Project 2
JD
10/13/2019
Question 1
We want to begin with importing our Project2data set as well as making a few packages active that we will use later.
We will start by creating a working copy that is a copy of our project data, in case we make any mistakes.
We will also start by separating our quantitative variables.
We can see from the schools in our data set that we 1.) Have many variables with missing values and 2.) some variables that have very odd distributions (i.e., Tuition has a kurtosis score of over 4000).
Project2Data<-read.csv("Project2Data.csv")
library(QuantPsyc)## Loading required package: boot## Loading required package: MASS##
## Attaching package: 'QuantPsyc'## The following object is masked from 'package:base':
##
## normlibrary(psych)##
## Attaching package: 'psych'## The following object is masked from 'package:boot':
##
## logitlibrary(corrr)
library(corrplot)## corrplot 0.84 loadedworkingcopy<-Project2Data
quantvariables<-subset(Project2Data, select = ADM_RATE:PCTFLOAN)
describe(quantvariables)## vars n mean sd median trimmed mad min
## ADM_RATE 1 2198 0.69 0.21 0.71 0.71 0.21 0
## SAT_AVG 2 1304 1059.07 133.36 1039.50 1048.34 104.52 720
## UGDS 3 6990 2332.16 5438.85 406.00 1052.09 526.32 0
## UGDS_WHITE 4 6990 0.51 0.29 0.56 0.52 0.34 0
## UGDS_BLACK 5 6990 0.19 0.22 0.10 0.14 0.12 0
## UGDS_HISP 6 6990 0.16 0.22 0.07 0.11 0.08 0
## UGDS_ASIAN 7 6990 0.03 0.08 0.01 0.02 0.02 0
## UGDS_AIAN 8 6990 0.01 0.07 0.00 0.00 0.00 0
## UGDS_NHPI 9 6990 0.00 0.03 0.00 0.00 0.00 0
## UGDS_2MOR 10 6990 0.02 0.03 0.02 0.02 0.03 0
## UGDS_NRA 11 6990 0.02 0.05 0.00 0.01 0.00 0
## UGDS_UNKN 12 6990 0.05 0.09 0.01 0.02 0.02 0
## PPTUG_EF 13 6969 0.23 0.25 0.15 0.19 0.22 0
## NPT4_PUB 14 1911 9624.66 4669.67 8751.00 9341.96 4293.61 -2434
## NPT4_PRIV 15 4688 18230.18 7272.13 18254.50 18021.04 7034.94 -581
## COSTT4_A 16 4030 24853.36 12762.63 22881.50 23321.23 12766.67 4610
## TUITFTE 17 7270 10401.08 17375.87 9015.00 9227.39 6676.15 0
## INEXPFTE 18 7270 7360.21 12726.34 5490.00 5875.23 3399.60 0
## PFTFAC 19 4045 0.57 0.31 0.54 0.57 0.40 0
## PCTPELL 20 6966 0.53 0.23 0.52 0.53 0.26 0
## C150_4 21 2481 0.48 0.21 0.47 0.47 0.22 0
## PFTFTUG1_EF 22 3664 0.53 0.26 0.53 0.53 0.31 0
## RET_FT4 23 2293 0.71 0.20 0.74 0.73 0.15 0
## PCTFLOAN 24 6966 0.52 0.28 0.58 0.54 0.28 0
## max range skew kurtosis se
## ADM_RATE 1.00 1.00 -0.58 -0.04 0.00
## SAT_AVG 1545.00 825.00 0.82 1.11 3.69
## UGDS 151558.00 151558.00 6.84 104.77 65.05
## UGDS_WHITE 1.00 1.00 -0.26 -1.08 0.00
## UGDS_BLACK 1.00 1.00 1.73 2.49 0.00
## UGDS_HISP 1.00 1.00 2.24 4.83 0.00
## UGDS_ASIAN 0.97 0.97 6.38 55.98 0.00
## UGDS_AIAN 1.00 1.00 11.16 136.65 0.00
## UGDS_NHPI 1.00 1.00 22.92 608.03 0.00
## UGDS_2MOR 0.53 0.53 4.11 36.08 0.00
## UGDS_NRA 0.93 0.93 8.29 101.58 0.00
## UGDS_UNKN 0.90 0.90 4.37 23.94 0.00
## PPTUG_EF 1.00 1.00 1.02 0.22 0.00
## NPT4_PUB 28201.00 30635.00 0.61 0.10 106.82
## NPT4_PRIV 89406.00 89987.00 0.73 3.89 106.21
## COSTT4_A 79212.00 74602.00 0.97 0.47 201.04
## TUITFTE 1292154.00 1292154.00 55.94 4076.80 203.79
## INEXPFTE 735077.00 735077.00 31.03 1570.11 149.26
## PFTFAC 1.00 1.00 0.06 -1.30 0.00
## PCTPELL 1.00 1.00 0.00 -0.79 0.00
## C150_4 1.00 1.00 0.13 -0.38 0.00
## PFTFTUG1_EF 1.00 1.00 -0.06 -0.99 0.00
## RET_FT4 1.00 1.00 -1.26 2.31 0.00
## PCTFLOAN 1.00 1.00 -0.53 -0.81 0.00Question 2 - Pick any 4 variables and display their relations through Scatterplots
Our relations would suggest a moderate negative relation between ADM_RATE and SAT_AVG, moderate negative relation between ADM_RATE and COST, and a minor negative correlation between ADM_RATE and Tuition. We find a strong positive correlation between SAT_AVG and COST and a strong positive correlation between SAT_AVG and Tuition. Our strongest correlation is a positive correlation between COST and TUITFTE.
our4variables<- subset(quantvariables, select=c(ADM_RATE, SAT_AVG, COSTT4_A, TUITFTE))
pairs.panels(our4variables,
method = "pearson",
lm = TRUE)
Question 3 Full Covariance and Correlation Matrices
The variable for SAT avg is appears to be strongly related with many of the other variables, reaching correlation coefficients of -0.7 and 0.8 at times. A variety of the demographic variables seem to be the least related to other variables (except for White, Black, and Hispanic).
corrplot(cor(quantvariables, use = "pairwise.complete.obs"), method = "square", type="upper", order="original", tl.col="black", tl.srt=45, tl.cex = .5, addCoef.col = TRUE, number.cex = .4)
cov(quantvariables, use = "pairwise.complete.obs")## ADM_RATE SAT_AVG UGDS UGDS_WHITE
## ADM_RATE 4.365108e-02 -9.152082e+00 -1.681531e+02 5.891843e-03
## SAT_AVG -9.152082e+00 1.778408e+04 2.437918e+05 6.366863e+00
## UGDS -1.681531e+02 2.437918e+05 2.958107e+07 6.762645e+00
## UGDS_WHITE 5.891843e-03 6.366863e+00 6.762645e+00 8.255418e-02
## UGDS_BLACK -1.159646e-03 -1.162703e+01 -1.190528e+02 -3.279614e-02
## UGDS_HISP 7.547608e-04 -3.110483e-01 3.636321e+01 -3.544616e-02
## UGDS_ASIAN -2.837813e-03 3.711274e+00 5.237768e+01 -4.642505e-03
## UGDS_AIAN 3.201771e-04 -3.600650e-01 -1.431268e+01 -1.798072e-03
## UGDS_NHPI 2.497858e-04 -7.126132e-02 -2.659666e+00 -8.763112e-04
## UGDS_2MOR -3.800944e-04 7.298147e-01 1.713435e+01 -2.126852e-04
## UGDS_NRA -2.637014e-03 2.263840e+00 3.074179e+01 -9.716440e-04
## UGDS_UNKN -2.024596e-04 -7.023401e-01 -5.019408e+00 -5.300157e-03
## PPTUG_EF 2.788057e-03 -5.866310e+00 2.170634e+02 -1.857259e-03
## NPT4_PUB 2.228791e+01 1.546401e+05 5.346029e+06 2.601627e+02
## NPT4_PRIV -1.626399e+02 3.143747e+05 3.119630e+06 8.120708e+01
## COSTT4_A -7.465148e+02 9.251042e+05 -1.364721e+07 2.951488e+02
## TUITFTE -2.154816e+02 4.676810e+05 -4.938153e+06 -5.386015e+01
## INEXPFTE -6.692570e+02 7.350076e+05 2.801231e+06 2.287237e+02
## PFTFAC -1.018346e-02 5.287238e+00 9.463431e+01 1.426599e-02
## PCTPELL 1.032733e-02 -1.375176e+01 -3.193147e+02 -2.280271e-02
## C150_4 -1.229116e-02 1.862141e+01 2.129771e+02 1.337822e-02
## PFTFTUG1_EF -2.831299e-03 1.049133e+01 -1.132397e+02 5.217475e-03
## RET_FT4 -6.093242e-03 1.115780e+01 2.366524e+02 1.138734e-02
## PCTFLOAN 4.891957e-03 -1.155212e+01 -2.813073e+02 8.903602e-04
## UGDS_BLACK UGDS_HISP UGDS_ASIAN UGDS_AIAN
## ADM_RATE -1.159646e-03 7.547608e-04 -2.837813e-03 3.201771e-04
## SAT_AVG -1.162703e+01 -3.110483e-01 3.711274e+00 -3.600650e-01
## UGDS -1.190528e+02 3.636321e+01 5.237768e+01 -1.431268e+01
## UGDS_WHITE -3.279614e-02 -3.544616e-02 -4.642505e-03 -1.798072e-03
## UGDS_BLACK 5.049219e-02 -1.025673e-02 -2.185419e-03 -1.476804e-03
## UGDS_HISP -1.025673e-02 4.955006e-02 5.524350e-04 -9.225330e-04
## UGDS_ASIAN -2.185419e-03 5.524350e-04 5.654128e-03 -2.552887e-04
## UGDS_AIAN -1.476804e-03 -9.225330e-04 -2.552887e-04 4.851592e-03
## UGDS_NHPI -3.723387e-04 -1.164985e-04 2.582712e-04 -1.226498e-05
## UGDS_2MOR -6.786910e-04 -6.156348e-04 2.505822e-04 -3.743798e-05
## UGDS_NRA -1.361128e-03 -6.364885e-04 6.094753e-04 -1.180458e-04
## UGDS_UNKN -1.174675e-03 -1.946117e-03 -2.078060e-04 -2.174059e-04
## PPTUG_EF 1.450254e-03 -3.621910e-04 7.184478e-04 7.024979e-04
## NPT4_PUB -2.465739e+01 -2.043260e+02 7.956598e+00 -5.032745e+01
## NPT4_PRIV -4.845459e+01 -3.223476e+02 4.436821e+01 -1.953968e+01
## COSTT4_A -1.890390e+02 -4.658808e+02 1.161101e+02 -1.202998e+02
## TUITFTE 5.525877e+01 -1.782413e+02 3.339505e+01 -5.397685e+01
## INEXPFTE -1.779024e+02 -2.108016e+02 5.956125e+01 8.012348e+00
## PFTFAC -8.998135e-03 -6.329072e-03 -3.399748e-04 1.005123e-03
## PCTPELL 1.799104e-02 1.037559e-02 -2.565856e-03 1.867542e-04
## C150_4 -1.375469e-02 -2.437542e-03 3.741012e-03 -1.613990e-03
## PFTFTUG1_EF -3.383117e-03 -1.987702e-03 -3.710226e-04 -4.316542e-04
## RET_FT4 -1.226377e-02 -7.882165e-04 2.978017e-03 -8.138075e-04
## PCTFLOAN 1.366736e-02 -1.118120e-02 -3.315926e-03 -2.840080e-03
## UGDS_NHPI UGDS_2MOR UGDS_NRA UGDS_UNKN
## ADM_RATE 2.497858e-04 -3.800944e-04 -2.637014e-03 -2.024596e-04
## SAT_AVG -7.126132e-02 7.298147e-01 2.263840e+00 -7.023401e-01
## UGDS -2.659666e+00 1.713435e+01 3.074179e+01 -5.019408e+00
## UGDS_WHITE -8.763112e-04 -2.126852e-04 -9.716440e-04 -5.300157e-03
## UGDS_BLACK -3.723387e-04 -6.786910e-04 -1.361128e-03 -1.174675e-03
## UGDS_HISP -1.164985e-04 -6.156348e-04 -6.364885e-04 -1.946117e-03
## UGDS_ASIAN 2.582712e-04 2.505822e-04 6.094753e-04 -2.078060e-04
## UGDS_AIAN -1.226498e-05 -3.743798e-05 -1.180458e-04 -2.174059e-04
## UGDS_NHPI 1.080576e-03 6.748210e-05 -1.042071e-05 -1.391733e-05
## UGDS_2MOR 6.748210e-05 9.724945e-04 4.673154e-05 2.310853e-04
## UGDS_NRA -1.042071e-05 4.673154e-05 2.492304e-03 -3.470947e-05
## UGDS_UNKN -1.391733e-05 2.310853e-04 -3.470947e-05 8.708988e-03
## PPTUG_EF 9.356161e-05 2.083970e-04 -9.876967e-04 3.399619e-05
## NPT4_PUB -1.792213e+01 5.157079e+00 2.182463e+01 2.137406e+00
## NPT4_PRIV -8.932016e-02 4.382842e+01 9.224635e+01 1.279576e+02
## COSTT4_A -2.589760e+01 3.858757e+01 2.133744e+02 1.334981e+02
## TUITFTE -2.347438e+00 2.416997e+01 7.408646e+01 9.782208e+01
## INEXPFTE -5.790654e-01 1.921055e+01 7.398386e+01 -9.153065e-01
## PFTFAC -1.511376e-05 1.831850e-04 1.925859e-03 -1.779038e-03
## PCTPELL 2.954484e-04 -7.441574e-04 -3.139439e-03 4.440981e-04
## C150_4 -5.271869e-05 6.519264e-04 2.900199e-03 -2.949484e-03
## PFTFTUG1_EF -3.650252e-05 -5.498730e-05 2.314861e-03 -1.267634e-03
## RET_FT4 -1.330618e-04 4.767810e-04 2.665523e-03 -3.509056e-03
## PCTFLOAN -4.383001e-04 4.538808e-04 -1.369073e-03 4.274429e-03
## PPTUG_EF NPT4_PUB NPT4_PRIV COSTT4_A
## ADM_RATE 2.788057e-03 2.228791e+01 -1.626399e+02 -7.465148e+02
## SAT_AVG -5.866310e+00 1.546401e+05 3.143747e+05 9.251042e+05
## UGDS 2.170634e+02 5.346029e+06 3.119630e+06 -1.364721e+07
## UGDS_WHITE -1.857259e-03 2.601627e+02 8.120708e+01 2.951488e+02
## UGDS_BLACK 1.450254e-03 -2.465739e+01 -4.845459e+01 -1.890390e+02
## UGDS_HISP -3.621910e-04 -2.043260e+02 -3.223476e+02 -4.658808e+02
## UGDS_ASIAN 7.184478e-04 7.956598e+00 4.436821e+01 1.161101e+02
## UGDS_AIAN 7.024979e-04 -5.032745e+01 -1.953968e+01 -1.202998e+02
## UGDS_NHPI 9.356161e-05 -1.792213e+01 -8.932016e-02 -2.589760e+01
## UGDS_2MOR 2.083970e-04 5.157079e+00 4.382842e+01 3.858757e+01
## UGDS_NRA -9.876967e-04 2.182463e+01 9.224635e+01 2.133744e+02
## UGDS_UNKN 3.399619e-05 2.137406e+00 1.279576e+02 1.334981e+02
## PPTUG_EF 6.070846e-02 -4.947463e+02 -3.315144e+01 -1.464035e+03
## NPT4_PUB -4.947463e+02 2.180583e+07 NA 2.042028e+07
## NPT4_PRIV -3.315144e+01 NA 5.288381e+07 6.025956e+07
## COSTT4_A -1.464035e+03 2.042028e+07 6.025956e+07 1.628847e+08
## TUITFTE -2.149797e+02 1.121518e+07 2.901148e+07 7.589102e+07
## INEXPFTE -7.992215e+01 6.239927e+06 1.265891e+07 3.807836e+07
## PFTFAC -1.754014e-02 2.924302e+02 -6.924581e+01 4.986624e+02
## PCTPELL -7.358276e-03 -8.278810e+01 -4.995591e+02 -6.864275e+02
## C150_4 -1.715897e-02 4.508953e+02 5.209488e+02 1.501587e+03
## PFTFTUG1_EF -4.279065e-02 3.593479e+02 2.369126e+02 1.522746e+03
## RET_FT4 -1.376131e-02 1.611303e+02 2.937806e+02 8.095945e+02
## PCTFLOAN -1.607461e-02 7.296435e+02 5.258666e+02 1.551442e+03
## TUITFTE INEXPFTE PFTFAC PCTPELL
## ADM_RATE -2.154816e+02 -6.692570e+02 -1.018346e-02 1.032733e-02
## SAT_AVG 4.676810e+05 7.350076e+05 5.287238e+00 -1.375176e+01
## UGDS -4.938153e+06 2.801231e+06 9.463431e+01 -3.193147e+02
## UGDS_WHITE -5.386015e+01 2.287237e+02 1.426599e-02 -2.280271e-02
## UGDS_BLACK 5.525877e+01 -1.779024e+02 -8.998135e-03 1.799104e-02
## UGDS_HISP -1.782413e+02 -2.108016e+02 -6.329072e-03 1.037559e-02
## UGDS_ASIAN 3.339505e+01 5.956125e+01 -3.399748e-04 -2.565856e-03
## UGDS_AIAN -5.397685e+01 8.012348e+00 1.005123e-03 1.867542e-04
## UGDS_NHPI -2.347438e+00 -5.790654e-01 -1.511376e-05 2.954484e-04
## UGDS_2MOR 2.416997e+01 1.921055e+01 1.831850e-04 -7.441574e-04
## UGDS_NRA 7.408646e+01 7.398386e+01 1.925859e-03 -3.139439e-03
## UGDS_UNKN 9.782208e+01 -9.153065e-01 -1.779038e-03 4.440981e-04
## PPTUG_EF -2.149797e+02 -7.992215e+01 -1.754014e-02 -7.358276e-03
## NPT4_PUB 1.121518e+07 6.239927e+06 2.924302e+02 -8.278810e+01
## NPT4_PRIV 2.901148e+07 1.265891e+07 -6.924581e+01 -4.995591e+02
## COSTT4_A 7.589102e+07 3.807836e+07 4.986624e+02 -6.864275e+02
## TUITFTE 3.019208e+08 1.614892e+08 2.028547e+02 -2.086541e+02
## INEXPFTE 1.614892e+08 1.619598e+08 7.321315e+02 -5.666061e+02
## PFTFAC 2.028547e+02 7.321315e+02 9.379814e-02 -1.725719e-02
## PCTPELL -2.086541e+02 -5.666061e+02 -1.725719e-02 5.104940e-02
## C150_4 5.559162e+02 7.636612e+02 1.863125e-02 -2.292341e-02
## PFTFTUG1_EF 7.464979e+02 4.506753e+02 1.708395e-02 -1.498526e-03
## RET_FT4 2.666704e+02 5.309794e+02 1.593969e-02 -1.823553e-02
## PCTFLOAN 6.643038e+02 -1.785005e+02 -3.634241e-03 2.686950e-02
## C150_4 PFTFTUG1_EF RET_FT4 PCTFLOAN
## ADM_RATE -1.229116e-02 -2.831299e-03 -6.093242e-03 4.891957e-03
## SAT_AVG 1.862141e+01 1.049133e+01 1.115780e+01 -1.155212e+01
## UGDS 2.129771e+02 -1.132397e+02 2.366524e+02 -2.813073e+02
## UGDS_WHITE 1.337822e-02 5.217475e-03 1.138734e-02 8.903602e-04
## UGDS_BLACK -1.375469e-02 -3.383117e-03 -1.226377e-02 1.366736e-02
## UGDS_HISP -2.437542e-03 -1.987702e-03 -7.882165e-04 -1.118120e-02
## UGDS_ASIAN 3.741012e-03 -3.710226e-04 2.978017e-03 -3.315926e-03
## UGDS_AIAN -1.613990e-03 -4.316542e-04 -8.138075e-04 -2.840080e-03
## UGDS_NHPI -5.271869e-05 -3.650252e-05 -1.330618e-04 -4.383001e-04
## UGDS_2MOR 6.519264e-04 -5.498730e-05 4.767810e-04 4.538808e-04
## UGDS_NRA 2.900199e-03 2.314861e-03 2.665523e-03 -1.369073e-03
## UGDS_UNKN -2.949484e-03 -1.267634e-03 -3.509056e-03 4.274429e-03
## PPTUG_EF -1.715897e-02 -4.279065e-02 -1.376131e-02 -1.607461e-02
## NPT4_PUB 4.508953e+02 3.593479e+02 1.611303e+02 7.296435e+02
## NPT4_PRIV 5.209488e+02 2.369126e+02 2.937806e+02 5.258666e+02
## COSTT4_A 1.501587e+03 1.522746e+03 8.095945e+02 1.551442e+03
## TUITFTE 5.559162e+02 7.464979e+02 2.666704e+02 6.643038e+02
## INEXPFTE 7.636612e+02 4.506753e+02 5.309794e+02 -1.785005e+02
## PFTFAC 1.863125e-02 1.708395e-02 1.593969e-02 -3.634241e-03
## PCTPELL -2.292341e-02 -1.498526e-03 -1.823553e-02 2.686950e-02
## C150_4 4.570058e-02 2.178981e-02 2.320601e-02 -4.459163e-03
## PFTFTUG1_EF 2.178981e-02 6.611554e-02 1.861752e-02 1.560087e-02
## RET_FT4 2.320601e-02 1.861752e-02 3.827693e-02 -1.095776e-02
## PCTFLOAN -4.459163e-03 1.560087e-02 -1.095776e-02 8.070627e-02Question 4 Strongest/ Weakest Relations
The strongest relation exists between NPT4_PUB & COSTT4_A at 0.92. Multiple variable combinations exist that demonstrate weak or no correlations, particularly for certain combinations of the demographic variables (i.e., AIAN, NHPI). Other than that, most variables have at least one moderate correlation with another variable.
Question 5 Comparisons of Public, For Profit, Nonprofit Schools
I am going to begin by inserting the control variable back into our quantitative data set.
One of the biggest things we notice is that their are quite a few more For Profit schools represented in our total sample, compared to other schools, yet they only report 6 scores for SAT_AVG.
quantvariables$CONTROL<-Project2Data$CONTROL
public<-subset(quantvariables, CONTROL==1)
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## vars n mean sd median trimmed mad min
## ADM_RATE 1 636 0.69 0.18 0.71 0.70 0.19 0.16
## SAT_AVG 2 516 1038.56 111.64 1029.00 1032.59 102.30 774.00
## UGDS 3 1970 6032.04 7745.08 3211.50 4462.04 4077.89 5.00
## UGDS_WHITE 4 1970 0.59 0.26 0.64 0.61 0.25 0.00
## UGDS_BLACK 5 1970 0.14 0.18 0.08 0.10 0.09 0.00
## UGDS_HISP 6 1970 0.14 0.18 0.06 0.10 0.07 0.00
## UGDS_ASIAN 7 1970 0.03 0.06 0.01 0.02 0.02 0.00
## UGDS_AIAN 8 1970 0.03 0.11 0.00 0.01 0.00 0.00
## UGDS_NHPI 9 1970 0.01 0.05 0.00 0.00 0.00 0.00
## UGDS_2MOR 10 1970 0.03 0.03 0.02 0.02 0.02 0.00
## UGDS_NRA 11 1970 0.01 0.02 0.00 0.01 0.01 0.00
## UGDS_UNKN 12 1970 0.03 0.04 0.01 0.02 0.02 0.00
## PPTUG_EF 13 1970 0.35 0.24 0.35 0.35 0.31 0.00
## NPT4_PUB 14 1911 9624.66 4669.67 8751.00 9341.96 4293.61 -2434.00
## NPT4_PRIV 15 0 NaN NA NA NaN NA Inf
## COSTT4_A 16 1619 14922.46 4956.71 13646.00 14485.10 4318.81 4610.00
## TUITFTE 17 1984 4505.03 5395.95 3119.50 3726.21 2775.43 9.00
## INEXPFTE 18 1984 8340.32 11578.61 6332.50 6743.12 2484.10 0.00
## PFTFAC 19 1627 0.60 0.28 0.57 0.60 0.37 0.00
## PCTPELL 20 1968 0.42 0.17 0.40 0.41 0.16 0.00
## C150_4 21 668 0.46 0.18 0.44 0.45 0.18 0.04
## PFTFTUG1_EF 22 1597 0.45 0.20 0.43 0.44 0.23 0.02
## RET_FT4 23 624 0.74 0.12 0.75 0.75 0.11 0.00
## PCTFLOAN 24 1968 0.32 0.26 0.31 0.30 0.34 0.00
## CONTROL 25 2044 1.00 0.00 1.00 1.00 0.00 1.00
## max range skew kurtosis se
## ADM_RATE 1.00 0.84 -0.44 -0.36 0.01
## SAT_AVG 1400.00 626.00 0.53 0.27 4.91
## UGDS 77657.00 77652.00 2.60 10.47 174.50
## UGDS_WHITE 1.00 1.00 -0.66 -0.44 0.01
## UGDS_BLACK 0.96 0.96 2.36 6.11 0.00
## UGDS_HISP 1.00 1.00 2.41 6.36 0.00
## UGDS_ASIAN 0.44 0.44 3.56 15.03 0.00
## UGDS_AIAN 1.00 1.00 7.12 53.41 0.00
## UGDS_NHPI 1.00 1.00 17.81 335.12 0.00
## UGDS_2MOR 0.43 0.43 5.46 51.55 0.00
## UGDS_NRA 0.29 0.29 3.53 19.80 0.00
## UGDS_UNKN 0.44 0.44 3.67 21.92 0.00
## PPTUG_EF 1.00 1.00 0.17 -1.08 0.01
## NPT4_PUB 28201.00 30635.00 0.61 0.10 106.82
## NPT4_PRIV -Inf -Inf NA NA NA
## COSTT4_A 33826.00 29216.00 0.86 0.43 123.19
## TUITFTE 109761.00 109752.00 8.62 131.16 121.14
## INEXPFTE 357489.00 357489.00 16.72 435.66 259.95
## PFTFAC 1.00 1.00 0.14 -1.35 0.01
## PCTPELL 1.00 1.00 0.57 0.40 0.00
## C150_4 0.94 0.90 0.24 -0.35 0.01
## PFTFTUG1_EF 1.00 0.98 0.24 -0.77 0.01
## RET_FT4 1.00 1.00 -0.79 2.74 0.00
## PCTFLOAN 1.00 1.00 0.33 -0.91 0.01
## CONTROL 1.00 0.00 NaN NaN 0.00nonprofit<-subset(quantvariables, CONTROL==2)
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## vars n mean sd median trimmed mad min
## ADM_RATE 1 1177 0.65 0.21 0.67 0.66 0.20 0
## SAT_AVG 2 782 1073.09 144.36 1049.00 1060.34 109.71 720
## UGDS 3 1636 1694.12 3054.70 930.50 1133.83 1146.79 0
## UGDS_WHITE 4 1636 0.57 0.28 0.64 0.60 0.25 0
## UGDS_BLACK 5 1636 0.14 0.20 0.06 0.09 0.07 0
## UGDS_HISP 6 1636 0.12 0.21 0.06 0.07 0.06 0
## UGDS_ASIAN 7 1636 0.04 0.07 0.02 0.02 0.02 0
## UGDS_AIAN 8 1636 0.01 0.07 0.00 0.00 0.00 0
## UGDS_NHPI 9 1636 0.00 0.03 0.00 0.00 0.00 0
## UGDS_2MOR 10 1636 0.02 0.03 0.02 0.02 0.03 0
## UGDS_NRA 11 1636 0.04 0.08 0.01 0.02 0.02 0
## UGDS_UNKN 12 1636 0.05 0.07 0.02 0.03 0.03 0
## PPTUG_EF 13 1623 0.15 0.22 0.06 0.10 0.09 0
## NPT4_PUB 14 0 NaN NA NA NaN NA Inf
## NPT4_PRIV 15 1477 20266.36 7663.64 20045.00 20210.20 6932.64 1881
## COSTT4_A 16 1396 35607.98 13581.30 35299.00 35346.38 14768.18 6428
## TUITFTE 17 1872 15178.31 30872.95 13017.50 13641.76 6831.08 0
## INEXPFTE 18 1872 11332.52 20326.59 8285.00 9015.70 4754.70 0
## PFTFAC 19 1521 0.66 0.29 0.67 0.68 0.41 0
## PCTPELL 20 1623 0.42 0.21 0.40 0.41 0.20 0
## C150_4 21 1274 0.54 0.21 0.54 0.54 0.21 0
## PFTFTUG1_EF 22 1321 0.63 0.25 0.68 0.65 0.26 0
## RET_FT4 23 1272 0.74 0.17 0.76 0.75 0.14 0
## PCTFLOAN 24 1623 0.56 0.26 0.63 0.59 0.20 0
## CONTROL 25 1956 2.00 0.00 2.00 2.00 0.00 2
## max range skew kurtosis se
## ADM_RATE 1.00 1.00 -0.48 -0.02 0.01
## SAT_AVG 1545.00 825.00 0.81 0.88 5.16
## UGDS 49340.00 49340.00 7.37 83.70 75.52
## UGDS_WHITE 1.00 1.00 -0.67 -0.47 0.01
## UGDS_BLACK 1.00 1.00 2.63 6.78 0.01
## UGDS_HISP 1.00 1.00 3.22 10.19 0.01
## UGDS_ASIAN 0.95 0.95 5.22 42.56 0.00
## UGDS_AIAN 0.95 0.95 11.74 142.12 0.00
## UGDS_NHPI 0.95 0.95 29.87 1036.52 0.00
## UGDS_2MOR 0.53 0.53 5.22 73.88 0.00
## UGDS_NRA 0.93 0.93 5.20 40.78 0.00
## UGDS_UNKN 0.71 0.71 3.60 20.53 0.00
## PPTUG_EF 1.00 1.00 2.06 4.06 0.01
## NPT4_PUB -Inf -Inf NA NA NA
## NPT4_PRIV 46509.00 44628.00 0.15 0.15 199.41
## COSTT4_A 64988.00 58560.00 0.12 -0.78 363.50
## TUITFTE 1292154.00 1292154.00 37.87 1560.77 713.55
## INEXPFTE 735077.00 735077.00 25.19 861.92 469.80
## PFTFAC 1.00 1.00 -0.34 -1.11 0.01
## PCTPELL 1.00 1.00 0.52 -0.23 0.01
## C150_4 1.00 1.00 -0.17 -0.26 0.01
## PFTFTUG1_EF 1.00 1.00 -0.62 -0.45 0.01
## RET_FT4 1.00 1.00 -1.30 3.21 0.00
## PCTFLOAN 1.00 1.00 -0.90 -0.07 0.01
## CONTROL 2.00 0.00 NaN NaN 0.00forprofit<-subset(quantvariables, CONTROL==3)
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## vars n mean sd median trimmed mad min
## ADM_RATE 1 385 0.83 0.17 0.88 0.86 0.15 0.1
## SAT_AVG 2 6 995.67 129.57 971.50 995.67 103.04 855.0
## UGDS 3 3384 486.73 3180.20 161.00 219.51 166.05 0.0
## UGDS_WHITE 4 3384 0.43 0.29 0.42 0.43 0.36 0.0
## UGDS_BLACK 5 3384 0.24 0.25 0.16 0.20 0.19 0.0
## UGDS_HISP 6 3384 0.20 0.25 0.09 0.14 0.12 0.0
## UGDS_ASIAN 7 3384 0.03 0.09 0.01 0.01 0.02 0.0
## UGDS_AIAN 8 3384 0.01 0.02 0.00 0.00 0.00 0.0
## UGDS_NHPI 9 3384 0.00 0.02 0.00 0.00 0.00 0.0
## UGDS_2MOR 10 3384 0.02 0.03 0.01 0.02 0.02 0.0
## UGDS_NRA 11 3384 0.01 0.04 0.00 0.00 0.00 0.0
## UGDS_UNKN 12 3384 0.06 0.12 0.01 0.02 0.02 0.0
## PPTUG_EF 13 3376 0.19 0.24 0.08 0.14 0.11 0.0
## NPT4_PUB 14 0 NaN NA NA NaN NA Inf
## NPT4_PRIV 15 3211 17293.57 6886.68 17346.00 17135.56 6763.62 -581.0
## COSTT4_A 16 1015 25902.30 6036.42 25962.00 25912.42 4213.55 8160.0
## TUITFTE 17 3414 11207.99 8380.16 9899.00 10430.98 4869.60 0.0
## INEXPFTE 18 3414 4612.49 4876.88 3701.00 4031.71 2258.00 0.0
## PFTFAC 19 897 0.35 0.28 0.26 0.31 0.22 0.0
## PCTPELL 20 3375 0.65 0.20 0.67 0.66 0.19 0.0
## C150_4 21 539 0.37 0.20 0.34 0.35 0.17 0.0
## PFTFTUG1_EF 22 746 0.52 0.31 0.53 0.52 0.40 0.0
## RET_FT4 23 397 0.54 0.28 0.52 0.55 0.26 0.0
## PCTFLOAN 24 3375 0.62 0.25 0.67 0.65 0.21 0.0
## CONTROL 25 3703 3.00 0.00 3.00 3.00 0.00 3.0
## max range skew kurtosis se
## ADM_RATE 1.00 0.90 -1.48 2.41 0.01
## SAT_AVG 1211.00 356.00 0.48 -1.44 52.90
## UGDS 151558.00 151558.00 34.90 1540.42 54.67
## UGDS_WHITE 1.00 1.00 0.16 -1.14 0.00
## UGDS_BLACK 1.00 1.00 1.23 0.74 0.00
## UGDS_HISP 1.00 1.00 1.80 2.72 0.00
## UGDS_ASIAN 0.97 0.97 6.86 56.74 0.00
## UGDS_AIAN 0.40 0.40 7.45 82.40 0.00
## UGDS_NHPI 0.67 0.67 18.44 443.00 0.00
## UGDS_2MOR 0.44 0.44 3.21 20.21 0.00
## UGDS_NRA 0.87 0.87 13.05 209.30 0.00
## UGDS_UNKN 0.90 0.90 3.57 14.47 0.00
## PPTUG_EF 1.00 1.00 1.36 1.38 0.00
## NPT4_PUB -Inf -Inf NA NA NA
## NPT4_PRIV 89406.00 89987.00 1.06 7.33 121.53
## COSTT4_A 79212.00 71052.00 0.71 7.16 189.47
## TUITFTE 248996.00 248996.00 10.05 229.30 143.42
## INEXPFTE 199372.00 199372.00 20.23 753.35 83.47
## PFTFAC 1.00 1.00 1.03 0.09 0.01
## PCTPELL 1.00 1.00 -0.69 0.39 0.00
## C150_4 1.00 1.00 0.75 0.75 0.01
## PFTFTUG1_EF 1.00 1.00 -0.12 -1.27 0.01
## RET_FT4 1.00 1.00 -0.11 -0.49 0.01
## PCTFLOAN 1.00 1.00 -1.02 0.52 0.00
## CONTROL 3.00 0.00 NaN NaN 0.00Question 6 Scatterplots for Different Institutions
The magnitude of ADM_RATE & SAT_AVG changes from our total data set, with a weaker correlation in public schools but stronger correlation for both private institutions. In general, this trend holds true, with our different variables reporting weaker correlations at public schools compared to their private counterparts. This is true for all except COST & TUITFTE, with a stronger correlation reported in public schools than in their private counterparts or the total sample.
our4variablespublic<- subset(public, select=c(ADM_RATE, SAT_AVG, COSTT4_A, TUITFTE))
pairs.panels(our4variablespublic,
method = "pearson",
lm = TRUE)
our4variablesnonprofit<- subset(nonprofit, select=c(ADM_RATE, SAT_AVG, COSTT4_A, TUITFTE))
pairs.panels(our4variablesnonprofit,
method = "pearson",
lm = TRUE)
our4variablesforprofit<- subset(forprofit, select=c(ADM_RATE, SAT_AVG, COSTT4_A, TUITFTE))
pairs.panels(our4variablesforprofit,
method = "pearson",
lm = TRUE)
Question 7 Correlation and Covariance Matrices of our 3 School Types
Within Public universities, the NPTF_Pub & COSTT variable are the strongest relation, similar to our original analysis and what we would expect considering the NPTF_PUB variable only applies to public universities. Interestingly, some demographic variables emerge as stronger correlations than in the total data set correlation matrix. Weak correlations still exist for some demographics (i.e., AIAN, NHPI).
Within Nonprofit universities, our strongest correlation becomes SAT_AVG & C150. Weak correlations emerge with the UGDS variable.
Within For Profit universities, we see many of the variables now become weakly correlated (and we should be suspect of any correlations with SATAVG because of the small n of observations)
corrplot(cor(public, use = "pairwise.complete.obs"), main = "Public", type="upper", order="original", tl.col="black", tl.srt=45, tl.cex = .5, addCoef.col = TRUE, number.cex = .4)## Warning in cor(public, use = "pairwise.complete.obs"): the standard
## deviation is zero
cov(public, use = "pairwise.complete.obs")## ADM_RATE SAT_AVG UGDS UGDS_WHITE
## ADM_RATE 3.360117e-02 -3.868647e+00 -2.125850e+02 1.240260e-02
## SAT_AVG -3.868647e+00 1.246351e+04 5.450683e+05 7.768440e+00
## UGDS -2.125850e+02 5.450683e+05 5.998626e+07 -4.026432e+02
## UGDS_WHITE 1.240260e-02 7.768440e+00 -4.026432e+02 6.554591e-02
## UGDS_BLACK -7.653838e-03 -1.128908e+01 -7.028814e+01 -2.081700e-02
## UGDS_HISP -1.708462e-03 -5.753930e-02 3.051411e+02 -2.769155e-02
## UGDS_ASIAN -3.384347e-03 2.972124e+00 1.640611e+02 -5.566508e-03
## UGDS_AIAN 7.446680e-04 -5.342317e-01 -1.074524e+02 -6.626126e-03
## UGDS_NHPI 6.792911e-04 -3.247896e-02 -1.215033e+01 -1.916665e-03
## UGDS_2MOR 2.595622e-04 3.434692e-01 3.082565e+01 -9.362987e-04
## UGDS_NRA -4.671890e-04 1.260189e+00 7.681463e+01 -9.054697e-04
## UGDS_UNKN -8.725182e-04 -4.301800e-01 1.569799e+01 -1.085878e-03
## PPTUG_EF 9.543694e-05 -4.229417e+00 8.946758e+01 -1.006654e-02
## NPT4_PUB 2.228791e+01 1.546401e+05 5.346029e+06 2.601627e+02
## NPT4_PRIV NA NA NA NA
## COSTT4_A -1.032139e+02 2.261949e+05 1.114200e+07 1.699173e+02
## TUITFTE -1.018153e+01 2.279867e+05 6.336576e+06 1.879837e+02
## INEXPFTE -1.510772e+02 2.410387e+05 -1.806406e+06 5.803787e+01
## PFTFAC 1.630107e-03 2.444422e+00 -4.365770e+01 5.844623e-03
## PCTPELL -5.362106e-04 -9.470237e+00 -2.844552e+02 -6.598399e-03
## C150_4 -5.241809e-03 1.425736e+01 7.574312e+02 1.182786e-02
## PFTFTUG1_EF 1.184064e-03 5.269431e+00 1.814096e+02 4.703051e-03
## RET_FT4 -4.300130e-03 7.840027e+00 4.918125e+02 4.100246e-04
## PCTFLOAN 1.566870e-03 -6.513858e+00 9.105230e+01 1.582585e-02
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## UGDS_BLACK UGDS_HISP UGDS_ASIAN UGDS_AIAN
## ADM_RATE -7.653838e-03 -1.708462e-03 -3.384347e-03 7.446680e-04
## SAT_AVG -1.128908e+01 -5.753930e-02 2.972124e+00 -5.342317e-01
## UGDS -7.028814e+01 3.051411e+02 1.640611e+02 -1.074524e+02
## UGDS_WHITE -2.081700e-02 -2.769155e-02 -5.566508e-03 -6.626126e-03
## UGDS_BLACK 3.093196e-02 -5.093818e-03 -1.004513e-03 -2.462275e-03
## UGDS_HISP -5.093818e-03 3.269396e-02 2.241202e-03 -1.872419e-03
## UGDS_ASIAN -1.004513e-03 2.241202e-03 3.378545e-03 -6.222649e-04
## UGDS_AIAN -2.462275e-03 -1.872419e-03 -6.222649e-04 1.229328e-02
## UGDS_NHPI -4.834959e-04 -2.986142e-04 3.475660e-04 -7.651158e-05
## UGDS_2MOR -5.724160e-04 -7.591289e-05 6.569181e-04 -1.897741e-04
## UGDS_NRA -3.026625e-04 1.092018e-04 4.981175e-04 -2.098941e-04
## UGDS_UNKN -1.961427e-04 -1.232269e-05 7.089872e-05 -2.340234e-04
## PPTUG_EF -3.448588e-04 8.220827e-03 9.672637e-04 6.569355e-04
## NPT4_PUB -2.465739e+01 -2.043260e+02 7.956598e+00 -5.032745e+01
## NPT4_PRIV NA NA NA NA
## COSTT4_A -3.620696e+01 -1.694033e+02 5.245991e+01 -5.323768e+01
## TUITFTE -6.069906e+01 -1.354007e+02 2.646566e+01 -4.336759e+01
## INEXPFTE -4.392371e+01 -8.083123e+01 5.022575e+01 1.726056e+01
## PFTFAC -7.702821e-04 -6.623997e-03 -1.241610e-03 1.389657e-03
## PCTPELL 1.039038e-02 -1.385046e-03 -1.894008e-03 1.189288e-03
## C150_4 -1.046351e-02 -2.019975e-03 3.753202e-03 -3.535197e-03
## PFTFTUG1_EF -1.083308e-03 -3.213946e-03 -1.163898e-03 6.136038e-04
## RET_FT4 -5.770553e-03 2.552484e-03 3.028595e-03 -1.130038e-03
## PCTFLOAN 5.410460e-03 -1.450111e-02 -1.420587e-03 -5.309695e-03
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## UGDS_NHPI UGDS_2MOR UGDS_NRA UGDS_UNKN
## ADM_RATE 6.792911e-04 2.595622e-04 -4.671890e-04 -8.725182e-04
## SAT_AVG -3.247896e-02 3.434692e-01 1.260189e+00 -4.301800e-01
## UGDS -1.215033e+01 3.082565e+01 7.681463e+01 1.569799e+01
## UGDS_WHITE -1.916665e-03 -9.362987e-04 -9.054697e-04 -1.085878e-03
## UGDS_BLACK -4.834959e-04 -5.724160e-04 -3.026625e-04 -1.961427e-04
## UGDS_HISP -2.986142e-04 -7.591289e-05 1.092018e-04 -1.232269e-05
## UGDS_ASIAN 3.475660e-04 6.569181e-04 4.981175e-04 7.089872e-05
## UGDS_AIAN -7.651158e-05 -1.897741e-04 -2.098941e-04 -2.340234e-04
## UGDS_NHPI 2.374568e-03 8.111316e-05 2.475399e-05 -5.262125e-05
## UGDS_2MOR 8.111316e-05 9.008865e-04 1.255937e-04 9.915596e-06
## UGDS_NRA 2.475399e-05 1.255937e-04 6.214688e-04 3.896061e-05
## UGDS_UNKN -5.262125e-05 9.915596e-06 3.896061e-05 1.461287e-03
## PPTUG_EF 9.753696e-05 2.580145e-04 -1.120198e-03 1.331121e-03
## NPT4_PUB -1.792213e+01 5.157079e+00 2.182463e+01 2.137406e+00
## NPT4_PRIV NA NA NA NA
## COSTT4_A -2.352689e+01 1.339656e+01 4.396388e+01 2.642081e+00
## TUITFTE -6.358758e+00 2.775516e+00 2.794397e+01 6.592411e-01
## INEXPFTE -5.031347e+00 -3.977466e+00 1.624281e+01 -8.017755e+00
## PFTFAC 2.952458e-04 6.410420e-05 1.256147e-03 -2.140569e-04
## PCTPELL 9.818011e-04 -9.317130e-04 -7.846350e-04 -9.678444e-04
## C150_4 -7.818610e-04 2.391049e-04 1.634943e-03 -6.543867e-04
## PFTFTUG1_EF 7.842150e-04 -5.159151e-04 9.330706e-04 -1.056923e-03
## RET_FT4 2.091550e-04 6.617733e-05 9.719275e-04 -3.378427e-04
## PCTFLOAN -9.334880e-04 4.543542e-06 7.577333e-04 1.666833e-04
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## PPTUG_EF NPT4_PUB NPT4_PRIV COSTT4_A
## ADM_RATE 9.543694e-05 2.228791e+01 NA -1.032139e+02
## SAT_AVG -4.229417e+00 1.546401e+05 NA 2.261949e+05
## UGDS 8.946758e+01 5.346029e+06 NA 1.114200e+07
## UGDS_WHITE -1.006654e-02 2.601627e+02 NA 1.699173e+02
## UGDS_BLACK -3.448588e-04 -2.465739e+01 NA -3.620696e+01
## UGDS_HISP 8.220827e-03 -2.043260e+02 NA -1.694033e+02
## UGDS_ASIAN 9.672637e-04 7.956598e+00 NA 5.245991e+01
## UGDS_AIAN 6.569355e-04 -5.032745e+01 NA -5.323768e+01
## UGDS_NHPI 9.753696e-05 -1.792213e+01 NA -2.352689e+01
## UGDS_2MOR 2.580145e-04 5.157079e+00 NA 1.339656e+01
## UGDS_NRA -1.120198e-03 2.182463e+01 NA 4.396388e+01
## UGDS_UNKN 1.331121e-03 2.137406e+00 NA 2.642081e+00
## PPTUG_EF 5.591984e-02 -4.947463e+02 NA -6.629519e+02
## NPT4_PUB -4.947463e+02 2.180583e+07 NA 2.042028e+07
## NPT4_PRIV NA NA NA NA
## COSTT4_A -6.629519e+02 2.042028e+07 NA 2.456897e+07
## TUITFTE -3.994381e+02 1.121518e+07 NA 1.348679e+07
## INEXPFTE -4.640903e+02 6.239927e+06 NA 8.950068e+06
## PFTFAC -2.557631e-02 2.924302e+02 NA 3.681358e+02
## PCTPELL -7.516323e-03 -8.278810e+01 NA -1.531094e+02
## C150_4 -1.773768e-02 4.508953e+02 NA 5.956546e+02
## PFTFTUG1_EF -3.289604e-02 3.593479e+02 NA 4.447050e+02
## RET_FT4 -7.870056e-03 1.611303e+02 NA 2.552317e+02
## PCTFLOAN -2.711538e-02 7.296435e+02 NA 7.172317e+02
## CONTROL 0.000000e+00 0.000000e+00 NA 0.000000e+00
## TUITFTE INEXPFTE PFTFAC PCTPELL
## ADM_RATE -1.018153e+01 -1.510772e+02 1.630107e-03 -5.362106e-04
## SAT_AVG 2.279867e+05 2.410387e+05 2.444422e+00 -9.470237e+00
## UGDS 6.336576e+06 -1.806406e+06 -4.365770e+01 -2.844552e+02
## UGDS_WHITE 1.879837e+02 5.803787e+01 5.844623e-03 -6.598399e-03
## UGDS_BLACK -6.069906e+01 -4.392371e+01 -7.702821e-04 1.039038e-02
## UGDS_HISP -1.354007e+02 -8.083123e+01 -6.623997e-03 -1.385046e-03
## UGDS_ASIAN 2.646566e+01 5.022575e+01 -1.241610e-03 -1.894008e-03
## UGDS_AIAN -4.336759e+01 1.726056e+01 1.389657e-03 1.189288e-03
## UGDS_NHPI -6.358758e+00 -5.031347e+00 2.952458e-04 9.818011e-04
## UGDS_2MOR 2.775516e+00 -3.977466e+00 6.410420e-05 -9.317130e-04
## UGDS_NRA 2.794397e+01 1.624281e+01 1.256147e-03 -7.846350e-04
## UGDS_UNKN 6.592411e-01 -8.017755e+00 -2.140569e-04 -9.678444e-04
## PPTUG_EF -3.994381e+02 -4.640903e+02 -2.557631e-02 -7.516323e-03
## NPT4_PUB 1.121518e+07 6.239927e+06 2.924302e+02 -8.278810e+01
## NPT4_PRIV NA NA NA NA
## COSTT4_A 1.348679e+07 8.950068e+06 3.681358e+02 -1.531094e+02
## TUITFTE 2.911632e+07 2.504544e+07 2.977349e+02 -9.895271e+01
## INEXPFTE 2.504544e+07 1.340642e+08 3.706367e+02 -1.699340e+02
## PFTFAC 2.977349e+02 3.706367e+02 7.795924e-02 -9.690150e-05
## PCTPELL -9.895271e+01 -1.699340e+02 -9.690150e-05 2.886076e-02
## C150_4 4.226993e+02 3.750481e+02 5.839147e-03 -1.389922e-02
## PFTFTUG1_EF 3.233810e+02 2.118222e+02 1.643322e-02 2.801677e-03
## RET_FT4 1.971872e+02 2.082404e+02 2.286057e-03 -6.631786e-03
## PCTFLOAN 4.816868e+02 3.850509e+02 1.963037e-02 1.051458e-02
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## C150_4 PFTFTUG1_EF RET_FT4 PCTFLOAN
## ADM_RATE -5.241809e-03 1.184064e-03 -4.300130e-03 1.566870e-03
## SAT_AVG 1.425736e+01 5.269431e+00 7.840027e+00 -6.513858e+00
## UGDS 7.574312e+02 1.814096e+02 4.918125e+02 9.105230e+01
## UGDS_WHITE 1.182786e-02 4.703051e-03 4.100246e-04 1.582585e-02
## UGDS_BLACK -1.046351e-02 -1.083308e-03 -5.770553e-03 5.410460e-03
## UGDS_HISP -2.019975e-03 -3.213946e-03 2.552484e-03 -1.450111e-02
## UGDS_ASIAN 3.753202e-03 -1.163898e-03 3.028595e-03 -1.420587e-03
## UGDS_AIAN -3.535197e-03 6.136038e-04 -1.130038e-03 -5.309695e-03
## UGDS_NHPI -7.818610e-04 7.842150e-04 2.091550e-04 -9.334880e-04
## UGDS_2MOR 2.391049e-04 -5.159151e-04 6.617733e-05 4.543542e-06
## UGDS_NRA 1.634943e-03 9.330706e-04 9.719275e-04 7.577333e-04
## UGDS_UNKN -6.543867e-04 -1.056923e-03 -3.378427e-04 1.666833e-04
## PPTUG_EF -1.773768e-02 -3.289604e-02 -7.870056e-03 -2.711538e-02
## NPT4_PUB 4.508953e+02 3.593479e+02 1.611303e+02 7.296435e+02
## NPT4_PRIV NA NA NA NA
## COSTT4_A 5.956546e+02 4.447050e+02 2.552317e+02 7.172317e+02
## TUITFTE 4.226993e+02 3.233810e+02 1.971872e+02 4.816868e+02
## INEXPFTE 3.750481e+02 2.118222e+02 2.082404e+02 3.850509e+02
## PFTFAC 5.839147e-03 1.643322e-02 2.286057e-03 1.963037e-02
## PCTPELL -1.389922e-02 2.801677e-03 -6.631786e-03 1.051458e-02
## C150_4 3.231275e-02 1.513416e-02 1.640806e-02 4.159769e-03
## PFTFTUG1_EF 1.513416e-02 4.096281e-02 7.702755e-03 1.932124e-02
## RET_FT4 1.640806e-02 7.702755e-03 1.367290e-02 -2.793926e-03
## PCTFLOAN 4.159769e-03 1.932124e-02 -2.793926e-03 6.593408e-02
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## CONTROL
## ADM_RATE 0
## SAT_AVG 0
## UGDS 0
## UGDS_WHITE 0
## UGDS_BLACK 0
## UGDS_HISP 0
## UGDS_ASIAN 0
## UGDS_AIAN 0
## UGDS_NHPI 0
## UGDS_2MOR 0
## UGDS_NRA 0
## UGDS_UNKN 0
## PPTUG_EF 0
## NPT4_PUB 0
## NPT4_PRIV NA
## COSTT4_A 0
## TUITFTE 0
## INEXPFTE 0
## PFTFAC 0
## PCTPELL 0
## C150_4 0
## PFTFTUG1_EF 0
## RET_FT4 0
## PCTFLOAN 0
## CONTROL 0corrplot(cor(nonprofit, use = "pairwise.complete.obs"), main = "Nonprofit", type="upper", order="original", tl.col="black", tl.srt=45, tl.cex = .5, addCoef.col = TRUE, number.cex = .4)## Warning in cor(nonprofit, use = "pairwise.complete.obs"): the standard
## deviation is zero
cov(nonprofit, use = "pairwise.complete.obs")## ADM_RATE SAT_AVG UGDS UGDS_WHITE
## ADM_RATE 4.536895e-02 -1.190873e+01 -1.107615e+02 1.274632e-02
## SAT_AVG -1.190873e+01 2.083891e+04 1.557286e+05 5.106529e+00
## UGDS -1.107615e+02 1.557286e+05 9.331219e+06 -2.059421e+01
## UGDS_WHITE 1.274632e-02 5.106529e+00 -2.059421e+01 7.755369e-02
## UGDS_BLACK -3.006599e-03 -1.160736e+01 -4.018257e+01 -2.965038e-02
## UGDS_HISP -2.319609e-03 -1.266250e-01 1.142529e+01 -3.265294e-02
## UGDS_ASIAN -3.135088e-03 4.317976e+00 2.103326e+01 -4.098247e-03
## UGDS_AIAN -8.715762e-05 -1.939833e-01 -9.410536e+00 -2.588628e-03
## UGDS_NHPI -5.079462e-05 -1.009831e-01 -1.799093e+00 -5.698056e-04
## UGDS_2MOR -9.704476e-04 1.023550e+00 9.216479e+00 -1.392742e-04
## UGDS_NRA -2.937042e-03 2.752199e+00 1.593747e+01 -3.803603e-03
## UGDS_UNKN -2.404558e-04 -1.171670e+00 1.954116e+01 -2.297023e-03
## PPTUG_EF 1.581536e-03 -6.234855e+00 -3.963589e+00 -6.997340e-03
## NPT4_PUB NA NA NA NA
## NPT4_PRIV -1.788793e+02 3.203899e+05 5.167513e+06 2.586921e+02
## COSTT4_A -8.001455e+02 1.113885e+06 1.043862e+07 5.887293e+02
## TUITFTE -4.044905e+02 5.173568e+05 3.227969e+06 -9.716158e+01
## INEXPFTE -8.531035e+02 1.032820e+06 3.532012e+06 4.865996e+01
## PFTFAC -3.387767e-03 7.623504e+00 2.394198e+01 7.097292e-03
## PCTPELL 5.326634e-03 -1.630479e+01 -1.228868e+02 -2.380767e-02
## C150_4 -1.325186e-02 2.046047e+01 1.312989e+02 9.853973e-03
## PFTFTUG1_EF -7.776027e-03 1.271935e+01 7.350802e+01 4.431194e-03
## RET_FT4 -5.604484e-03 1.333383e+01 9.572951e+01 7.280116e-03
## PCTFLOAN 2.975208e-03 -1.627136e+01 -1.627088e+01 1.903675e-03
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## UGDS_BLACK UGDS_HISP UGDS_ASIAN UGDS_AIAN
## ADM_RATE -3.006599e-03 -2.319609e-03 -3.135088e-03 -8.715762e-05
## SAT_AVG -1.160736e+01 -1.266250e-01 4.317976e+00 -1.939833e-01
## UGDS -4.018257e+01 1.142529e+01 2.103326e+01 -9.410536e+00
## UGDS_WHITE -2.965038e-02 -3.265294e-02 -4.098247e-03 -2.588628e-03
## UGDS_BLACK 4.140457e-02 -5.531855e-03 -1.783743e-03 -7.082901e-04
## UGDS_HISP -5.531855e-03 4.294322e-02 -1.636133e-04 -6.828854e-04
## UGDS_ASIAN -1.783743e-03 -1.636133e-04 4.632460e-03 -2.390501e-04
## UGDS_AIAN -7.082901e-04 -6.828854e-04 -2.390501e-04 4.698595e-03
## UGDS_NHPI -1.927936e-04 -4.221583e-05 1.194368e-04 2.420734e-06
## UGDS_2MOR -5.953970e-04 -4.574627e-04 3.545936e-04 -9.824162e-05
## UGDS_NRA -1.947165e-03 -1.252820e-03 1.301689e-03 -2.353237e-04
## UGDS_UNKN -5.703675e-04 -1.778657e-03 -9.591836e-06 -1.154609e-04
## PPTUG_EF 6.105967e-03 2.029921e-03 -1.149184e-03 3.236805e-04
## NPT4_PUB NA NA NA NA
## NPT4_PRIV -1.973060e+02 -4.058424e+02 1.125215e+02 -6.563269e+01
## COSTT4_A -6.333163e+02 -6.044283e+02 2.663787e+02 -1.372005e+02
## TUITFTE 3.764037e+01 -2.030514e+02 9.646182e+01 -6.679439e+01
## INEXPFTE -1.438109e+02 -2.028240e+02 1.735125e+02 -1.572635e+01
## PFTFAC -1.420142e-03 -3.236248e-03 -4.979777e-04 1.543920e-04
## PCTPELL 1.714417e-02 1.453299e-02 -2.603472e-03 1.850532e-03
## C150_4 -1.221938e-02 -4.649648e-03 4.144713e-03 -1.140529e-03
## PFTFTUG1_EF -5.915548e-03 -6.838199e-04 1.388544e-03 -5.606137e-04
## RET_FT4 -9.843601e-03 -1.349271e-03 2.794559e-03 -1.143036e-03
## PCTFLOAN 1.392197e-02 -1.018841e-02 -2.502309e-03 -1.655861e-03
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## UGDS_NHPI UGDS_2MOR UGDS_NRA UGDS_UNKN
## ADM_RATE -5.079462e-05 -9.704476e-04 -2.937042e-03 -2.404558e-04
## SAT_AVG -1.009831e-01 1.023550e+00 2.752199e+00 -1.171670e+00
## UGDS -1.799093e+00 9.216479e+00 1.593747e+01 1.954116e+01
## UGDS_WHITE -5.698056e-04 -1.392742e-04 -3.803603e-03 -2.297023e-03
## UGDS_BLACK -1.927936e-04 -5.953970e-04 -1.947165e-03 -5.703675e-04
## UGDS_HISP -4.221583e-05 -4.574627e-04 -1.252820e-03 -1.778657e-03
## UGDS_ASIAN 1.194368e-04 3.545936e-04 1.301689e-03 -9.591836e-06
## UGDS_AIAN 2.420734e-06 -9.824162e-05 -2.353237e-04 -1.154609e-04
## UGDS_NHPI 6.966427e-04 5.561508e-05 -3.241483e-05 -2.626496e-05
## UGDS_2MOR 5.561508e-05 7.657043e-04 1.630202e-04 2.178079e-05
## UGDS_NRA -3.241483e-05 1.630202e-04 5.919008e-03 7.906814e-06
## UGDS_UNKN -2.626496e-05 2.178079e-05 7.906814e-06 4.908971e-03
## PPTUG_EF 8.230183e-05 -4.914570e-04 -1.997066e-03 2.093184e-03
## NPT4_PUB NA NA NA NA
## NPT4_PRIV -3.867938e+00 6.443584e+01 1.272409e+02 1.112608e+02
## COSTT4_A -2.207545e+01 1.342530e+02 2.602727e+02 1.501018e+02
## TUITFTE -1.023563e+01 8.164403e+01 8.786793e+01 7.008077e+01
## INEXPFTE -7.209269e+00 6.211886e+01 1.171903e+02 -2.900858e+01
## PFTFAC -4.781543e-05 -8.385646e-05 -7.298864e-04 -1.491022e-03
## PCTPELL 3.678032e-04 -1.218142e-03 -4.989582e-03 -1.530720e-03
## C150_4 2.905697e-04 1.400528e-03 2.895213e-03 -7.973277e-04
## PFTFTUG1_EF -3.039270e-04 8.282901e-04 2.382618e-03 -1.567152e-03
## RET_FT4 -2.770611e-04 6.279306e-04 2.456673e-03 -5.466105e-04
## PCTFLOAN -3.314764e-04 8.719972e-04 -3.886695e-03 2.487782e-03
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## PPTUG_EF NPT4_PUB NPT4_PRIV COSTT4_A
## ADM_RATE 1.581536e-03 NA -1.788793e+02 -8.001455e+02
## SAT_AVG -6.234855e+00 NA 3.203899e+05 1.113885e+06
## UGDS -3.963589e+00 NA 5.167513e+06 1.043862e+07
## UGDS_WHITE -6.997340e-03 NA 2.586921e+02 5.887293e+02
## UGDS_BLACK 6.105967e-03 NA -1.973060e+02 -6.333163e+02
## UGDS_HISP 2.029921e-03 NA -4.058424e+02 -6.044283e+02
## UGDS_ASIAN -1.149184e-03 NA 1.125215e+02 2.663787e+02
## UGDS_AIAN 3.236805e-04 NA -6.563269e+01 -1.372005e+02
## UGDS_NHPI 8.230183e-05 NA -3.867938e+00 -2.207545e+01
## UGDS_2MOR -4.914570e-04 NA 6.443584e+01 1.342530e+02
## UGDS_NRA -1.997066e-03 NA 1.272409e+02 2.602727e+02
## UGDS_UNKN 2.093184e-03 NA 1.112608e+02 1.501018e+02
## PPTUG_EF 4.632924e-02 NA -2.350124e+02 -9.195262e+02
## NPT4_PUB NA NA NA NA
## NPT4_PRIV -2.350124e+02 NA 5.873135e+07 7.961180e+07
## COSTT4_A -9.195262e+02 NA 7.961180e+07 1.844518e+08
## TUITFTE 5.113895e+02 NA 3.802106e+07 7.140962e+07
## INEXPFTE 7.483286e+01 NA 1.986666e+07 6.515278e+07
## PFTFAC -9.203744e-03 NA -7.520620e+01 3.165501e+02
## PCTPELL 3.912476e-03 NA -8.397928e+02 -1.882063e+03
## C150_4 -1.208337e-02 NA 7.086510e+02 1.800918e+03
## PFTFTUG1_EF -3.038821e-02 NA 4.240169e+02 1.497041e+03
## RET_FT4 -7.911504e-03 NA 3.445869e+02 1.051291e+03
## PCTFLOAN 2.890825e-03 NA 5.262233e+02 4.206266e+02
## CONTROL 0.000000e+00 NA 0.000000e+00 0.000000e+00
## TUITFTE INEXPFTE PFTFAC PCTPELL
## ADM_RATE -4.044905e+02 -8.531035e+02 -3.387767e-03 5.326634e-03
## SAT_AVG 5.173568e+05 1.032820e+06 7.623504e+00 -1.630479e+01
## UGDS 3.227969e+06 3.532012e+06 2.394198e+01 -1.228868e+02
## UGDS_WHITE -9.716158e+01 4.865996e+01 7.097292e-03 -2.380767e-02
## UGDS_BLACK 3.764037e+01 -1.438109e+02 -1.420142e-03 1.714417e-02
## UGDS_HISP -2.030514e+02 -2.028240e+02 -3.236248e-03 1.453299e-02
## UGDS_ASIAN 9.646182e+01 1.735125e+02 -4.979777e-04 -2.603472e-03
## UGDS_AIAN -6.679439e+01 -1.572635e+01 1.543920e-04 1.850532e-03
## UGDS_NHPI -1.023563e+01 -7.209269e+00 -4.781543e-05 3.678032e-04
## UGDS_2MOR 8.164403e+01 6.211886e+01 -8.385646e-05 -1.218142e-03
## UGDS_NRA 8.786793e+01 1.171903e+02 -7.298864e-04 -4.989582e-03
## UGDS_UNKN 7.008077e+01 -2.900858e+01 -1.491022e-03 -1.530720e-03
## PPTUG_EF 5.113895e+02 7.483286e+01 -9.203744e-03 3.912476e-03
## NPT4_PUB NA NA NA NA
## NPT4_PRIV 3.802106e+07 1.986666e+07 -7.520620e+01 -8.397928e+02
## COSTT4_A 7.140962e+07 6.515278e+07 3.165501e+02 -1.882063e+03
## TUITFTE 9.531392e+08 5.429300e+08 2.949318e+02 -8.968566e+02
## INEXPFTE 5.429300e+08 4.131702e+08 5.895843e+02 -8.973091e+02
## PFTFAC 2.949318e+02 5.895843e+02 8.264291e-02 -7.665825e-03
## PCTPELL -8.968566e+02 -8.973091e+02 -7.665825e-03 4.616285e-02
## C150_4 7.315198e+02 9.611969e+02 1.046738e-02 -2.442826e-02
## PFTFTUG1_EF 5.190187e+02 6.817941e+02 1.391281e-02 -1.257610e-02
## RET_FT4 4.255470e+02 5.632499e+02 6.734007e-03 -1.615475e-02
## PCTFLOAN -2.434516e+02 -6.885527e+02 -4.350305e-03 9.849093e-03
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## C150_4 PFTFTUG1_EF RET_FT4 PCTFLOAN
## ADM_RATE -1.325186e-02 -7.776027e-03 -5.604484e-03 2.975208e-03
## SAT_AVG 2.046047e+01 1.271935e+01 1.333383e+01 -1.627136e+01
## UGDS 1.312989e+02 7.350802e+01 9.572951e+01 -1.627088e+01
## UGDS_WHITE 9.853973e-03 4.431194e-03 7.280116e-03 1.903675e-03
## UGDS_BLACK -1.221938e-02 -5.915548e-03 -9.843601e-03 1.392197e-02
## UGDS_HISP -4.649648e-03 -6.838199e-04 -1.349271e-03 -1.018841e-02
## UGDS_ASIAN 4.144713e-03 1.388544e-03 2.794559e-03 -2.502309e-03
## UGDS_AIAN -1.140529e-03 -5.606137e-04 -1.143036e-03 -1.655861e-03
## UGDS_NHPI 2.905697e-04 -3.039270e-04 -2.770611e-04 -3.314764e-04
## UGDS_2MOR 1.400528e-03 8.282901e-04 6.279306e-04 8.719972e-04
## UGDS_NRA 2.895213e-03 2.382618e-03 2.456673e-03 -3.886695e-03
## UGDS_UNKN -7.973277e-04 -1.567152e-03 -5.466105e-04 2.487782e-03
## PPTUG_EF -1.208337e-02 -3.038821e-02 -7.911504e-03 2.890825e-03
## NPT4_PUB NA NA NA NA
## NPT4_PRIV 7.086510e+02 4.240169e+02 3.445869e+02 5.262233e+02
## COSTT4_A 1.800918e+03 1.497041e+03 1.051291e+03 4.206266e+02
## TUITFTE 7.315198e+02 5.190187e+02 4.255470e+02 -2.434516e+02
## INEXPFTE 9.611969e+02 6.817941e+02 5.632499e+02 -6.885527e+02
## PFTFAC 1.046738e-02 1.391281e-02 6.734007e-03 -4.350305e-03
## PCTPELL -2.442826e-02 -1.257610e-02 -1.615475e-02 9.849093e-03
## C150_4 4.577030e-02 2.076359e-02 1.968018e-02 -5.069604e-03
## PFTFTUG1_EF 2.076359e-02 6.132454e-02 1.508620e-02 -4.878319e-03
## RET_FT4 1.968018e-02 1.508620e-02 2.820645e-02 -1.052766e-02
## PCTFLOAN -5.069604e-03 -4.878319e-03 -1.052766e-02 6.508525e-02
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## CONTROL
## ADM_RATE 0
## SAT_AVG 0
## UGDS 0
## UGDS_WHITE 0
## UGDS_BLACK 0
## UGDS_HISP 0
## UGDS_ASIAN 0
## UGDS_AIAN 0
## UGDS_NHPI 0
## UGDS_2MOR 0
## UGDS_NRA 0
## UGDS_UNKN 0
## PPTUG_EF 0
## NPT4_PUB NA
## NPT4_PRIV 0
## COSTT4_A 0
## TUITFTE 0
## INEXPFTE 0
## PFTFAC 0
## PCTPELL 0
## C150_4 0
## PFTFTUG1_EF 0
## RET_FT4 0
## PCTFLOAN 0
## CONTROL 0corrplot(cor(forprofit, use = "pairwise.complete.obs"), main = "Forprofit", type="upper", order="original", tl.col="black", tl.srt=45, tl.ex = .5, addCoef.col = TRUE, number.cex = .4)## Warning in cor(forprofit, use = "pairwise.complete.obs"): the standard
## deviation is zero## Warning in text.default(PosNA[, 1], PosNA[, 2], font = number.font, col =
## na.label.col, : "tl.ex" is not a graphical parameter## Warning in text.default(pos.xlabel[, 1], pos.xlabel[, 2], newcolnames, srt
## = tl.srt, : "tl.ex" is not a graphical parameter## Warning in text.default(pos.ylabel[, 1], pos.ylabel[, 2], newrownames, col
## = tl.col, : "tl.ex" is not a graphical parameter## Warning in title(title, ...): "tl.ex" is not a graphical parameter
cov(forprofit, use = "pairwise.complete.obs")## ADM_RATE SAT_AVG UGDS UGDS_WHITE
## ADM_RATE 3.018528e-02 -5.813080e+00 -4.787506e+01 -1.894686e-03
## SAT_AVG -5.813080e+00 1.678867e+04 -1.404658e+05 -1.058373e+00
## UGDS -4.787506e+01 -1.404658e+05 1.011364e+07 -3.493332e+01
## UGDS_WHITE -1.894686e-03 -1.058373e+00 -3.493332e+01 8.337791e-02
## UGDS_BLACK -5.916370e-04 -1.020131e+01 1.742072e-02 -3.344426e-02
## UGDS_HISP 2.906497e-03 -2.564013e+00 1.141777e+00 -3.631938e-02
## UGDS_ASIAN -1.526879e-03 2.280160e+00 -2.534462e+00 -4.689344e-03
## UGDS_AIAN 2.675216e-04 -1.828133e-01 -1.088131e-01 4.826809e-04
## UGDS_NHPI 1.754811e-04 -5.924667e-02 4.945693e-01 -4.181693e-04
## UGDS_2MOR 3.023800e-04 1.649580e+00 5.106683e+00 -3.071243e-06
## UGDS_NRA -4.605336e-04 7.616167e+00 1.872580e+00 -1.104809e-03
## UGDS_UNKN 8.215073e-04 2.514260e+00 2.923280e+01 -7.626129e-03
## PPTUG_EF -3.562037e-03 -1.481329e+01 3.320511e+01 -1.022675e-03
## NPT4_PUB NA NA NA NA
## NPT4_PRIV -2.635406e+02 7.930320e+04 9.374831e+05 -1.240066e+02
## COSTT4_A -2.823340e+02 1.013990e+05 -1.054564e+06 1.366213e+02
## TUITFTE -5.482883e+01 3.643763e+05 3.612887e+05 2.582911e+01
## INEXPFTE -7.029751e+01 3.671487e+05 -5.252836e+05 7.644524e+01
## PFTFAC -3.889060e-03 1.503040e+01 -6.668619e+01 3.705677e-03
## PCTPELL 6.797696e-03 -8.236240e+00 -1.015440e+01 -1.429713e-02
## C150_4 -2.131956e-03 1.437395e+01 -1.009311e+02 2.664676e-03
## PFTFTUG1_EF 1.694741e-02 1.570487e+01 -1.321671e+02 3.386934e-03
## RET_FT4 -8.682872e-03 1.130607e+01 -1.158528e+02 8.031208e-03
## PCTFLOAN -9.220602e-04 -7.846287e+00 3.295771e+00 7.311984e-03
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## UGDS_BLACK UGDS_HISP UGDS_ASIAN UGDS_AIAN
## ADM_RATE -5.916370e-04 2.906497e-03 -1.526879e-03 2.675216e-04
## SAT_AVG -1.020131e+01 -2.564013e+00 2.280160e+00 -1.828133e-01
## UGDS 1.742072e-02 1.141777e+00 -2.534462e+00 -1.088131e-01
## UGDS_WHITE -3.344426e-02 -3.631938e-02 -4.689344e-03 4.826809e-04
## UGDS_BLACK 6.089201e-02 -1.902799e-02 -2.840582e-03 -7.049658e-04
## UGDS_HISP -1.902799e-02 6.032735e-02 6.762256e-05 -1.546391e-04
## UGDS_ASIAN -2.840582e-03 6.762256e-05 7.464686e-03 -6.426224e-05
## UGDS_AIAN -7.049658e-04 -1.546391e-04 -6.426224e-05 4.743664e-04
## UGDS_NHPI -4.023105e-04 -5.576631e-05 2.750342e-04 1.114916e-05
## UGDS_2MOR -6.730626e-04 -9.452677e-04 -3.839737e-05 5.467154e-05
## UGDS_NRA -6.023167e-04 -1.486824e-05 2.793003e-04 -2.517022e-05
## UGDS_UNKN -3.052765e-03 -3.761066e-03 -4.353933e-04 -6.910826e-05
## PPTUG_EF 4.049642e-03 -4.541317e-03 1.412896e-03 -3.013514e-04
## NPT4_PUB NA NA NA NA
## NPT4_PRIV 1.146384e+02 -2.180677e+02 6.730717e+00 -1.599170e+00
## COSTT4_A 1.071934e+02 -3.908326e+02 6.871751e+01 5.013602e+00
## TUITFTE 2.993496e+01 -2.307021e+02 4.957734e+00 -5.818548e-01
## INEXPFTE -3.257419e+01 -1.296399e+02 -1.961725e+00 -2.256223e+00
## PFTFAC -8.937824e-03 3.498506e-03 -1.258733e-06 4.505304e-04
## PCTPELL 1.086400e-02 7.576123e-03 -2.458619e-03 1.131439e-04
## C150_4 -9.138176e-03 8.380106e-03 2.282545e-03 -7.231991e-05
## PFTFTUG1_EF -1.067939e-03 3.722735e-03 -1.301617e-03 3.528656e-05
## RET_FT4 -1.197112e-02 3.612188e-03 1.901256e-03 8.727148e-05
## PCTFLOAN 8.454763e-03 -1.552422e-02 -4.525142e-03 7.705691e-05
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## UGDS_NHPI UGDS_2MOR UGDS_NRA UGDS_UNKN
## ADM_RATE 1.754811e-04 3.023800e-04 -4.605336e-04 8.215073e-04
## SAT_AVG -5.924667e-02 1.649580e+00 7.616167e+00 2.514260e+00
## UGDS 4.945693e-01 5.106683e+00 1.872580e+00 2.923280e+01
## UGDS_WHITE -4.181693e-04 -3.071243e-06 -1.104809e-03 -7.626129e-03
## UGDS_BLACK -4.023105e-04 -6.730626e-04 -6.023167e-04 -3.052765e-03
## UGDS_HISP -5.576631e-05 -9.452677e-04 -1.486824e-05 -3.761066e-03
## UGDS_ASIAN 2.750342e-04 -3.839737e-05 2.793003e-04 -4.353933e-04
## UGDS_AIAN 1.114916e-05 5.467154e-05 -2.517022e-05 -6.910826e-05
## UGDS_NHPI 5.126742e-04 6.369530e-05 -6.670523e-06 2.305510e-05
## UGDS_2MOR 6.369530e-05 1.109162e-03 -5.444729e-05 5.001657e-04
## UGDS_NRA -6.670523e-06 -5.444729e-05 1.551995e-03 -1.969338e-05
## UGDS_UNKN 2.305510e-05 5.001657e-04 -1.969338e-05 1.447376e-02
## PPTUG_EF 2.529098e-06 2.556290e-04 8.796026e-05 5.664905e-05
## NPT4_PUB NA NA NA NA
## NPT4_PRIV 2.583758e+00 3.388250e+01 4.199023e+01 1.438584e+02
## COSTT4_A -5.355119e-02 1.402869e+01 5.864873e+01 6.722633e-01
## TUITFTE 8.882462e+00 2.083927e+01 4.763389e+01 9.350436e+01
## INEXPFTE 6.679664e+00 9.212449e+00 2.367812e+01 5.031074e+01
## PFTFAC -1.125309e-04 2.065476e-04 1.134849e-03 -4.440726e-05
## PCTPELL -1.515557e-04 -1.542680e-04 -1.215527e-03 -9.672852e-05
## C150_4 3.514270e-04 -2.985267e-04 2.738086e-04 -4.443238e-03
## PFTFTUG1_EF -8.173915e-04 1.067049e-04 -7.699709e-05 -3.988181e-03
## RET_FT4 2.451845e-04 -9.552644e-05 1.845032e-03 -3.655752e-03
## PCTFLOAN -9.339149e-05 9.465330e-04 -9.316870e-04 4.371320e-03
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## PPTUG_EF NPT4_PUB NPT4_PRIV COSTT4_A
## ADM_RATE -3.562037e-03 NA -2.635406e+02 -2.823340e+02
## SAT_AVG -1.481329e+01 NA 7.930320e+04 1.013990e+05
## UGDS 3.320511e+01 NA 9.374831e+05 -1.054564e+06
## UGDS_WHITE -1.022675e-03 NA -1.240066e+02 1.366213e+02
## UGDS_BLACK 4.049642e-03 NA 1.146384e+02 1.071934e+02
## UGDS_HISP -4.541317e-03 NA -2.180677e+02 -3.908326e+02
## UGDS_ASIAN 1.412896e-03 NA 6.730717e+00 6.871751e+01
## UGDS_AIAN -3.013514e-04 NA -1.599170e+00 5.013602e+00
## UGDS_NHPI 2.529098e-06 NA 2.583758e+00 -5.355119e-02
## UGDS_2MOR 2.556290e-04 NA 3.388250e+01 1.402869e+01
## UGDS_NRA 8.796026e-05 NA 4.199023e+01 5.864873e+01
## UGDS_UNKN 5.664905e-05 NA 1.438584e+02 6.722633e-01
## PPTUG_EF 5.709555e-02 NA 9.444090e+01 7.811069e+01
## NPT4_PUB NA NA NA NA
## NPT4_PRIV 9.444090e+01 NA 4.742631e+07 3.652982e+07
## COSTT4_A 7.811069e+01 NA 3.652982e+07 3.643841e+07
## TUITFTE 1.735878e+02 NA 2.180722e+07 1.813643e+07
## INEXPFTE 2.332564e+01 NA 4.297221e+06 5.311617e+06
## PFTFAC -1.706967e-02 NA -2.505588e+01 1.523769e+02
## PCTPELL -3.937273e-03 NA -1.326173e+02 -3.559557e+02
## C150_4 -8.996381e-03 NA 1.999895e+02 1.954150e+02
## PFTFTUG1_EF -4.286071e-02 NA -3.757500e+01 -8.427464e+01
## RET_FT4 -1.335981e-02 NA 2.950110e+02 2.920637e+02
## PCTFLOAN 1.270867e-03 NA 5.772991e+02 2.539930e+02
## CONTROL 0.000000e+00 NA 0.000000e+00 0.000000e+00
## TUITFTE INEXPFTE PFTFAC PCTPELL
## ADM_RATE -5.482883e+01 -7.029751e+01 -3.889060e-03 6.797696e-03
## SAT_AVG 3.643763e+05 3.671487e+05 1.503040e+01 -8.236240e+00
## UGDS 3.612887e+05 -5.252836e+05 -6.668619e+01 -1.015440e+01
## UGDS_WHITE 2.582911e+01 7.644524e+01 3.705677e-03 -1.429713e-02
## UGDS_BLACK 2.993496e+01 -3.257419e+01 -8.937824e-03 1.086400e-02
## UGDS_HISP -2.307021e+02 -1.296399e+02 3.498506e-03 7.576123e-03
## UGDS_ASIAN 4.957734e+00 -1.961725e+00 -1.258733e-06 -2.458619e-03
## UGDS_AIAN -5.818548e-01 -2.256223e+00 4.505304e-04 1.131439e-04
## UGDS_NHPI 8.882462e+00 6.679664e+00 -1.125309e-04 -1.515557e-04
## UGDS_2MOR 2.083927e+01 9.212449e+00 2.065476e-04 -1.542680e-04
## UGDS_NRA 4.763389e+01 2.367812e+01 1.134849e-03 -1.215527e-03
## UGDS_UNKN 9.350436e+01 5.031074e+01 -4.440726e-05 -9.672852e-05
## PPTUG_EF 1.735878e+02 2.332564e+01 -1.706967e-02 -3.937273e-03
## NPT4_PUB NA NA NA NA
## NPT4_PRIV 2.180722e+07 4.297221e+06 -2.505588e+01 -1.326173e+02
## COSTT4_A 1.813643e+07 5.311617e+06 1.523769e+02 -3.559557e+02
## TUITFTE 7.022704e+07 2.692307e+07 2.607751e+01 -1.916434e+02
## INEXPFTE 2.692307e+07 2.378391e+07 2.548895e+02 -1.097408e+02
## PFTFAC 2.607751e+01 2.548895e+02 7.681149e-02 -7.948022e-03
## PCTPELL -1.916434e+02 -1.097408e+02 -7.948022e-03 3.975721e-02
## C150_4 8.835031e+01 1.082532e+02 1.605758e-02 -2.823815e-03
## PFTFTUG1_EF 2.007595e+02 -8.561791e+01 9.990057e-04 1.193181e-02
## RET_FT4 2.260812e+02 8.775900e+01 1.481703e-02 -6.302667e-03
## PCTFLOAN 3.373045e+02 3.263181e+01 -4.795995e-03 2.206536e-02
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## C150_4 PFTFTUG1_EF RET_FT4 PCTFLOAN
## ADM_RATE -2.131956e-03 1.694741e-02 -8.682872e-03 -9.220602e-04
## SAT_AVG 1.437395e+01 1.570487e+01 1.130607e+01 -7.846287e+00
## UGDS -1.009311e+02 -1.321671e+02 -1.158528e+02 3.295771e+00
## UGDS_WHITE 2.664676e-03 3.386934e-03 8.031208e-03 7.311984e-03
## UGDS_BLACK -9.138176e-03 -1.067939e-03 -1.197112e-02 8.454763e-03
## UGDS_HISP 8.380106e-03 3.722735e-03 3.612188e-03 -1.552422e-02
## UGDS_ASIAN 2.282545e-03 -1.301617e-03 1.901256e-03 -4.525142e-03
## UGDS_AIAN -7.231991e-05 3.528656e-05 8.727148e-05 7.705691e-05
## UGDS_NHPI 3.514270e-04 -8.173915e-04 2.451845e-04 -9.339149e-05
## UGDS_2MOR -2.985267e-04 1.067049e-04 -9.552644e-05 9.465330e-04
## UGDS_NRA 2.738086e-04 -7.699709e-05 1.845032e-03 -9.316870e-04
## UGDS_UNKN -4.443238e-03 -3.988181e-03 -3.655752e-03 4.371320e-03
## PPTUG_EF -8.996381e-03 -4.286071e-02 -1.335981e-02 1.270867e-03
## NPT4_PUB NA NA NA NA
## NPT4_PRIV 1.999895e+02 -3.757500e+01 2.950110e+02 5.772991e+02
## COSTT4_A 1.954150e+02 -8.427464e+01 2.920637e+02 2.539930e+02
## TUITFTE 8.835031e+01 2.007595e+02 2.260812e+02 3.373045e+02
## INEXPFTE 1.082532e+02 -8.561791e+01 8.775900e+01 3.263181e+01
## PFTFAC 1.605758e-02 9.990057e-04 1.481703e-02 -4.795995e-03
## PCTPELL -2.823815e-03 1.193181e-02 -6.302667e-03 2.206536e-02
## C150_4 4.177170e-02 1.157788e-02 2.106522e-02 2.240202e-05
## PFTFTUG1_EF 1.157788e-02 9.410520e-02 1.291551e-02 1.934220e-03
## RET_FT4 2.106522e-02 1.291551e-02 7.748550e-02 1.649988e-04
## PCTFLOAN 2.240202e-05 1.934220e-03 1.649988e-04 6.270230e-02
## CONTROL 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## CONTROL
## ADM_RATE 0
## SAT_AVG 0
## UGDS 0
## UGDS_WHITE 0
## UGDS_BLACK 0
## UGDS_HISP 0
## UGDS_ASIAN 0
## UGDS_AIAN 0
## UGDS_NHPI 0
## UGDS_2MOR 0
## UGDS_NRA 0
## UGDS_UNKN 0
## PPTUG_EF 0
## NPT4_PUB NA
## NPT4_PRIV 0
## COSTT4_A 0
## TUITFTE 0
## INEXPFTE 0
## PFTFAC 0
## PCTPELL 0
## C150_4 0
## PFTFTUG1_EF 0
## RET_FT4 0
## PCTFLOAN 0
## CONTROL 0Question 8 Are There Differences as function of a university
Differences exist, most notably, between Public vs. Nonprofit universities. For example, the correlation between C150 & COST is -0.21 in the Public sample but jumps up to -0.67 in the Nonprofit Private sample. Also, SAT_AVG is not as strongly related in the Public data set as it is in the Nonprofit. Differences also exist in the For Profit schools from both Public & Nonprofit schools in that nearly all correlations shrink significantly in the For Profit schools.
Question 9 - 16 Simple Regressions
9.) y = -22454 + 51.9x As SAT_AVG increases, cost of attending the university increases
10.) y = 43930 + (-17799.4x) As Admission rate increases, cost of attendance decreases
11.) y = -8999.2 + 13.7x As Avg SAT score increases, the # of students increases
12.) y = 6474.7 + (-3852.2x) As admission rate increases, the number of students decreases
13.) y = -0.57 + 0.001x As SAT Score increases, completion rate increases by 0.001.
14.) y = 0.734 + (-0.3x) As admission rate increases, completion rate slightly decreases
15.) y = 1.276 + (-0.0006x) As Avg SAT score increases, % of students with Federal Student loans slightly decreases.
16.) y = 0.51 = 0.11x As admission rate increases, so does % of students with federal student loans.
Additional Analyses
Prediciting Tuition from Instructional Expenditures - this would suggest that, as instructional expenditures increases, net tuition per student increase by 0.9. y = 3062 + 0.9x
Prediciting Tuition from Percent of Undergrads recieving a federal loan - this would suggest that as the percentage of students with a Federal Student loan increases, the net tuition increases. y = 5701.5 + 8234.7x
AVGCOSTfromAVGSATLM<-lm(COSTT4_A ~ SAT_AVG, data = Project2Data)
summary(AVGCOSTfromAVGSATLM)##
## Call:
## lm(formula = COSTT4_A ~ SAT_AVG, data = Project2Data)
##
## 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-16COSTfromADMRATlm<-lm(COSTT4_A ~ ADM_RATE, data = Project2Data)
summary(COSTfromADMRATlm)##
## Call:
## lm(formula = COSTT4_A ~ ADM_RATE, data = Project2Data)
##
## 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-16NUMOFSTUDfromAVGSATlm<-lm(UGDS ~ SAT_AVG, data = Project2Data)
summary(NUMOFSTUDfromAVGSATlm)##
## Call:
## lm(formula = UGDS ~ SAT_AVG, data = Project2Data)
##
## 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-16NUMOFSTUDfromADMRATlm<-lm(UGDS ~ ADM_RATE, data = Project2Data)
summary(NUMOFSTUDfromADMRATlm)##
## Call:
## lm(formula = UGDS ~ ADM_RATE, data = Project2Data)
##
## 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-09COMPRATEfromAVGSATlm<-lm(C150_4 ~ SAT_AVG, data = Project2Data)
summary(COMPRATEfromAVGSATlm)##
## Call:
## lm(formula = C150_4 ~ SAT_AVG, data = Project2Data)
##
## 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-16COMPRATEfromADMRATEAlm<-lm(C150_4 ~ ADM_RATE, data = Project2Data)
summary(COMPRATEfromADMRATEAlm)##
## Call:
## lm(formula = C150_4 ~ ADM_RATE, data = Project2Data)
##
## 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-16PCTFLOANfromAVGSATlm<-lm(PCTFLOAN ~ SAT_AVG, data = Project2Data)
summary(PCTFLOANfromAVGSATlm)##
## Call:
## lm(formula = PCTFLOAN ~ SAT_AVG, data = Project2Data)
##
## 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-16PCTFLOANfromADMRATlm<-lm(PCTFLOAN ~ ADM_RATE, data = Project2Data)
summary(PCTFLOANfromADMRATlm)##
## Call:
## lm(formula = PCTFLOAN ~ ADM_RATE, data = Project2Data)
##
## 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-07TUITIONfromINSTRUCTREVlm<-lm(TUITFTE ~ INEXPFTE, data = Project2Data)
summary(TUITIONfromINSTRUCTREVlm)##
## Call:
## lm(formula = TUITFTE ~ INEXPFTE, data = Project2Data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -349111 -4614 571 4279 556150
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.062e+03 1.608e+02 19.04 <2e-16 ***
## INEXPFTE 9.971e-01 1.094e-02 91.14 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11870 on 7268 degrees of freedom
## (433 observations deleted due to missingness)
## Multiple R-squared: 0.5333, Adjusted R-squared: 0.5333
## F-statistic: 8306 on 1 and 7268 DF, p-value: < 2.2e-16TUITIONfromPCTFLOANlm<-lm(TUITFTE ~ PCTFLOAN, data = Project2Data)
summary(TUITIONfromPCTFLOANlm)##
## Call:
## lm(formula = TUITFTE ~ PCTFLOAN, data = Project2Data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13812 -4544 -1656 2328 1286094
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5701.5 431.7 13.21 <2e-16 ***
## PCTFLOAN 8234.7 725.0 11.36 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17180 on 6960 degrees of freedom
## (741 observations deleted due to missingness)
## Multiple R-squared: 0.0182, Adjusted R-squared: 0.01806
## F-statistic: 129 on 1 and 6960 DF, p-value: < 2.2e-1617 Are the distributions of average SAT score, admission rate, and total number of undergraduate students normal or non-normal?
Technically, we might say that the ADM_Rate variable is normally distributed, since its skewness and kurtosis scores are less than 1, and its mean and median are pretty close to one another. The AVG_SAT score variable appears normal, however it has a kurtosis score above 1. The UGDS variable is very obviously not normal with extreme kurtosis scores.
hist(Project2Data$SAT_AVG)
describe(Project2Data$SAT_AVG)## vars n mean sd median trimmed mad min max range skew
## X1 1 1304 1059.07 133.36 1039.5 1048.34 104.52 720 1545 825 0.82
## kurtosis se
## X1 1.11 3.69describe(Project2Data$ADM_RATE)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2198 0.69 0.21 0.71 0.71 0.21 0 1 1 -0.58 -0.04 0hist(Project2Data$ADM_RATE)
describe(Project2Data$UGDS)## vars n mean sd median trimmed mad min max range skew
## X1 1 6990 2332.16 5438.85 406 1052.09 526.32 0 151558 151558 6.84
## kurtosis se
## X1 104.77 65.05hist(Project2Data$UGDS)
18 For any of the distributions that were not normal in your previous answer, how could you transform them to be normal?
We are going to use the Make.Z function to transform our data into normal distributions.
Upon transformation, the mean becomes 0, sd becomes 1, and variance becomes 1.
satavgzscore<- Make.Z(Project2Data$SAT_AVG)
admratezscore<- Make.Z(Project2Data$ADM_RATE)
ugdszscore<-Make.Z(Project2Data$UGDS)
describe(satavgzscore)## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 1304 0 1 -0.15 -0.08 0.78 -2.54 3.64 6.19 0.82 1.11
## se
## X1 0.03describe(admratezscore)## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 2198 0 1 0.1 0.07 1 -3.31 1.48 4.79 -0.58 -0.04
## se
## X1 0.02describe(ugdszscore)## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 6990 0 1 -0.35 -0.24 0.1 -0.43 27.44 27.87 6.84 104.77
## se
## X1 0.01var(satavgzscore, use = "pairwise.complete.obs")## [,1]
## [1,] 1var(admratezscore, use = "pairwise.complete.obs")## [,1]
## [1,] 1var(ugdszscore, use = "pairwise.complete.obs")## [,1]
## [1,] 119 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?
Above 1400 = 0.5% Less than 800 = 2.6%
pnorm(1400,1059.07,133.36,lower.tail = FALSE)## [1] 0.005287105pnorm(800,1059.07,133.36)## [1] 0.0260300520 Imagine that the distribution of average SAT scores was perfectly normal. Answer both parts of Question 18 again using the observed mean and standard deviation as your parameters.
Above 1400 = 0.5% Less than 800 = 2.6%
pnorm(1400,1059.07,133.36,lower.tail = FALSE)## [1] 0.005287105pnorm(800,1059.07,133.36)## [1] 0.02603005