library(lmtest)
## Warning: package 'lmtest' was built under R version 4.4.2
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
library(car)
## Warning: package 'car' was built under R version 4.4.2
## Loading required package: carData
library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ ggplot2   3.5.1     ✔ tibble    3.2.1
## ✔ lubridate 1.9.3     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ✖ dplyr::recode() masks car::recode()
## ✖ purrr::some()   masks car::some()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(readxl)


District<-read_xls("District.xls")
summary(District)
##    DISTNAME           DISTRICT           DZCNTYNM            REGION         
##  Length:1207        Length:1207        Length:1207        Length:1207       
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##                                                                             
##    DZRATING            DZCAMPUS          DPETALLC           DPETBLAP     
##  Length:1207        Min.   :  1.000   Min.   :     4.0   Min.   : 0.000  
##  Class :character   1st Qu.:  2.000   1st Qu.:   337.5   1st Qu.: 0.700  
##  Mode  :character   Median :  3.000   Median :   884.0   Median : 2.900  
##                     Mean   :  7.428   Mean   :  4476.3   Mean   : 8.765  
##                     3rd Qu.:  5.000   3rd Qu.:  2746.0   3rd Qu.:10.750  
##                     Max.   :273.000   Max.   :193727.0   Max.   :98.100  
##                                                                          
##     DPETHISP         DPETWHIP        DPETINDP          DPETASIP     
##  Min.   :  0.00   Min.   : 0.00   Min.   : 0.0000   Min.   : 0.000  
##  1st Qu.: 21.00   1st Qu.:18.55   1st Qu.: 0.0000   1st Qu.: 0.000  
##  Median : 37.90   Median :44.40   Median : 0.2000   Median : 0.400  
##  Mean   : 43.29   Mean   :43.15   Mean   : 0.3283   Mean   : 1.614  
##  3rd Qu.: 61.90   3rd Qu.:67.75   3rd Qu.: 0.4000   3rd Qu.: 1.000  
##  Max.   :100.00   Max.   :97.10   Max.   :19.8000   Max.   :54.300  
##                                                                     
##     DPETPCIP          DPETTWOP         DPETECOP         DPETLEPP     
##  Min.   : 0.0000   Min.   : 0.000   Min.   :  0.00   Min.   :  0.00  
##  1st Qu.: 0.0000   1st Qu.: 1.200   1st Qu.: 47.95   1st Qu.:  2.90  
##  Median : 0.0000   Median : 2.400   Median : 61.90   Median :  7.50  
##  Mean   : 0.1005   Mean   : 2.758   Mean   : 60.75   Mean   : 12.69  
##  3rd Qu.: 0.1000   3rd Qu.: 3.900   3rd Qu.: 77.15   3rd Qu.: 17.00  
##  Max.   :14.5000   Max.   :15.000   Max.   :100.00   Max.   :100.00  
##                                                                      
##     DPETSPEP        DPETBILP         DPETVOCP        DPETGIFP      
##  Min.   : 0.00   Min.   :  0.00   Min.   : 0.00   Min.   :  0.000  
##  1st Qu.: 9.90   1st Qu.:  2.90   1st Qu.:23.00   1st Qu.:  3.100  
##  Median :12.10   Median :  7.30   Median :27.80   Median :  5.400  
##  Mean   :12.27   Mean   : 12.58   Mean   :26.47   Mean   :  5.574  
##  3rd Qu.:14.20   3rd Qu.: 16.80   3rd Qu.:32.90   3rd Qu.:  7.500  
##  Max.   :51.70   Max.   :100.00   Max.   :82.80   Max.   :100.000  
##                                                                    
##     DA0AT21R       DA0912DR21R       DAGC4X21R        DAGC5X20R     
##  Min.   : -1.00   Min.   :-1.000   Min.   : -1.00   Min.   : -1.00  
##  1st Qu.: 94.05   1st Qu.: 0.000   1st Qu.: 93.20   1st Qu.: 95.50  
##  Median : 95.40   Median : 0.400   Median : 96.90   Median : 98.30  
##  Mean   : 94.76   Mean   : 1.243   Mean   : 93.91   Mean   : 95.76  
##  3rd Qu.: 96.40   3rd Qu.: 1.400   3rd Qu.:100.00   3rd Qu.:100.00  
##  Max.   :100.00   Max.   :50.500   Max.   :100.00   Max.   :100.00  
##  NA's   :4        NA's   :112      NA's   :133      NA's   :141     
##    DAGC6X19R         DA0GR21N          DA0GS21N      DDA00A001S22R   
##  Min.   : -1.00   Min.   :    1.0   Min.   :   0.0   Min.   :  4.00  
##  1st Qu.: 95.20   1st Qu.:   29.0   1st Qu.:  26.0   1st Qu.: 68.00  
##  Median : 98.20   Median :   69.0   Median :  61.0   Median : 76.00  
##  Mean   : 95.72   Mean   :  331.6   Mean   : 278.9   Mean   : 74.77  
##  3rd Qu.:100.00   3rd Qu.:  208.0   3rd Qu.: 167.0   3rd Qu.: 83.00  
##  Max.   :100.00   Max.   :11588.0   Max.   :9607.0   Max.   :100.00  
##  NA's   :149      NA's   :126       NA's   :126      NA's   :5       
##  DDA00A001222R   DDA00A001322R   DDA00AR01S22R    DDA00AR01222R   
##  Min.   : 0.00   Min.   : 0.00   Min.   : -1.00   Min.   : -1.00  
##  1st Qu.:37.00   1st Qu.:15.00   1st Qu.: 70.00   1st Qu.: 43.00  
##  Median :46.00   Median :20.00   Median : 77.00   Median : 52.00  
##  Mean   :46.48   Mean   :21.05   Mean   : 76.22   Mean   : 52.12  
##  3rd Qu.:55.00   3rd Qu.:26.00   3rd Qu.: 84.00   3rd Qu.: 61.00  
##  Max.   :88.00   Max.   :64.00   Max.   :100.00   Max.   :100.00  
##  NA's   :5       NA's   :5       NA's   :5        NA's   :5       
##  DDA00AR01322R   DDA00AM01S22R    DDA00AM01222R   DDA00AM01322R  
##  Min.   :-1.00   Min.   : -1.00   Min.   :-1.00   Min.   :-1.00  
##  1st Qu.:17.00   1st Qu.: 66.00   1st Qu.:30.00   1st Qu.:11.00  
##  Median :22.00   Median : 74.00   Median :40.00   Median :17.00  
##  Mean   :23.64   Mean   : 72.78   Mean   :40.51   Mean   :18.21  
##  3rd Qu.:29.00   3rd Qu.: 82.00   3rd Qu.:50.00   3rd Qu.:23.00  
##  Max.   :66.00   Max.   :100.00   Max.   :91.00   Max.   :65.00  
##  NA's   :5       NA's   :5        NA's   :5       NA's   :5      
##  DDA00AC01S22R    DDA00AC01222R    DDA00AC01322R   DDA00AS01S22R   
##  Min.   : -1.00   Min.   : -1.00   Min.   :-1.00   Min.   : -1.00  
##  1st Qu.: 68.00   1st Qu.: 34.00   1st Qu.:10.00   1st Qu.: 66.00  
##  Median : 77.00   Median : 44.00   Median :16.00   Median : 75.00  
##  Mean   : 75.04   Mean   : 44.29   Mean   :17.39   Mean   : 73.09  
##  3rd Qu.: 85.00   3rd Qu.: 55.00   3rd Qu.:23.00   3rd Qu.: 83.00  
##  Max.   :100.00   Max.   :100.00   Max.   :56.00   Max.   :100.00  
##  NA's   :11       NA's   :11       NA's   :11      NA's   :43      
##  DDA00AS01222R   DDA00AS01322R   DDB00A001S22R    DDB00A001222R  
##  Min.   : -1.0   Min.   :-1.00   Min.   : -1.00   Min.   : -1.0  
##  1st Qu.: 37.0   1st Qu.:17.00   1st Qu.: 50.00   1st Qu.: 21.0  
##  Median : 46.0   Median :24.00   Median : 63.00   Median : 31.0  
##  Mean   : 45.7   Mean   :25.29   Mean   : 57.65   Mean   : 31.5  
##  3rd Qu.: 55.0   3rd Qu.:32.00   3rd Qu.: 74.50   3rd Qu.: 43.0  
##  Max.   :100.0   Max.   :77.00   Max.   :100.00   Max.   :100.0  
##  NA's   :43      NA's   :43      NA's   :192      NA's   :192    
##  DDB00A001322R   DDH00A001S22R   DDH00A001222R    DDH00A001322R  
##  Min.   :-1.00   Min.   : -1.0   Min.   : -1.00   Min.   :-1.00  
##  1st Qu.: 5.00   1st Qu.: 66.0   1st Qu.: 34.00   1st Qu.:12.00  
##  Median :11.00   Median : 73.0   Median : 41.00   Median :16.00  
##  Mean   :12.45   Mean   : 71.7   Mean   : 41.63   Mean   :16.86  
##  3rd Qu.:17.00   3rd Qu.: 80.0   3rd Qu.: 49.00   3rd Qu.:21.00  
##  Max.   :90.00   Max.   :100.0   Max.   :100.00   Max.   :59.00  
##  NA's   :192     NA's   :6       NA's   :6        NA's   :6      
##  DDW00A001S22R    DDW00A001222R    DDW00A001322R   DDI00A001S22R  
##  Min.   : -1.00   Min.   : -1.00   Min.   :-1.00   Min.   : -1.0  
##  1st Qu.: 75.00   1st Qu.: 45.00   1st Qu.:19.00   1st Qu.: -1.0  
##  Median : 82.00   Median : 54.00   Median :26.00   Median : 66.0  
##  Mean   : 78.69   Mean   : 53.24   Mean   :26.15   Mean   : 50.8  
##  3rd Qu.: 88.00   3rd Qu.: 63.00   3rd Qu.:33.00   3rd Qu.: 83.0  
##  Max.   :100.00   Max.   :100.00   Max.   :79.00   Max.   :100.0  
##  NA's   :26       NA's   :26       NA's   :26      NA's   :472    
##  DDI00A001222R    DDI00A001322R    DD300A001S22R   DD300A001222R   
##  Min.   : -1.00   Min.   : -1.00   Min.   : -1.0   Min.   : -1.00  
##  1st Qu.: -1.00   1st Qu.: -1.00   1st Qu.: 50.0   1st Qu.: 17.00  
##  Median : 35.00   Median : 11.00   Median : 89.0   Median : 67.00  
##  Mean   : 32.08   Mean   : 14.35   Mean   : 67.8   Mean   : 53.76  
##  3rd Qu.: 54.00   3rd Qu.: 23.00   3rd Qu.: 96.0   3rd Qu.: 80.00  
##  Max.   :100.00   Max.   :100.00   Max.   :100.0   Max.   :100.00  
##  NA's   :472      NA's   :472      NA's   :423     NA's   :423     
##  DD300A001322R    DD400A001S22R    DD400A001222R    DD400A001322R  
##  Min.   : -1.00   Min.   : -1.00   Min.   : -1.00   Min.   :-1.00  
##  1st Qu.:  0.00   1st Qu.: -1.00   1st Qu.: -1.00   1st Qu.:-1.00  
##  Median : 37.00   Median : 60.00   Median : 22.50   Median : 0.00  
##  Mean   : 33.08   Mean   : 44.08   Mean   : 29.23   Mean   :14.05  
##  3rd Qu.: 52.00   3rd Qu.: 83.00   3rd Qu.: 56.75   3rd Qu.:25.75  
##  Max.   :100.00   Max.   :100.00   Max.   :100.00   Max.   :83.00  
##  NA's   :423      NA's   :797      NA's   :797      NA's   :797    
##  DD200A001S22R    DD200A001222R    DD200A001322R    DDE00A001S22R   
##  Min.   : -1.00   Min.   : -1.00   Min.   : -1.00   Min.   : -1.00  
##  1st Qu.: 64.00   1st Qu.: 33.00   1st Qu.: 10.00   1st Qu.: 63.00  
##  Median : 76.00   Median : 47.00   Median : 20.00   Median : 70.00  
##  Mean   : 68.18   Mean   : 43.98   Mean   : 21.06   Mean   : 69.68  
##  3rd Qu.: 86.00   3rd Qu.: 60.00   3rd Qu.: 30.00   3rd Qu.: 77.00  
##  Max.   :100.00   Max.   :100.00   Max.   :100.00   Max.   :100.00  
##  NA's   :133      NA's   :133      NA's   :133      NA's   :10      
##  DDE00A001222R    DDE00A001322R     DA0CT21R         DA0CC21R    
##  Min.   : -1.00   Min.   :-1.0   Min.   : -2.00   Min.   :-1.00  
##  1st Qu.: 32.00   1st Qu.:12.0   1st Qu.: 40.42   1st Qu.:12.90  
##  Median : 39.00   Median :15.0   Median : 63.05   Median :23.55  
##  Mean   : 39.23   Mean   :15.9   Mean   : 60.76   Mean   :26.10  
##  3rd Qu.: 46.00   3rd Qu.:19.0   3rd Qu.: 85.38   3rd Qu.:37.08  
##  Max.   :100.00   Max.   :80.0   Max.   :100.00   Max.   :97.70  
##  NA's   :10       NA's   :10     NA's   :125      NA's   :147    
##    DA0CSA21R        DA0CAA21R        DPSATOFC          DPSTTOFC       
##  Min.   :  -1.0   Min.   :-1.00   Min.   :    1.0   Min.   :    0.00  
##  1st Qu.: 887.0   1st Qu.:16.30   1st Qu.:   58.9   1st Qu.:   30.57  
##  Median : 973.0   Median :19.00   Median :  144.1   Median :   72.00  
##  Mean   : 823.9   Mean   :16.13   Mean   :  622.5   Mean   :  307.06  
##  3rd Qu.:1039.0   3rd Qu.:21.20   3rd Qu.:  405.2   3rd Qu.:  196.50  
##  Max.   :1344.0   Max.   :31.40   Max.   :23716.2   Max.   :10619.50  
##  NA's   :262      NA's   :236     NA's   :3         NA's   :3         
##     DPSCTOFP         DPSSTOFP         DPSUTOFP         DPSTTOFP    
##  Min.   : 0.000   Min.   :  0.00   Min.   : 0.000   Min.   : 0.00  
##  1st Qu.: 1.200   1st Qu.:  2.60   1st Qu.: 4.100   1st Qu.:46.60  
##  Median : 1.800   Median :  3.10   Median : 6.600   Median :50.80  
##  Mean   : 2.178   Mean   :  3.58   Mean   : 7.169   Mean   :50.98  
##  3rd Qu.: 2.600   3rd Qu.:  3.90   3rd Qu.: 9.800   3rd Qu.:54.80  
##  Max.   :14.900   Max.   :100.00   Max.   :49.700   Max.   :88.30  
##  NA's   :3        NA's   :3        NA's   :3        NA's   :3      
##     DPSETOFP        DPSXTOFP        DPSCTOSA         DPSSTOSA     
##  Min.   : 0.00   Min.   : 0.00   Min.   :    -2   Min.   :    -2  
##  1st Qu.: 9.70   1st Qu.:19.38   1st Qu.: 95459   1st Qu.: 73469  
##  Median :12.60   Median :23.65   Median :106674   Median : 78723  
##  Mean   :12.95   Mean   :23.14   Mean   :108039   Mean   : 79435  
##  3rd Qu.:16.20   3rd Qu.:27.50   3rd Qu.:119540   3rd Qu.: 84945  
##  Max.   :48.80   Max.   :55.40   Max.   :270000   Max.   :192500  
##  NA's   :3       NA's   :3       NA's   :10       NA's   :11      
##     DPSUTOSA         DPSTTOSA         DPSAMIFP         DPSAKIDR      
##  Min.   :    -2   Min.   : 36081   Min.   :  0.00   Min.   :  0.100  
##  1st Qu.: 57969   1st Qu.: 50439   1st Qu.: 13.30   1st Qu.:  5.400  
##  Median : 63015   Median : 53382   Median : 26.60   Median :  6.300  
##  Mean   : 62424   Mean   : 53971   Mean   : 35.24   Mean   :  6.734  
##  3rd Qu.: 67941   3rd Qu.: 56919   3rd Qu.: 50.62   3rd Qu.:  7.300  
##  Max.   :228972   Max.   :110560   Max.   :100.00   Max.   :349.100  
##  NA's   :54       NA's   :4        NA's   :3        NA's   :3        
##     DPSTKIDR        DPST05FP         DPSTEXPA        DPSTADFP    
##  Min.   :-2.00   Min.   :  0.00   Min.   : 0.00   Min.   : 0.00  
##  1st Qu.:10.80   1st Qu.: 24.35   1st Qu.:10.07   1st Qu.:14.88  
##  Median :12.70   Median : 32.40   Median :12.00   Median :20.90  
##  Mean   :12.56   Mean   : 34.88   Mean   :11.75   Mean   :20.86  
##  3rd Qu.:14.40   3rd Qu.: 41.65   3rd Qu.:13.90   3rd Qu.:26.12  
##  Max.   :37.30   Max.   :100.00   Max.   :22.90   Max.   :78.70  
##  NA's   :3       NA's   :3        NA's   :3       NA's   :3      
##     DPSTURNR         DPSTBLFP         DPSTHIFP         DPSTWHFP     
##  Min.   :  0.00   Min.   :  0.00   Min.   :  0.00   Min.   :  0.00  
##  1st Qu.: 14.80   1st Qu.:  0.00   1st Qu.:  4.20   1st Qu.: 58.67  
##  Median : 19.50   Median :  1.60   Median : 10.10   Median : 82.40  
##  Mean   : 21.51   Mean   :  6.99   Mean   : 19.05   Mean   : 71.57  
##  3rd Qu.: 25.90   3rd Qu.:  6.20   3rd Qu.: 22.50   3rd Qu.: 92.60  
##  Max.   :100.00   Max.   :100.00   Max.   :100.00   Max.   :100.00  
##  NA's   :7        NA's   :3        NA's   :3        NA's   :3       
##     DPSTINFP          DPSTASFP         DPSTPIFP          DPSTTWFP      
##  Min.   : 0.0000   Min.   : 0.000   Min.   :0.00000   Min.   : 0.0000  
##  1st Qu.: 0.0000   1st Qu.: 0.000   1st Qu.:0.00000   1st Qu.: 0.0000  
##  Median : 0.0000   Median : 0.000   Median :0.00000   Median : 0.0000  
##  Mean   : 0.3566   Mean   : 1.118   Mean   :0.08206   Mean   : 0.7566  
##  3rd Qu.: 0.3000   3rd Qu.: 0.900   3rd Qu.:0.00000   3rd Qu.: 1.2000  
##  Max.   :16.7000   Max.   :94.800   Max.   :7.80000   Max.   :11.7000  
##  NA's   :3         NA's   :3        NA's   :3         NA's   :3        
##     DPSTREFP         DPSTSPFP         DPSTCOFP         DPSTBIFP     
##  Min.   :  0.00   Min.   : 0.000   Min.   : 0.000   Min.   : 0.000  
##  1st Qu.: 71.00   1st Qu.: 4.500   1st Qu.: 0.000   1st Qu.: 0.000  
##  Median : 76.90   Median : 7.000   Median : 3.350   Median : 0.000  
##  Mean   : 76.87   Mean   : 7.145   Mean   : 4.131   Mean   : 2.311  
##  3rd Qu.: 82.42   3rd Qu.: 9.600   3rd Qu.: 6.125   3rd Qu.: 2.100  
##  Max.   :100.00   Max.   :22.800   Max.   :32.500   Max.   :94.300  
##  NA's   :3        NA's   :3        NA's   :3        NA's   :3       
##     DPSTVOFP         DPSTGOFP         DPFVTOTK           DPFTADPR     
##  Min.   : 0.000   Min.   : 0.000   Min.   :       0   Min.   :0.0000  
##  1st Qu.: 4.800   1st Qu.: 0.000   1st Qu.:  238299   1st Qu.:0.9892  
##  Median : 7.000   Median : 1.200   Median :  419144   Median :1.1670  
##  Mean   : 7.154   Mean   : 2.308   Mean   :  665067   Mean   :1.0212  
##  3rd Qu.: 9.425   3rd Qu.: 3.700   3rd Qu.:  670248   3rd Qu.:1.3017  
##  Max.   :71.900   Max.   :30.800   Max.   :26416597   Max.   :1.7480  
##  NA's   :3        NA's   :3        NA's   :5          NA's   :5       
##    DPFRAALLT           DPFRAALLK        DPFRAOPRT           DPFRASTAP     
##  Min.   :6.428e+05   Min.   :  8923   Min.   :6.428e+05   Min.   :  1.70  
##  1st Qu.:5.828e+06   1st Qu.: 12953   1st Qu.:5.524e+06   1st Qu.: 33.85  
##  Median :1.381e+07   Median : 14653   Median :1.241e+07   Median : 51.00  
##  Mean   :5.995e+07   Mean   : 16365   Mean   :5.129e+07   Mean   : 49.05  
##  3rd Qu.:3.805e+07   3rd Qu.: 17081   3rd Qu.:3.241e+07   3rd Qu.: 64.80  
##  Max.   :2.619e+09   Max.   :214078   Max.   :2.213e+09   Max.   :103.40  
##  NA's   :5           NA's   :5        NA's   :5           NA's   :5       
##     DZRVLOCP       DPFRAFEDP       DPFRAORVT           DPFUNAB1T        
##  Min.   :-6.20   Min.   : 0.00   Min.   :  -655726   Min.   :  -746998  
##  1st Qu.:21.10   1st Qu.: 8.70   1st Qu.:    98311   1st Qu.:  1226730  
##  Median :35.30   Median :12.30   Median :  1093332   Median :  3589384  
##  Mean   :37.92   Mean   :13.04   Mean   :  8659622   Mean   : 13498263  
##  3rd Qu.:53.70   3rd Qu.:16.20   3rd Qu.:  4471240   3rd Qu.:  9357248  
##  Max.   :97.60   Max.   :49.00   Max.   :405596099   Max.   :662450197  
##  NA's   :5       NA's   :5       NA's   :5           NA's   :5          
##     DPFUNA4T           DPFEAALLT           DPFEAOPFT           DPFEAOPFK     
##  Min.   : -7033092   Min.   :6.229e+05   Min.   :6.120e+05   Min.   :  6755  
##  1st Qu.:        0   1st Qu.:5.475e+06   1st Qu.:4.754e+06   1st Qu.: 10916  
##  Median :        0   Median :1.328e+07   Median :1.102e+07   Median : 12228  
##  Mean   :   510514   Mean   :6.597e+07   Mean   :4.951e+07   Mean   : 13121  
##  3rd Qu.:        0   3rd Qu.:3.787e+07   3rd Qu.:3.038e+07   3rd Qu.: 14012  
##  Max.   :126144201   Max.   :2.656e+09   Max.   :2.068e+09   Max.   :178467  
##  NA's   :5           NA's   :5           NA's   :5           NA's   :5       
##    DPFEAINSP        DZEXADMP         DZEXADSP         DZEXPLAP    
##  Min.   :18.50   Min.   : 2.700   Min.   : 0.000   Min.   : 0.20  
##  1st Qu.:52.00   1st Qu.: 7.125   1st Qu.: 4.900   1st Qu.:10.40  
##  Median :55.10   Median : 8.800   Median : 5.700   Median :11.80  
##  Mean   :54.73   Mean   : 9.606   Mean   : 6.015   Mean   :12.46  
##  3rd Qu.:57.80   3rd Qu.:11.200   3rd Qu.: 6.400   3rd Qu.:13.50  
##  Max.   :84.40   Max.   :35.800   Max.   :22.700   Max.   :43.10  
##  NA's   :5       NA's   :5        NA's   :5        NA's   :5      
##     DZEXOTHP       DPFEAINST           DPFEAINSK       DPFPAREGP    
##  Min.   : 0.30   Min.   :2.439e+05   Min.   : 3122   Min.   : 0.00  
##  1st Qu.:15.30   1st Qu.:2.563e+06   1st Qu.: 6056   1st Qu.:35.12  
##  Median :18.00   Median :6.013e+06   Median : 6702   Median :39.70  
##  Mean   :17.15   Mean   :2.835e+07   Mean   : 7074   Mean   :39.80  
##  3rd Qu.:20.00   3rd Qu.:1.683e+07   3rd Qu.: 7577   3rd Qu.:43.90  
##  Max.   :69.30   Max.   :1.177e+09   Max.   :54954   Max.   :79.10  
##  NA's   :5       NA's   :5           NA's   :5       NA's   :5      
##    DPFPASPEP        DPFPACOMP        DPFPABILP         DPFPAVOCP    
##  Min.   : 0.000   Min.   : 0.000   Min.   : 0.0000   Min.   : 0.00  
##  1st Qu.: 5.800   1st Qu.: 6.500   1st Qu.: 0.1000   1st Qu.: 2.90  
##  Median : 8.900   Median : 9.200   Median : 0.4000   Median : 4.10  
##  Mean   : 9.711   Mean   : 9.883   Mean   : 0.7496   Mean   : 3.96  
##  3rd Qu.:12.500   3rd Qu.:12.100   3rd Qu.: 1.0000   3rd Qu.: 5.20  
##  Max.   :49.000   Max.   :90.600   Max.   :26.0000   Max.   :19.80  
##  NA's   :5        NA's   :5        NA's   :5         NA's   :5      
##    DPFPAGIFP        DPFPAATHP       DPFPAHSAP         DPFPREKP      
##  Min.   :0.0000   Min.   :0.000   Min.   :0.0000   Min.   : 0.0000  
##  1st Qu.:0.0000   1st Qu.:1.600   1st Qu.:0.0000   1st Qu.: 0.0000  
##  Median :0.2000   Median :2.900   Median :0.0000   Median : 0.6000  
##  Mean   :0.3823   Mean   :2.809   Mean   :0.1578   Mean   : 0.8909  
##  3rd Qu.:0.4000   3rd Qu.:4.000   3rd Qu.:0.1000   3rd Qu.: 1.3000  
##  Max.   :6.9000   Max.   :9.000   Max.   :3.4000   Max.   :31.7000  
##  NA's   :5        NA's   :5       NA's   :5        NA's   :5        
##    DPFPAOTHP       DISTSIZE           COMMTYPE           PROPWLTH        
##  Min.   : 3.50   Length:1207        Length:1207        Length:1207       
##  1st Qu.:25.40   Class :character   Class :character   Class :character  
##  Median :28.70   Mode  :character   Mode  :character   Mode  :character  
##  Mean   :29.22                                                           
##  3rd Qu.:32.40                                                           
##  Max.   :76.30                                                           
##  NA's   :5                                                               
##    TAXRATE         
##  Length:1207       
##  Class :character  
##  Mode  :character  
##                    
##                    
##                    
##

#summary of all variables of data

head(District)
## # A tibble: 6 × 137
##   DISTNAME DISTRICT DZCNTYNM REGION DZRATING DZCAMPUS DPETALLC DPETBLAP DPETHISP
##   <chr>    <chr>    <chr>    <chr>  <chr>       <dbl>    <dbl>    <dbl>    <dbl>
## 1 CAYUGA … 001902   001 AND… 07     A               3      574      4.4     11.5
## 2 ELKHART… 001903   001 AND… 07     A               4     1150      4       11.8
## 3 FRANKST… 001904   001 AND… 07     A               3      808      8.5     11.3
## 4 NECHES … 001906   001 AND… 07     A               2      342      8.2     13.5
## 5 PALESTI… 001907   001 AND… 07     B               6     3360     25.1     42.9
## 6 WESTWOO… 001908   001 AND… 07     B               4     1332     19.7     26.2
## # ℹ 128 more variables: DPETWHIP <dbl>, DPETINDP <dbl>, DPETASIP <dbl>,
## #   DPETPCIP <dbl>, DPETTWOP <dbl>, DPETECOP <dbl>, DPETLEPP <dbl>,
## #   DPETSPEP <dbl>, DPETBILP <dbl>, DPETVOCP <dbl>, DPETGIFP <dbl>,
## #   DA0AT21R <dbl>, DA0912DR21R <dbl>, DAGC4X21R <dbl>, DAGC5X20R <dbl>,
## #   DAGC6X19R <dbl>, DA0GR21N <dbl>, DA0GS21N <dbl>, DDA00A001S22R <dbl>,
## #   DDA00A001222R <dbl>, DDA00A001322R <dbl>, DDA00AR01S22R <dbl>,
## #   DDA00AR01222R <dbl>, DDA00AR01322R <dbl>, DDA00AM01S22R <dbl>, …
str(District)
## tibble [1,207 × 137] (S3: tbl_df/tbl/data.frame)
##  $ DISTNAME     : chr [1:1207] "CAYUGA ISD" "ELKHART ISD" "FRANKSTON ISD" "NECHES ISD" ...
##  $ DISTRICT     : chr [1:1207] "001902" "001903" "001904" "001906" ...
##  $ DZCNTYNM     : chr [1:1207] "001 ANDERSON" "001 ANDERSON" "001 ANDERSON" "001 ANDERSON" ...
##  $ REGION       : chr [1:1207] "07" "07" "07" "07" ...
##  $ DZRATING     : chr [1:1207] "A" "A" "A" "A" ...
##  $ DZCAMPUS     : num [1:1207] 3 4 3 2 6 4 2 6 4 5 ...
##  $ DPETALLC     : num [1:1207] 574 1150 808 342 3360 ...
##  $ DPETBLAP     : num [1:1207] 4.4 4 8.5 8.2 25.1 19.7 0.3 0.8 15.7 7.2 ...
##  $ DPETHISP     : num [1:1207] 11.5 11.8 11.3 13.5 42.9 26.2 8.6 68.7 31.2 27.9 ...
##  $ DPETWHIP     : num [1:1207] 79.1 80.3 75.2 75.1 27.3 48 87 28.2 48.5 60.6 ...
##  $ DPETINDP     : num [1:1207] 0 0.3 0.4 0.3 0.2 0.7 0 0.3 0.1 0.3 ...
##  $ DPETASIP     : num [1:1207] 0.5 0.2 1 0.3 0.7 0.5 0.6 0.3 1 1 ...
##  $ DPETPCIP     : num [1:1207] 0 0 0 0 0.1 0.1 0 0 0.1 0.1 ...
##  $ DPETTWOP     : num [1:1207] 4.5 3.4 3.6 2.6 3.7 4.9 3.6 1.7 3.4 3 ...
##  $ DPETECOP     : num [1:1207] 40.8 45.4 54.2 54.1 81.6 74 46.8 49.6 57.8 50.1 ...
##  $ DPETLEPP     : num [1:1207] 1 2.8 4.1 2 17.7 7.1 0.6 14.2 5.1 6.9 ...
##  $ DPETSPEP     : num [1:1207] 14.6 12.1 13.1 10.5 13.5 14.5 14.7 10.4 11.6 11.9 ...
##  $ DPETBILP     : num [1:1207] 1 2.7 4.1 2 16.1 6.8 0.6 15.2 5 6 ...
##  $ DPETVOCP     : num [1:1207] 30.5 31.8 43.9 29.5 30.6 38.7 37.7 24.8 18.9 34.4 ...
##  $ DPETGIFP     : num [1:1207] 6.1 4.6 7.3 5.6 2.3 3.2 3.3 6.8 9.2 6 ...
##  $ DA0AT21R     : num [1:1207] 96.7 96 95.4 95.8 93.7 94.5 96.7 92.8 97.3 95.2 ...
##  $ DA0912DR21R  : num [1:1207] 0 0.3 0.4 0 0 0 0 0.4 0.4 0.7 ...
##  $ DAGC4X21R    : num [1:1207] 100 100 95.2 95.8 99 97.8 100 96.8 100 94.1 ...
##  $ DAGC5X20R    : num [1:1207] 100 98.9 100 97 99.6 97 100 97.2 100 95.6 ...
##  $ DAGC6X19R    : num [1:1207] 96 98.8 33.3 100 98.6 97.4 100 96.7 100 95.9 ...
##  $ DA0GR21N     : num [1:1207] 36 91 41 23 201 95 32 293 52 196 ...
##  $ DA0GS21N     : num [1:1207] 34 79 40 17 198 77 27 238 52 154 ...
##  $ DDA00A001S22R: num [1:1207] 84 85 83 90 74 69 86 76 82 86 ...
##  $ DDA00A001222R: num [1:1207] 62 59 57 64 46 40 55 47 56 60 ...
##  $ DDA00A001322R: num [1:1207] 33 30 25 27 20 16 25 21 30 31 ...
##  $ DDA00AR01S22R: num [1:1207] 81 85 84 87 72 70 86 75 82 84 ...
##  $ DDA00AR01222R: num [1:1207] 67 64 63 67 48 45 66 50 60 62 ...
##  $ DDA00AR01322R: num [1:1207] 39 34 24 30 20 19 31 22 31 31 ...
##  $ DDA00AM01S22R: num [1:1207] 88 84 85 94 75 66 81 76 81 88 ...
##  $ DDA00AM01222R: num [1:1207] 65 49 57 69 44 34 42 44 53 62 ...
##  $ DDA00AM01322R: num [1:1207] 34 23 26 27 20 14 19 21 29 33 ...
##  $ DDA00AC01S22R: num [1:1207] 85 86 81 90 78 73 96 75 83 84 ...
##  $ DDA00AC01222R: num [1:1207] 54 63 49 54 48 41 45 46 57 52 ...
##  $ DDA00AC01322R: num [1:1207] 22 29 21 23 22 15 16 18 27 21 ...
##  $ DDA00AS01S22R: num [1:1207] 78 90 74 83 72 68 92 81 82 87 ...
##  $ DDA00AS01222R: num [1:1207] 47 63 48 51 42 38 73 50 51 60 ...
##  $ DDA00AS01322R: num [1:1207] 21 42 26 26 20 15 38 27 32 36 ...
##  $ DDB00A001S22R: num [1:1207] 60 46 74 88 64 56 -1 71 68 71 ...
##  $ DDB00A001222R: num [1:1207] 17 22 38 48 33 26 -1 41 38 37 ...
##  $ DDB00A001322R: num [1:1207] 3 8 6 19 11 11 -1 13 14 14 ...
##  $ DDH00A001S22R: num [1:1207] 74 85 75 91 73 69 87 72 81 81 ...
##  $ DDH00A001222R: num [1:1207] 53 56 46 69 44 36 57 42 50 53 ...
##  $ DDH00A001322R: num [1:1207] 24 25 19 26 19 12 20 17 24 24 ...
##  $ DDW00A001S22R: num [1:1207] 87 88 85 89 83 75 86 84 88 89 ...
##  $ DDW00A001222R: num [1:1207] 66 61 62 66 60 48 55 58 67 66 ...
##  $ DDW00A001322R: num [1:1207] 35 32 28 29 29 21 26 29 40 35 ...
##  $ DDI00A001S22R: num [1:1207] NA 100 80 -1 75 NA NA 83 -1 62 ...
##  $ DDI00A001222R: num [1:1207] NA 100 20 -1 50 NA NA 28 -1 8 ...
##  $ DDI00A001322R: num [1:1207] NA 100 20 -1 17 NA NA 6 -1 0 ...
##  $ DD300A001S22R: num [1:1207] 33 -1 84 -1 85 100 NA 100 93 97 ...
##  $ DD300A001222R: num [1:1207] 33 -1 53 -1 77 100 NA 87 73 82 ...
##  $ DD300A001322R: num [1:1207] 17 -1 16 -1 44 88 NA 67 53 56 ...
##  $ DD400A001S22R: num [1:1207] NA NA NA NA -1 -1 NA NA -1 -1 ...
##  $ DD400A001222R: num [1:1207] NA NA NA NA -1 -1 NA NA -1 -1 ...
##  $ DD400A001322R: num [1:1207] NA NA NA NA -1 -1 NA NA -1 -1 ...
##  $ DD200A001S22R: num [1:1207] 83 77 75 -1 74 62 88 85 74 83 ...
##  $ DD200A001222R: num [1:1207] 54 46 58 -1 44 38 50 58 48 50 ...
##  $ DD200A001322R: num [1:1207] 34 23 28 -1 18 13 6 31 13 29 ...
##  $ DDE00A001S22R: num [1:1207] 76 77 77 86 70 65 81 67 77 78 ...
##  $ DDE00A001222R: num [1:1207] 50 42 49 53 40 34 45 36 48 46 ...
##  $ DDE00A001322R: num [1:1207] 23 19 17 17 16 14 17 14 23 19 ...
##  $ DA0CT21R     : num [1:1207] 58.3 51.6 92.7 87 43.3 40 12.5 42 9.6 38.3 ...
##  $ DA0CC21R     : num [1:1207] 19 27.7 36.8 15 49.4 28.9 -1 35.8 60 60 ...
##  $ DA0CSA21R    : num [1:1207] 980 979 980 1007 1048 ...
##  $ DA0CAA21R    : num [1:1207] NA -1 -1 18.8 21 -1 -1 22.3 NA 23.1 ...
##  $ DPSATOFC     : num [1:1207] 99.9 186.6 146.7 60.1 553.4 ...
##  $ DPSTTOFC     : num [1:1207] 46.7 104.9 74.5 30.2 260.3 ...
##  $ DPSCTOFP     : num [1:1207] 1.5 1.1 1.4 3.1 2.1 1.1 4.1 1.5 4.5 0.9 ...
##  $ DPSSTOFP     : num [1:1207] 5 2.1 3.5 5 3.4 4.6 3.4 2.6 3.1 3.9 ...
##  $ DPSUTOFP     : num [1:1207] 5.4 4.9 2 1.7 8.3 4.4 3 5.8 10 6 ...
##  $ DPSTTOFP     : num [1:1207] 46.8 56.2 50.8 50.3 47 45.5 56.7 50.8 50 49.7 ...
##  $ DPSETOFP     : num [1:1207] 14.8 16.2 15 13.7 19.7 19.2 9.8 15.4 11.1 8.2 ...
##  $ DPSXTOFP     : num [1:1207] 26.5 19.5 27.4 26.2 19.5 25.2 23 23.9 21.4 31.3 ...
##  $ DPSCTOSA     : num [1:1207] 93333 100313 98293 85537 99324 ...
##  $ DPSSTOSA     : num [1:1207] 73300 79305 71215 81593 80415 ...
##  $ DPSUTOSA     : num [1:1207] 59550 60616 58022 77642 63829 ...
##  $ DPSTTOSA     : num [1:1207] 55570 47916 50382 55346 48825 ...
##  $ DPSAMIFP     : num [1:1207] 15.6 13.4 10.9 16.3 32.1 29.9 1.9 41.3 22.2 18.8 ...
##  $ DPSAKIDR     : num [1:1207] 5.7 6.2 5.5 5.7 6.1 5 5.2 7.3 7.4 6.5 ...
##  $ DPSTKIDR     : num [1:1207] 12.3 11 10.8 11.3 12.9 11 9.3 14.4 14.8 13.2 ...
##  $ DPST05FP     : num [1:1207] 10.4 23.8 32.7 9.7 33.8 44.8 17.9 21.5 35 21.9 ...
##  $ DPSTEXPA     : num [1:1207] 16.7 13.5 12.8 14.8 12.7 10.3 15.4 13.8 10.2 13.8 ...
##  $ DPSTADFP     : num [1:1207] 14.8 19 30.7 9.6 15.4 17.4 16.9 24.3 18.5 22.4 ...
##  $ DPSTURNR     : num [1:1207] 19.1 13.9 21.6 18.3 17.9 30.6 14.6 11.5 17 9.5 ...
##  $ DPSTBLFP     : num [1:1207] 8.3 2.9 4 6.5 9.6 11.6 0 1.4 4.4 0.5 ...
##  $ DPSTHIFP     : num [1:1207] 0 6.7 1.3 0 13.8 6.6 0 25.7 8.9 5.6 ...
##  $ DPSTWHFP     : num [1:1207] 91.7 90.5 93.3 93.5 74.6 80.9 100 69 86.7 93.9 ...
##  $ DPSTINFP     : num [1:1207] 0 0 0 0 0 0.8 0 0.3 0 0 ...
##  $ DPSTASFP     : num [1:1207] 0 0 0 0 0 0 0 0.7 0 0 ...
##  $ DPSTPIFP     : num [1:1207] 0 0 0 0 0 0 0 0 0 0 ...
##  $ DPSTTWFP     : num [1:1207] 0 0 1.3 0 1.9 0 0 2.8 0 0 ...
##  $ DPSTREFP     : num [1:1207] 81.6 71.5 87.6 70 71.4 71.4 61 41.7 82.7 66.4 ...
##  $ DPSTSPFP     : num [1:1207] 9.9 8.4 7.5 5.5 10.2 6.4 5.8 14.4 6.8 9.6 ...
##  $ DPSTCOFP     : num [1:1207] 0 4.9 2.7 12 5 6.1 19.2 6.5 7.4 9.2 ...
##   [list output truncated]

#this reformats the data

#DAGC6X20R 6-YR LONGITUDINAL GRADUATION RATE (CLASS OF 2020) DISTRICT EXCL

#DA0AT22R ATTENDANCE RATE (2019-20) - independent variable

#DA0912DR22R ANNUAL DROPOUT RATE GR. 9-12 (2019-20) - independent variable

#DPETECOP STUDENTS: % ECONOMICALLY DISADVANTAGED - independent variable

#DPSAMIFP STAFF: % MINORITY - independent variable

#DPSTURNR TEACHER: TURNOVER RATE - independent variable

#DPFEAOPFK - TOTAL ACTUAL OPERATING EXPENDITURES PER PUPIL - independent variable

#DPFPAHSAP - EXPENDITURE: % HIGH SCHOOL ALLOTMENT (no. of money for each student who attends school that day) - independent variable

colnames(District)
##   [1] "DISTNAME"      "DISTRICT"      "DZCNTYNM"      "REGION"       
##   [5] "DZRATING"      "DZCAMPUS"      "DPETALLC"      "DPETBLAP"     
##   [9] "DPETHISP"      "DPETWHIP"      "DPETINDP"      "DPETASIP"     
##  [13] "DPETPCIP"      "DPETTWOP"      "DPETECOP"      "DPETLEPP"     
##  [17] "DPETSPEP"      "DPETBILP"      "DPETVOCP"      "DPETGIFP"     
##  [21] "DA0AT21R"      "DA0912DR21R"   "DAGC4X21R"     "DAGC5X20R"    
##  [25] "DAGC6X19R"     "DA0GR21N"      "DA0GS21N"      "DDA00A001S22R"
##  [29] "DDA00A001222R" "DDA00A001322R" "DDA00AR01S22R" "DDA00AR01222R"
##  [33] "DDA00AR01322R" "DDA00AM01S22R" "DDA00AM01222R" "DDA00AM01322R"
##  [37] "DDA00AC01S22R" "DDA00AC01222R" "DDA00AC01322R" "DDA00AS01S22R"
##  [41] "DDA00AS01222R" "DDA00AS01322R" "DDB00A001S22R" "DDB00A001222R"
##  [45] "DDB00A001322R" "DDH00A001S22R" "DDH00A001222R" "DDH00A001322R"
##  [49] "DDW00A001S22R" "DDW00A001222R" "DDW00A001322R" "DDI00A001S22R"
##  [53] "DDI00A001222R" "DDI00A001322R" "DD300A001S22R" "DD300A001222R"
##  [57] "DD300A001322R" "DD400A001S22R" "DD400A001222R" "DD400A001322R"
##  [61] "DD200A001S22R" "DD200A001222R" "DD200A001322R" "DDE00A001S22R"
##  [65] "DDE00A001222R" "DDE00A001322R" "DA0CT21R"      "DA0CC21R"     
##  [69] "DA0CSA21R"     "DA0CAA21R"     "DPSATOFC"      "DPSTTOFC"     
##  [73] "DPSCTOFP"      "DPSSTOFP"      "DPSUTOFP"      "DPSTTOFP"     
##  [77] "DPSETOFP"      "DPSXTOFP"      "DPSCTOSA"      "DPSSTOSA"     
##  [81] "DPSUTOSA"      "DPSTTOSA"      "DPSAMIFP"      "DPSAKIDR"     
##  [85] "DPSTKIDR"      "DPST05FP"      "DPSTEXPA"      "DPSTADFP"     
##  [89] "DPSTURNR"      "DPSTBLFP"      "DPSTHIFP"      "DPSTWHFP"     
##  [93] "DPSTINFP"      "DPSTASFP"      "DPSTPIFP"      "DPSTTWFP"     
##  [97] "DPSTREFP"      "DPSTSPFP"      "DPSTCOFP"      "DPSTBIFP"     
## [101] "DPSTVOFP"      "DPSTGOFP"      "DPFVTOTK"      "DPFTADPR"     
## [105] "DPFRAALLT"     "DPFRAALLK"     "DPFRAOPRT"     "DPFRASTAP"    
## [109] "DZRVLOCP"      "DPFRAFEDP"     "DPFRAORVT"     "DPFUNAB1T"    
## [113] "DPFUNA4T"      "DPFEAALLT"     "DPFEAOPFT"     "DPFEAOPFK"    
## [117] "DPFEAINSP"     "DZEXADMP"      "DZEXADSP"      "DZEXPLAP"     
## [121] "DZEXOTHP"      "DPFEAINST"     "DPFEAINSK"     "DPFPAREGP"    
## [125] "DPFPASPEP"     "DPFPACOMP"     "DPFPABILP"     "DPFPAVOCP"    
## [129] "DPFPAGIFP"     "DPFPAATHP"     "DPFPAHSAP"     "DPFPREKP"     
## [133] "DPFPAOTHP"     "DISTSIZE"      "COMMTYPE"      "PROPWLTH"     
## [137] "TAXRATE"
shapiro.test(District$DAGC5X20R)
## 
##  Shapiro-Wilk normality test
## 
## data:  District$DAGC5X20R
## W = 0.34119, p-value < 2.2e-16
shapiro.test(District$DPETECOP)
## 
##  Shapiro-Wilk normality test
## 
## data:  District$DPETECOP
## W = 0.97963, p-value = 5.308e-12
shapiro.test(District$DA0AT21R)
## 
##  Shapiro-Wilk normality test
## 
## data:  District$DA0AT21R
## W = 0.36008, p-value < 2.2e-16
shapiro.test(District$DA0912DR21R)
## 
##  Shapiro-Wilk normality test
## 
## data:  District$DA0912DR21R
## W = 0.33387, p-value < 2.2e-16
shapiro.test(District$DPSAMIFP)
## 
##  Shapiro-Wilk normality test
## 
## data:  District$DPSAMIFP
## W = 0.8865, p-value < 2.2e-16
shapiro.test(District$DPSTURNR)
## 
##  Shapiro-Wilk normality test
## 
## data:  District$DPSTURNR
## W = 0.88901, p-value < 2.2e-16
shapiro.test(District$DPFEAOPFK)
## 
##  Shapiro-Wilk normality test
## 
## data:  District$DPFEAOPFK
## W = 0.34785, p-value < 2.2e-16
shapiro.test(District$DPFPAHSAP)
## 
##  Shapiro-Wilk normality test
## 
## data:  District$DPFPAHSAP
## W = 0.50227, p-value < 2.2e-16
District_model<-lm(DAGC5X20R~DA0AT21R,data=District)

bptest(District_model)
## 
##  studentized Breusch-Pagan test
## 
## data:  District_model
## BP = 0.65103, df = 1, p-value = 0.4197
District_model<-lm(DAGC5X20R~DA0AT21R,data=District)

bptest(District_model)
## 
##  studentized Breusch-Pagan test
## 
## data:  District_model
## BP = 0.65103, df = 1, p-value = 0.4197
District_model<-lm(DAGC5X20R~DA0912DR21R,data = District)

bptest(District_model)
## 
##  studentized Breusch-Pagan test
## 
## data:  District_model
## BP = 0.179, df = 1, p-value = 0.6722
District_model<-lm(DAGC5X20R~DPSAMIFP,data = District)

bptest(District_model)
## 
##  studentized Breusch-Pagan test
## 
## data:  District_model
## BP = 3.1214, df = 1, p-value = 0.07727
District_model<-lm(DAGC5X20R~DPSTURNR,data = District)

bptest(District_model)
## 
##  studentized Breusch-Pagan test
## 
## data:  District_model
## BP = 5.5964, df = 1, p-value = 0.018
District_model<-lm(DAGC5X20R~DPFEAOPFK,data = District)

bptest(District_model)
## 
##  studentized Breusch-Pagan test
## 
## data:  District_model
## BP = 52.222, df = 1, p-value = 4.958e-13
District_model<-lm(DAGC5X20R~DPFPAHSAP,data = District)

bptest(District_model)
## 
##  studentized Breusch-Pagan test
## 
## data:  District_model
## BP = 0.45031, df = 1, p-value = 0.5022
District_correlated<-lm(DAGC5X20R~DA0AT21R+DA0912DR21R+DPSAMIFP+DPSTURNR+DPFEAOPFK+DPFPAHSAP,data = District)

durbinWatsonTest(District_correlated)
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.01809631      2.036065   0.532
##  Alternative hypothesis: rho != 0
District_correlated<-lm(DAGC5X20R~DA0AT21R+DA0912DR21R+DPSAMIFP+DPSTURNR+DPFEAOPFK+DPFPAHSAP,data = District)

durbinWatsonTest(District_correlated)
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.01809631      2.036065   0.536
##  Alternative hypothesis: rho != 0
vif_model<-lm(DAGC5X20R~DA0AT21R+DA0912DR21R+DPSAMIFP+DPSTURNR+DPFEAOPFK+DPFPAHSAP,data = District)

vif(vif_model)
##    DA0AT21R DA0912DR21R    DPSAMIFP    DPSTURNR   DPFEAOPFK   DPFPAHSAP 
##    1.635059    1.563269    1.115151    1.055213    1.008634    1.007169

cars_model<-lm(mpg~cyl,data=mtcars) raintest(cars_model)

District_model<-lm(DAGC5X20R~DA0AT21R,data = District)

raintest(District_model)
## 
##  Rainbow test
## 
## data:  District_model
## Rain = 2.5775, df1 = 533, df2 = 531, p-value < 2.2e-16
District_model<-lm(DAGC5X20R~DA0912DR21R,data = District)

raintest(District_model)
## 
##  Rainbow test
## 
## data:  District_model
## Rain = 3.2389, df1 = 533, df2 = 531, p-value < 2.2e-16
District_model<-lm(DAGC5X20R~DPSAMIFP,data = District)

raintest(District_model)
## 
##  Rainbow test
## 
## data:  District_model
## Rain = 2.9542, df1 = 532, df2 = 530, p-value < 2.2e-16
District_model<-lm(DAGC5X20R~DPSTURNR,data = District)

raintest(District_model)
## 
##  Rainbow test
## 
## data:  District_model
## Rain = 2.8706, df1 = 532, df2 = 529, p-value < 2.2e-16
District_model<-lm(DAGC5X20R~DPFEAOPFK,data = District)

raintest(District_model)
## 
##  Rainbow test
## 
## data:  District_model
## Rain = 2.81, df1 = 533, df2 = 531, p-value < 2.2e-16
District_model<-lm(DAGC5X20R~DPFPAHSAP,data = District)

raintest(District_model)
## 
##  Rainbow test
## 
## data:  District_model
## Rain = 2.8829, df1 = 533, df2 = 531, p-value < 2.2e-16
DAGC5X20R_DA0AT21R<-lm(DAGC5X20R~DA0912DR21R+DPSAMIFP+DPSTURNR+DPFEAOPFK+DPFPAHSAP,data = District)

plot(DAGC5X20R_DA0AT21R,which=1)

durbinWatsonTest(DAGC5X20R_DA0AT21R)
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.01954981      2.038967   0.524
##  Alternative hypothesis: rho != 0
DAGC5X20R_DA0AT21R<-lm(DAGC5X20R_DA0AT21R,data = District)
plot(DAGC5X20R_DA0AT21R,which = 3)

DAGC5X20R_DA0912DR21R<-lm(DAGC5X20R~DA0AT21R+DPSAMIFP+DPSTURNR+DPFEAOPFK+DPFPAHSAP,data = District)

plot(DAGC5X20R_DA0912DR21R,which=1)

durbinWatsonTest(DAGC5X20R_DA0912DR21R)
##  lag Autocorrelation D-W Statistic p-value
##    1      0.04050184      1.918682   0.212
##  Alternative hypothesis: rho != 0
DAGC5X20R_DPSAMIFP<-lm(DAGC5X20R~DA0AT21R+DA0912DR21R+DPSTURNR+DPFEAOPFK+DPFPAHSAP,data = District)

plot(DAGC5X20R_DPSAMIFP,which=1)

durbinWatsonTest(DAGC5X20R_DPSAMIFP)
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.01853426      2.036938   0.498
##  Alternative hypothesis: rho != 0
DAGC5X20R_DPSTURNR<-lm(DAGC5X20R~DA0AT21R+DPSAMIFP+DA0912DR21R+DPFEAOPFK+DPFPAHSAP,data = District)

plot(DAGC5X20R_DPSTURNR,which=1)

durbinWatsonTest(DAGC5X20R_DPSTURNR)
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.01809042      2.036055   0.468
##  Alternative hypothesis: rho != 0
DAGC5X20R_DPFEAOPFK<-lm(DAGC5X20R~DA0AT21R+DPSAMIFP+DPSTURNR+DA0912DR21R+DPFPAHSAP,data = District)

plot(DAGC5X20R_DPFEAOPFK,which=1)

durbinWatsonTest(DAGC5X20R_DPFEAOPFK)
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.02542994      2.050814    0.29
##  Alternative hypothesis: rho != 0
DAGC5X20R_DPFPAHSAP<-lm(DAGC5X20R~DA0AT21R+DPSAMIFP+DPSTURNR+DA0912DR21R+DPFEAOPFK,data = District)

plot(DAGC5X20R_DPFPAHSAP,which=1)

summary(DAGC5X20R_DPFPAHSAP)
## 
## Call:
## lm(formula = DAGC5X20R ~ DA0AT21R + DPSAMIFP + DPSTURNR + DA0912DR21R + 
##     DPFEAOPFK, data = District)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -97.906  -0.817   0.924   2.416  30.006 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  9.794e+01  1.155e+01   8.482  < 2e-16 ***
## DA0AT21R     7.059e-02  1.189e-01   0.593   0.5530    
## DPSAMIFP    -3.507e-03  1.102e-02  -0.318   0.7503    
## DPSTURNR    -6.802e-02  3.117e-02  -2.182   0.0293 *  
## DA0912DR21R -1.778e+00  1.014e-01 -17.531  < 2e-16 ***
## DPFEAOPFK   -3.952e-04  7.234e-05  -5.464  5.8e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.886 on 1057 degrees of freedom
##   (144 observations deleted due to missingness)
## Multiple R-squared:  0.3489, Adjusted R-squared:  0.3459 
## F-statistic: 113.3 on 5 and 1057 DF,  p-value: < 2.2e-16
durbinWatsonTest(DAGC5X20R_DPFPAHSAP)
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.01926001      2.038401   0.474
##  Alternative hypothesis: rho != 0
plot(District_model,which=2)

plot(District_model,which=3)

plot(District_model,which=4)

plot(District_model,which=5)

DAGC5X20R_DA0AT21R_DA0912DR21R<-lm(DAGC5X20R~DA0AT21R+DA0912DR21R,data=District)

plot(DAGC5X20R_DA0AT21R_DA0912DR21R,which=3)

summary(DAGC5X20R_DA0AT21R_DA0912DR21R)
## 
## Call:
## lm(formula = DAGC5X20R ~ DA0AT21R + DA0912DR21R, data = District)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -99.517  -0.391   1.614   1.950  23.316 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  88.2227    11.1209   7.933 5.39e-15 ***
## DA0AT21R      0.1037     0.1164   0.890    0.374    
## DA0912DR21R  -1.8159     0.1017 -17.862  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.008 on 1063 degrees of freedom
##   (141 observations deleted due to missingness)
## Multiple R-squared:  0.3274, Adjusted R-squared:  0.3262 
## F-statistic: 258.8 on 2 and 1063 DF,  p-value: < 2.2e-16
DAGC5X20R_DPSTURNR_DPFEAOPFK<-lm(DAGC5X20R~DPSTURNR+DPFEAOPFK,data=District)

plot(DAGC5X20R_DPSTURNR_DPFEAOPFK,which=3)

summary(DAGC5X20R_DPSTURNR_DPFEAOPFK)
## 
## Call:
## lm(formula = DAGC5X20R ~ DPSTURNR + DPFEAOPFK, data = District)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -95.112  -1.060   1.719   3.895  30.623 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.050e+02  1.391e+00  75.518  < 2e-16 ***
## DPSTURNR    -1.345e-01  3.679e-02  -3.655  0.00027 ***
## DPFEAOPFK   -5.027e-04  8.732e-05  -5.757 1.12e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.76 on 1060 degrees of freedom
##   (144 observations deleted due to missingness)
## Multiple R-squared:  0.0425, Adjusted R-squared:  0.04069 
## F-statistic: 23.53 on 2 and 1060 DF,  p-value: 1.008e-10
DAGC5X20R_DPFPAHSAP_DPFEAOPFK<-lm(DAGC5X20R~DPFPAHSAP+DPFEAOPFK,data=District)

plot(DAGC5X20R_DPFPAHSAP_DPFEAOPFK,which=3)

summary(DAGC5X20R_DPFPAHSAP_DPFEAOPFK)
## 
## Call:
## lm(formula = DAGC5X20R ~ DPFPAHSAP + DPFEAOPFK, data = District)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -95.833  -0.909   1.926   3.960  33.325 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.023e+02  1.199e+00  85.343  < 2e-16 ***
## DPFPAHSAP    2.193e-01  8.668e-01   0.253      0.8    
## DPFEAOPFK   -5.070e-04  8.763e-05  -5.786 9.47e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.81 on 1063 degrees of freedom
##   (141 observations deleted due to missingness)
## Multiple R-squared:  0.03076,    Adjusted R-squared:  0.02893 
## F-statistic: 16.87 on 2 and 1063 DF,  p-value: 6.152e-08
ggplot(District,aes(x=DAGC5X20R,y=DA0AT21R,group = DAGC5X20R))+geom_boxplot()
## Warning: Removed 141 rows containing missing values or values outside the scale range
## (`stat_boxplot()`).

ggplot(District,aes(x=DA0AT21R,y=DA0912DR21R,group=DAGC5X20R)) + geom_boxplot()
## Warning: Removed 4 rows containing missing values or values outside the scale range
## (`stat_boxplot()`).
## Warning: Removed 108 rows containing non-finite outside the scale range
## (`stat_boxplot()`).

District_anova<-aov(DAGC5X20R~DPFPAHSAP,data = District)
summary(District_anova)
##               Df Sum Sq Mean Sq F value Pr(>F)
## DPFPAHSAP      1     30    29.7   0.246   0.62
## Residuals   1064 128209   120.5               
## 141 observations deleted due to missingness
District_anova<-aov(DAGC5X20R~DA0AT21R,data = District)
summary(District_anova)
##               Df Sum Sq Mean Sq F value Pr(>F)    
## DA0AT21R       1  16101   16101   152.8 <2e-16 ***
## Residuals   1064 112137     105                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 141 observations deleted due to missingness
District_anova<-aov(DAGC5X20R~DA0912DR21R,data = District)
summary(District_anova)
##               Df Sum Sq Mean Sq F value Pr(>F)    
## DA0912DR21R    1  41925   41925   516.8 <2e-16 ***
## Residuals   1064  86314      81                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 141 observations deleted due to missingness
District_anova<-aov(DAGC5X20R~DPSTURNR,data = District)
summary(District_anova)
##               Df Sum Sq Mean Sq F value  Pr(>F)    
## DPSTURNR       1   1611  1610.9    13.5 0.00025 ***
## Residuals   1061 126585   119.3                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 144 observations deleted due to missingness
District_anova<-aov(DAGC5X20R~DPFEAOPFK,data = District)
summary(District_anova)
##               Df Sum Sq Mean Sq F value   Pr(>F)    
## DPFEAOPFK      1   3937    3937    33.7 8.49e-09 ***
## Residuals   1064 124302     117                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 141 observations deleted due to missingness
pairs(~DAGC5X20R+DA0AT21R+DA0912DR21R+DPSAMIFP+DPSTURNR+DPFEAOPFK+DPFPAHSAP,data = District)

cor.test(District$DAGC5X20R,District$DA0912DR21R,method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  District$DAGC5X20R and District$DA0912DR21R
## t = -22.733, df = 1064, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6108476 -0.5299263
## sample estimates:
##       cor 
## -0.571776
cor.test(District$DAGC5X20R,District$DA0AT21R,method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  District$DAGC5X20R and District$DA0AT21R
## t = 12.36, df = 1064, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3006975 0.4057524
## sample estimates:
##       cor 
## 0.3543425
cor.test(District$DAGC5X20R,District$DPSAMIFP,method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  District$DAGC5X20R and District$DPSAMIFP
## t = -5.3746, df = 1062, p-value = 9.431e-08
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.2206674 -0.1036412
## sample estimates:
##        cor 
## -0.1627265
cor.test(District$DAGC5X20R,District$DPSTURNR,method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  District$DAGC5X20R and District$DPSTURNR
## t = -3.6746, df = 1061, p-value = 0.0002502
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.17107346 -0.05232482
## sample estimates:
##        cor 
## -0.1120993
cor.test(District$DAGC5X20R,District$DPFEAOPFK,method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  District$DAGC5X20R and District$DPFEAOPFK
## t = -5.805, df = 1064, p-value = 8.49e-09
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.2328031 -0.1163917
## sample estimates:
##        cor 
## -0.1752097
cor.test(District$DAGC5X20R,District$DPFPAHSAP,method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  District$DAGC5X20R and District$DPFPAHSAP
## t = 0.49649, df = 1064, p-value = 0.6197
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.04486446  0.07519283
## sample estimates:
##        cor 
## 0.01521904
District<-District
boxplot(DAGC5X20R~DA0AT21R,data = District)

boxplot(DAGC5X20R~DA0912DR21R,data = District)

boxplot(DAGC5X20R~DPSAMIFP,data = District)

boxplot(DAGC5X20R~DPSTURNR,data = District)