrplot 0.84 loaded
corrplot(cormatrix, type="upper", order="original", tl.col="black", tl.srt=45)

pairs(with(data2,data.frame(ADM_RATE,SAT_AVG,UGDS,C150_4)))

pairs(with(public,data.frame(ADM_RATE,SAT_AVG,UGDS,C150_4)))

pairs(with(nonprofit,data.frame(ADM_RATE,SAT_AVG,UGDS,C150_4)))

pairs(with(forprofit,data.frame(ADM_RATE,SAT_AVG,UGDS,C150_4)))

qplot(SAT_AVG, COSTT4_A, data=data2, geom = "point") + stat_smooth(method="lm")
## Warning: Removed 6405 rows containing non-finite values (stat_smooth).
## Warning: Removed 6405 rows containing missing values (geom_point).

qplot(ADM_RATE, COSTT4_A, data=data2, geom = "point") + stat_smooth(method="lm")
## Warning: Removed 5707 rows containing non-finite values (stat_smooth).
## Warning: Removed 5707 rows containing missing values (geom_point).

qplot(SAT_AVG, UGDS, data=data2, geom = "point") + stat_smooth(method="lm")
## Warning: Removed 6399 rows containing non-finite values (stat_smooth).
## Warning: Removed 6399 rows containing missing values (geom_point).

qplot(ADM_RATE, UGDS, data=data2, geom = "point") + stat_smooth(method="lm")
## Warning: Removed 5505 rows containing non-finite values (stat_smooth).
## Warning: Removed 5505 rows containing missing values (geom_point).

qplot(SAT_AVG, C150_4, data=data2, geom = "point") + stat_smooth(method="lm")
## Warning: Removed 6432 rows containing non-finite values (stat_smooth).
## Warning: Removed 6432 rows containing missing values (geom_point).

qplot(ADM_RATE, C150_4, data=data2, geom = "point") + stat_smooth(method="lm")
## Warning: Removed 5897 rows containing non-finite values (stat_smooth).
## Warning: Removed 5897 rows containing missing values (geom_point).

qplot(SAT_AVG, PCTFLOAN, data=data2, geom = "point") + stat_smooth(method="lm")
## Warning: Removed 6401 rows containing non-finite values (stat_smooth).
## Warning: Removed 6401 rows containing missing values (geom_point).

qplot(ADM_RATE, PCTFLOAN, data=data2, geom = "point") + stat_smooth(method="lm")
## Warning: Removed 5508 rows containing non-finite values (stat_smooth).
## Warning: Removed 5508 rows containing missing values (geom_point).

qplot(SAT_AVG, PCTPELL, data=data2, geom = "point") + stat_smooth(method="lm")
## Warning: Removed 6401 rows containing non-finite values (stat_smooth).
## Warning: Removed 6401 rows containing missing values (geom_point).

qplot(ADM_RATE, PCTPELL, data=data2, geom = "point") + stat_smooth(method="lm")
## Warning: Removed 5508 rows containing non-finite values (stat_smooth).
## Warning: Removed 5508 rows containing missing values (geom_point).

qplot(data2$SAT_AVG, geom = "density", na.rm=TRUE)

qplot(data2$ADM_RATE, geom = "density", na.rm=TRUE)

qplot(data2$UGDS, geom = "density", na.rm=TRUE)

p1<-qplot(x = SAT_AVG, data = data2)
p2<-qplot(x = log10(SAT_AVG + 1), data = data2)
p3<-qplot(x = sqrt(SAT_AVG), data = data2)
grid.arrange(p1, p2, p3, ncol = 1)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 6399 rows containing non-finite values (stat_bin).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 6399 rows containing non-finite values (stat_bin).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 6399 rows containing non-finite values (stat_bin).

p1<-qplot(x = ADM_RATE, data = data2)
p2<-qplot(x = log10(ADM_RATE + 1), data = data2)
p3<-qplot(x = sqrt(ADM_RATE), data = data2)
grid.arrange(p1, p2, p3, ncol = 1)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 5505 rows containing non-finite values (stat_bin).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 5505 rows containing non-finite values (stat_bin).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 5505 rows containing non-finite values (stat_bin).

p1<-qplot(x = UGDS, data = data2)
p2<-qplot(x = log10(UGDS + 1), data = data2)
p3<-qplot(x = sqrt(UGDS), data = data2)
grid.arrange(p1, p2, p3, ncol = 1)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 713 rows containing non-finite values (stat_bin).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 713 rows containing non-finite values (stat_bin).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 713 rows containing non-finite values (stat_bin).

ANALYSES

Run descriptive statistics on all of the quantitative variables. At a minimum, your statistics should include the mean, median, mode, standard deviation, variance, minimum, and maximum scores.

Importing the data set into R data2<-read.csv(“/Users/munira/Desktop/Education/Masters/Illinois Institute of Technology/Coursework/545-Stats/Completed/Lab Projects/Project2Data.csv”, header=TRUE)

Making a dataframe containing all quantitative variables (numeric and integer) numvar<-data2[,sapply(data2,is.numeric)]

Running descriptive statistics, including everything required except mode describe(numvar) summary(numvar) The summary function is useful in that it lists the frequency of missing data (NAs)

There is no easy way in R to get mode, but it can be done with one variable at a time in the following way names(which(max(table(data2\(ADM_RATE))==table(data2\)ADM_RATE))) names(which(max(table(data2\(SAT_AVG))==table(data2\)SAT_AVG))) names(which(max(table(data2\(UGDS))==table(data2\)UGDS))) names(which(max(table(data2\(UGDS_WHITE))==table(data2\)UGDS_WHITE))) names(which(max(table(data2\(UGDS_BLACK))==table(data2\)UGDS_BLACK))) names(which(max(table(data2\(UGDS_HISP))==table(data2\)UGDS_HISP))) names(which(max(table(data2\(UGDS_ASIAN))==table(data2\)UGDS_ASIAN))) names(which(max(table(data2\(UGDS_AIAN))==table(data2\)UGDS_AIAN))) names(which(max(table(data2\(UGDS_NHPI))==table(data2\)UGDS_NHPI))) names(which(max(table(data2\(UGDS_2MOR))==table(data2\)UGDS_2MOR))) names(which(max(table(data2\(UGDS_NRA))==table(data2\)UGDS_NRA))) names(which(max(table(data2\(UGDS_UNKN))==table(data2\)UGDS_UNKN))) names(which(max(table(data2\(PPTUG_EF))==table(data2\)PPTUG_EF))) names(which(max(table(data2\(NPT4_PUB))==table(data2\)NPT4_PUB))) names(which(max(table(data2\(NPT4_PRIV))==table(data2\)NPT4_PRIV))) names(which(max(table(data2\(COSTT4_A))==table(data2\)COSTT4_A))) names(which(max(table(data2\(TUITFTE))==table(data2\)TUITFTE))) names(which(max(table(data2\(INEXPFTE))==table(data2\)INEXPFTE))) names(which(max(table(data2\(PFTFAC))==table(data2\)PFTFAC))) names(which(max(table(data2\(PCTPELL))==table(data2\)PCTPELL))) names(which(max(table(data2\(C150_4))==table(data2\)C150_4))) names(which(max(table(data2\(PFTFTUG1_EF))==table(data2\)PFTFTUG1_EF))) names(which(max(table(data2\(RET_FT4))==table(data2\)RET_FT4))) names(which(max(table(data2\(PCTFLOAN))==table(data2\)PCTFLOAN)))

  1. Provide an interpretation of the overall characteristics of the schools in this dataset. Compute and visualize covariances and correlations between all quantitative variables

Interpretation of overall characteristics The sample size for the variables vary considerably, with only 1304 for Average equivalent SAT as the smallest sample and 7270 for Net tuition revenue and Instructional expenditure as the biggest sample, while the total number of schools included were 7703. The range of Average SAT is 720 to 1545 with a mean of 1059.07 and positively skewed. The average Admission rate is 69%, reported for only 2198 out of 7703 schools, whereas the average Completion rate for first-time, full-time students is 48% based on 2481 out of 7703 schools. The total share of enrollment for undergraduates who are white is much higher than the rest of the groups, with a mean of 0.51 while all others have a mean below 0.20, based on 6990 out of 7703 schools - however, all groups have positive skewness and kurtosis except for whites which is negatively skewed and platykurtic. Average Net price for public schools is almost half (9264.66) of that for private schools (18230.18), according to data from 1911 public schools and 4688 private schools. Average Net tuition revenue per full-time equivalent student (10401.08) exceeds average Instructional expenses (7360.21), based on 7270 schools, but the distribution for both is quite disperse, positively skewed and leptokurtic. Average Cost of attendance is 24853.36 with the minimum cost at 4610 and the maximum at 79212, based on 4030 schools. 52% of all federal undergraduates receive a federal student loan. The distribution of Average net price for public institutions has 6 modes, Average SAT is bimodal, while all other variables have nly one mode - though a lot of variables have 0 as mode (13 out of the 24 quantitative variables).

Computing, printing and plotting correlation - rounding it makes the table neat cormatrix<-cor(numvar, use = “p”) round(cormatrix,2) corrplot(cormatrix, type=“upper”, order=“original”, tl.col=“black”, tl.srt=45)

Computing and printing covariance - rounding it makes many relationaships 0 due to small covariance values covmatrix<-cov(numvar, use = “p”) round(covmatrix,2)

  1. Pick any 4 variables and display their relations through scatterplots (you should present this as a scatterplot matrix for efficiency). In addition to the scatterplots, provide an interpretation of what you think about the direction and magnitude of the each of the relations you report.

pairs(with(data2,data.frame(ADM_RATE,SAT_AVG,UGDS,C150_4)))

Creating a scatterplot among the variables Admission rate, Average equivalent SAT of admitted students, Enrollment of students and Completion rate, the relationship differs between the various variables. The relationship between SAT average and Completion rate is linear in the positive direction and appears to be quite strong with most data points clustered around it. The relationship of Enrolled students with the rest of the variables appears to be curvilinear with maximum strength in the middle and low on both ends. It is non-linear between Admission rate and SAT average as well as Admission rate and Completion rate.

  1. Report the full covariance and correlation matrix for all variables and provide an interpretation of what variables are most strongly related (either positive or negative) and what variables are relatively unrelated to one another.

Correlation Matrix cormatrix

The relationship between Average net price for private Title IV institutions and Average cost of attendance is the strongest at 0.92270809. The relationship between SAT average and Completion rate is also quite strong at 0.80147835 - this was evident from the scatterplot also (as shown above). The strongest negative relationship is between SAT average and Percentage of undergraduates who receive a Pell Grant, with a correlation of -0.71224956. There doesn’t seem to be any relationship between share of enrolled undergraduates who are Native Hawaiian/Pacific Islander and a number of other variables, including average net price for private institutions, net tuition revenue, instructional expenditure, and proportion of full-time faculty. There is also no significant relationship between share of enrolled undergraduates of unknown race and instructional expenditures, or between share of enrolled undergraduates who are white and percentage of undergraduates who receive federal loan.

Covariance Matrix covmatrix

The covariance values are not standardized, so it is not possible to compare the covariance relationship among various pairs. The positive and negative values tell the direction of the relationship. Thus, for example, there is positive relationship between SAT average and completion rate but negative relationship between SAT average and undergraduates receiving a Pell grant, as indicated by the correlation matrix also. However, from the covariance values we cannot determine the magnitude of the relationships.

  1. What is the strongest relation in the data? What are the variables involved and what is the correlation? What is the weakest relation in the data? What are the variables involved and what is the correlation?

The strongest relation is between Average net price for private Title IV institutions and Average cost of attendance, with a positive correlation of 0.92270809. The weakest relation is between Total share of enrollment of undergraduates whose race is unknown and Instructional expenditures per full-time equivalent student, with a negative correlation of -0.000812433.

Conduct the same analyses as you did for Questions 1 through 4, but separately for Public, Private (non-profit), and Private (for profit).

Making subsets of data by Public (CONTROL=1), Non-profit (CONTROL=2) and For=profit (CONTROL=3) public<-subset(numvar, CONTROL==1) nonprofit<-subset(numvar, CONTROL==2) forprofit<-subset(numvar, CONTROL==3)

Running descriptive statistics, including everything required except mode describe(public) describe(nonprofit) describe(forprofit)

  1. Provide an interpretation of the characteristics of the schools within each of these groups.

Interpretation of characteristics for each group in comparison with overall The sample includes 2044 public schools (26.54%), 1956 non-profit schools (25.39%) and 3703 for-profit schools (48.07%). The range of Average SAT within each group is: - Public schools, 774 to 1400 with a mean of 1038.56, positive skeweness of 0.53 and kurtosis of 0.27 - Non-profit schools, 720 to 1545 with a mean of 1073.09, positive skewness of 0.81 and kurtosis of 0.88 - For-profit schools, 855 to 1211 with a mean of 995.67, positive skewness of 0.48 and negative kurtosis of -1.44 - Overall, 720 to 1545 with a mean of 1059.07, positive skewness of 0.82 and kurtosis of 1.11 The average Admission rate within each group is: - Public schools, 69% - Non-profit schools, 65% - For-profit schools, 83% - Overall, 69% The average Completion rate for first-time, full-time students within each group is: - Public schools, 46% - Non-profit schools, 54% - For-profit schools, 37% - Overall, 48% As with the overall averages, the total share of enrollment for undergraduates who are white is much higher than the rest of the ethnicities within the groups also - with a mean of 0.59, 0.57 and 0.43 in public, non-profit and for-profit institutions respectively while all other ethnicities had a mean below 0.14 in public/non-profit and below 0.24 in for-profit institutions. The disparity between average net tuition revenue and average instructional expenses per full-time equivalent student is much more in case of for-profit institutions (11207.99 and 4612.49 respectively) than in non-profit (15178.31 and 11332.52 respectively), whereas the tuition revenue is less than the instuctional expenses in public institutions (4505.03 and 8340.32 respectively). The percentage of undergraduates receiving a grant or loan is: - Public schools, 42% Pell grant and 32% federal student loan - Non-profit schools, 42% Pell grant and 56% federal student loan - For-profit schools, 65% Pell grant and 62% federal student loan - Overall, 53% Pell grant and 52% federal student loan

  1. Pick the same 4 variables that you did for Question 2 and compute scatterplots separately for each of the three groups. In addition to the scatterplots, provide an interpretation of what you think about the direction and magnitude of the each of the relations you report. Are they different from what you observed in Question 2?

pairs(with(public,data.frame(ADM_RATE,SAT_AVG,UGDS,C150_4))) pairs(with(nonprofit,data.frame(ADM_RATE,SAT_AVG,UGDS,C150_4))) pairs(with(forprofit,data.frame(ADM_RATE,SAT_AVG,UGDS,C150_4)))

Creating a scatterplot as before among the variables, Admission rate, Average equivalent SAT of admitted students, Enrollment of students and Completion rate, depicts the relationship between the various variables within the defined groups.

The relationship between SAT average and Completion rate was overall linear in the positive direction and quite strong with most data points clustered around it. Similar trend is seen in case of public and non-profit institutions, but in case of for-profit there are only a few scattered data points though still in the positive direction. The relationship of Enrolled students with the rest of the variables overall appeared to be curvilinear with maximum strength in the middle and low on both ends. It seems less curvilenear now with more prominent outliers. The relationship between Admission rate and SAT average as well as Admission rate and Completion rate shows the same trend as overall in case of public and non-profit institutions - non-linear or no relation - but appear to be different in case of for-profit institutions, with only a few data points for relationship between Admission rate and SAT average showing a linear trend and clustered data points for relationship between Admission rate and Completion rate showing range restriction.

  1. Within each of the thee subsets of schools, report the full covariance and correlation matrix and provide an interpretation of what variables are most strongly related (either positive or negative) and what variables are relatively unrelated to one another.

Computing correlations within each group cormatrix1<-cor(public, use = “p”) cormatrix2<-cor(nonprofit, use = “p”) cormatrix3<-cor(forprofit, use = “p”)

Printing the correlations cormatrix1 cormatrix2 cormatrix3

Strongest positive correlations Public: The relationship between Average net price for private Title IV institutions and Average cost of attendance is the strongest at 0.92270809 - same as overall. Non-profit: The relationship between Average SAT and Completion rate is the strongest at 0.8121477946. For-profit: The relationship is between Average cost of attendance and Average net price of private institutions is the strongest at 0.96735756.

Strongest negative correlations Public: The strongest negative relationship is between SAT average and Percentage of undergraduates who receive a Pell Grant, with a correlation of -0.654831191 - which is the same relationship as overall but of lesser magnitude than the overall correlation of -0.71224956. Non-profit: The strongest negative relationship is between Average cost of attendance and Percentage of undergraduates who receive a Pell Grant, with a correlation of -0.67495495. For-profit: The strongest negative relationship is between Share of undergraduate students who are part-time and Share of undergraduate students who are first-time, full-time, degree- seeking undergraduates, with a correlation of -0.612138572.

No or insignificant correlations Public: The variables, share of undergraduates of two or more races and percentage of undergraduates receiving a federal loan, seem to be least related with a correlation of 0.0005894428. Non-profit: The variables, share of enrolled undergraduates who are American Indian/Alaska Native and share of enrolled undergraduates who are Native Hawaiian/Pacific Islander, seem to be least related with a correlation of 0.001338006. For-profit: The variables, Enrollment of undergraduate certificate/degree-seeking students and share of enrolled students who are black, seem to be least related with a correlation of 0.00002219894.

Computing covariance covmatrix1<-cov(public, use = “p”) covmatrix2<-cov(nonprofit, use = “p”) covmatrix3<-cov(forprofit, use = “p”)

Printing covariance covmatrix1 covmatrix2 covmatrix3

The covariance values are not standardized, so it is not possible to compare the covariance relationship among various pairs. The positive and negative values tell the direction of the relationship. However, a lot of the values are so small (relative to covariance values from the overall data) and not helpful in determining the magnitude of the relationships.

  1. Based on your analyses so far, are there differences in relations between variables as a function of the type of university? Support your answer using information from you analyses.

The strongest positive correlation among all three groups varies, with public institutions having the same strongest correlation as overall. However, the values of other relationships differ. Similarly the strongest negative correlation also varies among all three groups, with public institutions having same variable with strongest realtinship as overall but of slightly lesser magnitude. However, there are differences among other relationships. Thus, all three groups vary in their dynamics and inter-relationships - though the extent of variability is different for each relationship. There are similarities among the three groups in terms of variables with no or insignificant relationships.

Run the following simple regression analyses and provide an interpretation of each. For all analyses, you should use the full dataset.

Making sure the relavant libraries are active library(ggplot2) library(lm.beta) library(psych) library(QuantPsyc)

  1. Predict the average cost of attendance from average SAT score

qplot(SAT_AVG, COSTT4_A, data=data2, geom = “point”) + stat_smooth(method=“lm”) reg1 <- lm(COSTT4_A ~ SAT_AVG, data=data2) summary(reg1) coefficients(reg1) confint(reg1, level=0.95) lm.beta(reg1) fitted(reg1)

There is a positive linear relationship between Average Cost of Attendance and Average SAT score with a standard coefficient of 0.52. Thus, it is a significantly strong relationship.

  1. Predict the average cost of attendance from admission rate

qplot(ADM_RATE, COSTT4_A, data=data2, geom = “point”) + stat_smooth(method=“lm”) reg2 <- lm(COSTT4_A ~ ADM_RATE, data=data2) summary(reg2) coefficients(reg2) confint(reg2, level=0.95) lm.beta(reg2) fitted(reg2)

There is a negative linear relationship between Average Cost of Attendance and Admission Rate with a standard coefficient of -0.28. Hence, the relationship is not strong.

  1. Predict the number of students from average SAT score

qplot(SAT_AVG, UGDS, data=data2, geom = “point”) + stat_smooth(method=“lm”) reg3 <- lm(UGDS ~ SAT_AVG, data=data2) summary(reg3) coefficients(reg3) confint(reg3, level=0.95) lm.beta(reg3) fitted(reg3)

There is a positive linear relationship between Number of Students and Average SAT score with a standard coefficient of 0.25. Hence, the relationship is not strong.

  1. Predict the number of students from admission rate

qplot(ADM_RATE, UGDS, data=data2, geom = “point”) + stat_smooth(method=“lm”) reg4 <- lm(UGDS ~ ADM_RATE, data=data2) summary(reg4) coefficients(reg4) confint(reg4, level=0.95) lm.beta(reg4) fitted(reg4)

There does not appear to be a significant relationship between Number of Students and Admission Rate with a standard coefficient of -0.13.

  1. Predict completion rate from average SAT score

qplot(SAT_AVG, C150_4, data=data2, geom = “point”) + stat_smooth(method=“lm”) reg5 <- lm(C150_4 ~ SAT_AVG, data=data2) summary(reg5) coefficients(reg5) confint(reg5, level=0.95) lm.beta(reg5) fitted(reg5)

There is a very strong positive linear relationship between Completion Rate and Average SAT score with a standard coefficient of 0.80. This further describes the observation made with the help of paired scatterplots (in Question # 2 above).

  1. Predict completion rate from admission rate

qplot(ADM_RATE, C150_4, data=data2, geom = “point”) + stat_smooth(method=“lm”) reg6 <- lm(C150_4 ~ ADM_RATE, data=data2) summary(reg6) coefficients(reg6) confint(reg6, level=0.95) lm.beta(reg6) fitted(reg6)

There is a negative linear relationship between Completion Rate and Admission Rate with a standard coefficient of -0.32. Hence, the relationship is not strong.

  1. Predict the percentage of students with federal loans from average SAT score

qplot(SAT_AVG, PCTFLOAN, data=data2, geom = “point”) + stat_smooth(method=“lm”) reg7 <- lm(PCTFLOAN ~ SAT_AVG, data=data2) summary(reg7) coefficients(reg7) confint(reg7, level=0.95) lm.beta(reg7) fitted(reg7)

There is a negative linear relationship between Percentage of Students with Federal Loans and Average SAT score with a standard coefficient of -0.51. Thus, it is a significantly strong relationship.

  1. Predict the percentage of students with federal loans from admission rate

qplot(ADM_RATE, PCTFLOAN, data=data2, geom = “point”) + stat_smooth(method=“lm”) reg8 <- lm(PCTFLOAN ~ ADM_RATE, data=data2) summary(reg8) coefficients(reg8) confint(reg8, level=0.95) lm.beta(reg8) fitted(reg8)

There does not appear to be a significant relationship between Percentage of Students with Federal Loans and Admission Rate with a standard coefficient of 0.11.

Run two additional regression equations using any variables you like from the dataset. Provide an interpretation of the results of these additional analyses.

Predicting the percentage of students with Pell grant from average SAT score qplot(SAT_AVG, PCTPELL, data=data2, geom = “point”) + stat_smooth(method=“lm”) reg9 <- lm(PCTPELL ~ SAT_AVG, data=data2) summary(reg9) coefficients(reg9) confint(reg9, level=0.95) lm.beta(reg9) fitted(reg9)

There is a negative linear relationship between Percentage of Students with Pell Grant and Average SAT score with a standard coefficient of -0.71. Thus, it is a significantly strong relationship.

Predicting the percentage of students with Pell grant from admission rate qplot(ADM_RATE, PCTPELL, data=data2, geom = “point”) + stat_smooth(method=“lm”) reg10 <- lm(PCTPELL ~ ADM_RATE, data=data2) summary(reg10) coefficients(reg10) confint(reg10, level=0.95) lm.beta(reg10) fitted(reg10)

There is a positive linear relationship between Percentage of Students with Pell Grant and Admission Rate with a standard coefficient of 0.24. Hence, the relationship is not strong.

  1. Are the distributions of average SAT score, admission rate, and total number of undergraduate students normal or non-normal? What information did you use to answer this question?

Plotting the distributions of the three variables, choosing density plot as it is most suitable to determine normal curve qplot(data2\(SAT_AVG, geom = "density", na.rm=TRUE) qplot(data2\)ADM_RATE, geom = “density”, na.rm=TRUE) qplot(data2$UGDS, geom = “density”, na.rm=TRUE)

The distribution for Average SAT scores is positively skewed, hence not normal. The distribution for Admission Rate is negatively skewed, hence not normal. The distribution for Total Number of Undergraduate Students is a Pareto curve, hence not normal.

Descriptive analysis can also be used to check for skewness describe(data2\(SAT_AVG) describe(data2\)ADM_RATE) describe(data2$UGDS)

The distribution for Average SAT scores has a positive skewness of 0.82 and kurtosis of 1.11 (leptokurtic). The distribution for Admission Rate has a negative skewness of -0.58 and kurtosis of -0.04 (slightly platykurtic). The distribution for Total Number of Undergraduate Students is a Pareto curve, with positive skewness of 6.84 and kurtosis of 104.77 - Pareto distribution is always significantly positively skewed and leptokurtic.

  1. For any of the distributions that were not normal in your previous answer, how could you transform them to be normal? Perform the appropriate transformation and report the mean, standard deviation, and variance of the new transformed variable.

Using the sampling distribution of means, we can transform a non-normal distribution to normal

sample_means = rep(NA, 1000) for(i in 1:1000){ sample_means[i] = mean(rexp(40,0.2)) }

sample_means50000 <- rep(NA, 50000) for(i in 1:50000){ samp <- sample(data2$SAT_AVG, 50) sample_means50000[i] <- mean(samp) } hist(sample_means50000)

Another way of doing the approximation to normal distribution install.packages(“gridExtra”) library(gridExtra)

For Average SAT scores, the distribution was positively skewed but the sampling distribution of its means is closer to the normal distribution p1<-qplot(x = SAT_AVG, data = data2) p2<-qplot(x = log10(SAT_AVG + 1), data = data2) p3<-qplot(x = sqrt(SAT_AVG), data = data2) grid.arrange(p1, p2, p3, ncol = 1)

Similarly, for Admission Rate p1<-qplot(x = ADM_RATE, data = data2) p2<-qplot(x = log10(ADM_RATE + 1), data = data2) p3<-qplot(x = sqrt(ADM_RATE), data = data2) grid.arrange(p1, p2, p3, ncol = 1)

And for Total Number of Undergraduate Students p1<-qplot(x = UGDS, data = data2) p2<-qplot(x = log10(UGDS + 1), data = data2) p3<-qplot(x = sqrt(UGDS), data = data2) grid.arrange(p1, p2, p3, ncol = 1)

  1. Based on the distribution of scores, what is the probability that the average SAT score for a school is greater than 1400? What is the probability that the average SAT score for a school is less than 800?

Looking up mean and standand deviation for Average SAT scores distribution describe(data2$SAT_AVG)

pnorm(1400, mean=1059.07, sd=133.36, lower.tail=FALSE) The probability of greater than 1400 score will be 0.005287105.

pnorm(800, mean=1059.07, sd=133.36, lower.tail=TRUE) The probability of less than 800 score will be 0.02603005.

  1. Imagine that the distribution of average SAT scores was perfectly normal. Answer both parts of Question 19 again using the observed mean and standard deviation as your parameters.

The Mean and SD based on 2019 College Board report were 1059 and 210 respectively. Calculating probability on that basis would be:

pnorm(1400, mean=1059, sd=210, lower.tail=FALSE) The probability of greater than 1400 score will be 0.05220823.

pnorm(800, mean=1059, sd=210, lower.tail=TRUE) The probability of less than 800 score will be 0.1087257.

However, the Mean and Median of a normal distribution are the same. Since Median has been 1055 for the past 3 years, the probility based on that would be:

pnorm(1400, mean=1055, sd=210, lower.tail=FALSE) The probability of greater than 1400 score will be 0.05020625.

pnorm(800, mean=1055, sd=210, lower.tail=TRUE) The probability of less than 800 score will be 0.1123193.

The range of scores in SAT is 400-1600. Since Mean in a perfectly normal distribution is the middle point which is 1000, then probability would be:

pnorm(1400, mean=1000, sd=200, lower.tail=FALSE) The probability of greater than 1400 score will be 0.02275013.

pnorm(800, mean=1000, sd=200, lower.tail=TRUE) The probability of less than 800 score will be 0.1586553.

Thus, the probability of a perfectly normal distribution will be as given in the last step above.