library(wooldridge)
library(plm)
## Warning: package 'plm' was built under R version 4.2.2
data("Crime")
head(Crime, 10)
##    county year    crmrte   prbarr  prbconv  prbpris avgsen     polpc  density
## 1       1   81 0.0398849 0.289696 0.402062 0.472222   5.61 0.0017868 2.307159
## 2       1   82 0.0383449 0.338111 0.433005 0.506993   5.59 0.0017666 2.330254
## 3       1   83 0.0303048 0.330449 0.525703 0.479705   5.80 0.0018358 2.341801
## 4       1   84 0.0347259 0.362525 0.604706 0.520104   6.89 0.0018859 2.346420
## 5       1   85 0.0365730 0.325395 0.578723 0.497059   6.55 0.0019244 2.364896
## 6       1   86 0.0347524 0.326062 0.512324 0.439863   6.90 0.0018952 2.385681
## 7       1   87 0.0356036 0.298270 0.527596 0.436170   6.71 0.0018279 2.422633
## 8       3   81 0.0163921 0.202899 0.869048 0.465753   8.45 0.0005939 0.976834
## 9       3   82 0.0190651 0.162218 0.772152 0.377049   5.71 0.0007047 0.992278
## 10      3   83 0.0151492 0.181586 1.028170 0.438356   8.69 0.0006587 1.003861
##       taxpc  region smsa   pctmin     wcon      wtuc     wtrd     wfir     wser
## 1  25.69763 central   no 20.21870 206.4803  333.6209 182.3330 272.4492 215.7335
## 2  24.87425 central   no 20.21870 212.7542  369.2964 189.5414 300.8788 231.5767
## 3  26.45144 central   no 20.21870 219.7802 1394.8030 196.6395 309.9696 240.1568
## 4  26.84235 central   no 20.21870 223.4238  398.8604 200.5629 350.0863 252.4477
## 5  28.14034 central   no 20.21870 243.7562  358.7830 206.8827 383.0707 261.0861
## 6  29.74098 central   no 20.21870 257.9139  369.5465 218.5165 409.8842 269.6129
## 7  30.99368 central   no 20.21870 281.4259  408.7245 221.2701 453.1722 274.1775
## 8  14.56088 central   no  7.91632 188.7683  292.6422 151.4234 202.4292 191.3742
## 9  35.64073 central   no  7.91632 186.9658  345.7217 156.8826 225.0409 208.8190
## 10 19.26188 central   no  7.91632 193.5983  604.9115 157.1295 248.1390 219.0847
##      wmfg   wfed   wsta   wloc       mix   pctymle   lcrmrte   lprbarr
## 1  229.12 409.37 236.24 231.47 0.0999179 0.0876968 -3.221757 -1.238923
## 2  240.33 419.70 253.88 236.79 0.1030491 0.0863767 -3.261134 -1.084381
## 3  269.70 438.85 250.36 248.58 0.0806787 0.0850909 -3.496449 -1.107303
## 4  281.74 459.17 261.93 264.38 0.0785035 0.0838333 -3.360270 -1.014662
## 5  298.88 490.43 281.44 288.58 0.0932486 0.0823065 -3.308445 -1.122715
## 6  322.65 478.67 286.91 306.70 0.0973228 0.0800806 -3.359507 -1.120668
## 7  334.54 477.58 292.09 311.91 0.0801688 0.0778710 -3.335309 -1.209756
## 8  210.75 381.72 247.38 213.17 0.0561224 0.0870046 -4.110956 -1.595047
## 9  217.77 386.42 374.07 219.18 0.0473118 0.0864722 -3.959896 -1.818814
## 10 236.64 382.65 268.90 223.06 0.0596206 0.0859426 -4.189807 -1.706026
##      lprbconv   lprbpris  lavgsen    lpolpc   ldensity    lwcon    lwtuc
## 1  -0.9111490 -0.7503061 1.724551 -6.327340  0.8360171 5.330205 5.810005
## 2  -0.8370060 -0.6792581 1.720979 -6.338704  0.8459773 5.360137 5.911600
## 3  -0.6430188 -0.7345839 1.757858 -6.300291  0.8509204 5.392628 7.240509
## 4  -0.5030129 -0.6537265 1.930071 -6.273361  0.8528909 5.409070 5.988612
## 5  -0.5469313 -0.6990466 1.879465 -6.253162  0.8607340 5.496169 5.882718
## 6  -0.6687981 -0.8212920 1.931521 -6.268420  0.8694848 5.552626 5.912277
## 7  -0.6394244 -0.8297232 1.903599 -6.304609  0.8848549 5.639869 6.013041
## 8  -0.1403569 -0.7640998 2.134166 -7.428766 -0.0234386 5.240520 5.678950
## 9  -0.2585739 -0.9753801 1.742219 -7.257781 -0.0077520 5.230926 5.845634
## 10  0.0277805 -0.8247239 2.162173 -7.325303  0.0038535 5.265786 6.405082
##       lwtrd    lwfir    lwser    lwmfg    lwfed    lwsta    lwloc  lpctymle
## 1  5.205835 5.607452 5.374044 5.434246 6.014619 5.464848 5.444450 -2.433870
## 2  5.244607 5.706707 5.444911 5.482013 6.039540 5.536862 5.467174 -2.449038
## 3  5.281372 5.736475 5.481292 5.597310 6.084157 5.522900 5.515765 -2.464036
## 4  5.301128 5.858180 5.531204 5.640985 6.129421 5.568077 5.577387 -2.478925
## 5  5.332152 5.948220 5.564850 5.700042 6.195282 5.639919 5.664972 -2.497306
## 6  5.386862 6.015875 5.596987 5.776568 6.171011 5.659169 5.725870 -2.524721
## 7  5.399384 6.116272 5.613776 5.812757 6.168732 5.677062 5.742715 -2.552702
## 8  5.020080 5.310390 5.254230 5.350673 5.944687 5.510926 5.362090 -2.441794
## 9  5.055498 5.416282 5.341468 5.383440 5.956925 5.924443 5.389893 -2.447933
## 10 5.057070 5.513989 5.389459 5.466540 5.947121 5.594339 5.407441 -2.454076
##     lpctmin   ltaxpc      lmix
## 1  3.006608 3.246399 -2.303407
## 2  3.006608 3.213833 -2.272549
## 3  3.006608 3.275311 -2.517281
## 4  3.006608 3.289981 -2.544612
## 5  3.006608 3.337204 -2.372487
## 6  3.006608 3.392526 -2.329722
## 7  3.006608 3.433783 -2.523621
## 8  2.068926 2.678338 -2.880219
## 9  2.068926 3.573489 -3.050995
## 10 2.068926 2.958128 -2.819754
tail(Crime,10 )
##     county year    crmrte   prbarr  prbconv  prbpris avgsen     polpc   density
## 621    195   85 0.0236432 0.246970 1.564420 0.478431  12.49 0.0042988 1.7219250
## 622    195   86 0.0300950 0.208738 1.441860 0.475806   9.21 0.0043097 1.7272730
## 623    195   87 0.0313973 0.201397 1.670520 0.470588  13.02 0.0044592 1.7459890
## 624    197   81 0.0178621 0.158915 1.060980 0.356322  11.35 0.0008308 0.8571429
## 625    197   82 0.0180711 0.229167 0.545455 0.363636   6.64 0.0009241 0.8660714
## 626    197   83 0.0155747 0.226667 0.480392 0.428571   7.77 0.0010729 0.8690476
## 627    197   84 0.0136619 0.204188 1.410260 0.372727  10.11 0.0011087 0.8720238
## 628    197   85 0.0130857 0.180556 0.830769 0.333333   5.96 0.0010541 0.8750000
## 629    197   86 0.0128740 0.112676 2.250000 0.244444   7.68 0.0010879 0.8809524
## 630    197   87 0.0141928 0.207595 1.182930 0.360825  12.23 0.0011857 0.8898810
##        taxpc region smsa   pctmin     wcon     wtuc     wtrd     wfir     wser
## 621 36.02775  other   no 37.43110 279.4814 340.6775 216.4476 365.8724 278.1635
## 622 38.39109  other   no 37.43110 297.3497 373.8318 224.5291 387.5402 292.7820
## 623 53.66693  other   no 37.43110 315.1641 377.9356 246.0614 411.4330 296.8684
## 624 16.64038   west   no  5.46081 183.1502 291.3753 151.3533 228.9377 156.9114
## 625 17.61957   west   no  5.46081 194.2502 323.6862 151.1742 243.4275 171.5078
## 626 18.90585   west   no  5.46081 207.1006 317.9891 154.3210 254.8656 196.4637
## 627 22.70475   west   no  5.46081 230.2275 304.8781 170.5955 262.2378 192.6782
## 628 24.12361   west   no  5.46081 253.0364 283.4008 171.6738 271.7391 207.2574
## 629 24.98198   west   no  5.46081 280.5550 324.3744 180.0927 312.2946 215.2698
## 630 25.95258   west   no  5.46081 314.1660 341.8803 182.8020 348.1432 212.8205
##       wmfg   wfed   wsta   wloc       mix   pctymle   lcrmrte   lprbarr
## 621 362.04 459.44 283.40 309.10 0.2716763 0.0831767 -3.744680 -1.398488
## 622 381.86 458.69 307.84 306.63 0.1890332 0.0813075 -3.503396 -1.566675
## 623 392.27 480.79 303.11 337.28 0.1561238 0.0794507 -3.461033 -1.602477
## 624 230.08 317.48 260.86 209.10 0.0617284 0.0806272 -4.025074 -1.839386
## 625 238.94 330.27 278.94 225.22 0.1115789 0.0798224 -4.013441 -1.473304
## 626 256.19 352.65 345.27 235.90 0.1138614 0.0790195 -4.162107 -1.484273
## 627 268.59 345.90 354.21 246.89 0.1169591 0.0782327 -4.293144 -1.588714
## 628 279.17 357.84 354.78 275.01 0.0810811 0.0772219 -4.336235 -1.711714
## 629 306.09 376.54 355.64 294.49 0.0757576 0.0757007 -4.352546 -2.183239
## 630 322.92 391.72 385.65 306.85 0.0675676 0.0741989 -4.255021 -1.572166
##       lprbconv   lprbpris  lavgsen    lpolpc   ldensity    lwcon    lwtuc
## 621  0.4475151 -0.7372433 2.524928 -5.449429  0.5434429 5.632936 5.830936
## 622  0.3659339 -0.7427451 2.220290 -5.446882  0.5465437 5.694909 5.923806
## 623  0.5131349 -0.7537723 2.566487 -5.412779  0.5573214 5.753093 5.934724
## 624  0.0591930 -1.0319200 2.429218 -7.093133 -0.1541507 5.210307 5.674612
## 625 -0.6061350 -1.0116020 1.893112 -6.986701 -0.1437879 5.269147 5.779775
## 626 -0.7331528 -0.8472989 2.050270 -6.837371 -0.1403573 5.333205 5.762017
## 627  0.3437741 -0.9869090 2.313525 -6.804576 -0.1369385 5.439068 5.719912
## 628 -0.1854035 -1.0986130 1.785071 -6.855049 -0.1335314 5.533534 5.646862
## 629  0.8109302 -1.4087690 2.038620 -6.823469 -0.1267517 5.636770 5.781898
## 630  0.1679944 -1.0193620 2.503892 -6.737397 -0.1166676 5.749922 5.834461
##        lwtrd    lwfir    lwser    lwmfg    lwfed    lwsta    lwloc  lpctymle
## 621 5.377348 5.902285 5.628209 5.891755 6.130008 5.646859 5.733665 -2.486788
## 622 5.414005 5.959820 5.679429 5.945054 6.128375 5.729580 5.725642 -2.509517
## 623 5.505581 6.019646 5.693289 5.971951 6.175431 5.714096 5.820913 -2.532619
## 624 5.019617 5.433450 5.055681 5.438427 5.760415 5.563984 5.342813 -2.517919
## 625 5.018433 5.494819 5.144629 5.476213 5.799911 5.630997 5.417078 -2.527951
## 626 5.039035 5.540736 5.280478 5.545919 5.865476 5.844326 5.463408 -2.538060
## 627 5.139296 5.569252 5.261022 5.593186 5.846150 5.869890 5.508943 -2.548068
## 628 5.145596 5.604843 5.333961 5.631821 5.880086 5.871498 5.616807 -2.561072
## 629 5.193472 5.743947 5.371892 5.723879 5.931024 5.873919 5.685245 -2.580968
## 630 5.208404 5.852614 5.360449 5.777405 5.970547 5.954930 5.726359 -2.601006
##      lpctmin   ltaxpc      lmix
## 621 3.622502 3.584289 -1.303144
## 622 3.622502 3.647825 -1.665833
## 623 3.622502 3.982797 -1.857106
## 624 1.697597 2.811832 -2.785011
## 625 1.697597 2.869010 -2.193023
## 626 1.697597 2.939471 -2.172773
## 627 1.697597 3.122574 -2.145931
## 628 1.697597 3.183191 -2.512306
## 629 1.697597 3.218155 -2.580217
## 630 1.697597 3.256271 -2.694627
mymodel <- pdata.frame(crime4, index = c("county", "year") )
summary(mymodel)
##      county    year        crmrte             prbarr           prbconv        
##  1      :  7   81:90   Min.   :0.001812   Min.   :0.05882   Min.   : 0.06838  
##  3      :  7   82:90   1st Qu.:0.018352   1st Qu.:0.21790   1st Qu.: 0.34769  
##  5      :  7   83:90   Median :0.028441   Median :0.27824   Median : 0.47437  
##  7      :  7   84:90   Mean   :0.031588   Mean   :0.30737   Mean   : 0.68862  
##  9      :  7   85:90   3rd Qu.:0.038406   3rd Qu.:0.35252   3rd Qu.: 0.63560  
##  11     :  7   86:90   Max.   :0.163835   Max.   :2.75000   Max.   :37.00000  
##  (Other):588   87:90                                                          
##     prbpris           avgsen           polpc              density      
##  Min.   :0.1489   Min.   : 4.220   Min.   :0.0004585   Min.   :0.1977  
##  1st Qu.:0.3744   1st Qu.: 7.160   1st Qu.:0.0011913   1st Qu.:0.5329  
##  Median :0.4286   Median : 8.495   Median :0.0014506   Median :0.9526  
##  Mean   :0.4255   Mean   : 8.955   Mean   :0.0019168   Mean   :1.3861  
##  3rd Qu.:0.4832   3rd Qu.:10.197   3rd Qu.:0.0018032   3rd Qu.:1.5078  
##  Max.   :0.6786   Max.   :25.830   Max.   :0.0355781   Max.   :8.8277  
##                                                                        
##      taxpc             west           central           urban        
##  Min.   : 14.30   Min.   :0.0000   Min.   :0.0000   Min.   :0.00000  
##  1st Qu.: 23.43   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000  
##  Median : 27.79   Median :0.0000   Median :0.0000   Median :0.00000  
##  Mean   : 30.24   Mean   :0.2333   Mean   :0.3778   Mean   :0.08889  
##  3rd Qu.: 33.27   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:0.00000  
##  Max.   :119.76   Max.   :1.0000   Max.   :1.0000   Max.   :1.00000  
##                                                                      
##     pctmin80           wcon              wtuc              wtrd        
##  Min.   : 1.284   Min.   :  65.62   Min.   :  28.86   Min.   :  16.87  
##  1st Qu.:10.005   1st Qu.: 201.66   1st Qu.: 317.60   1st Qu.: 168.05  
##  Median :24.852   Median : 236.46   Median : 358.20   Median : 185.48  
##  Mean   :25.713   Mean   : 245.67   Mean   : 406.10   Mean   : 192.82  
##  3rd Qu.:38.223   3rd Qu.: 269.69   3rd Qu.: 411.02   3rd Qu.: 204.82  
##  Max.   :64.348   Max.   :2324.60   Max.   :3041.96   Max.   :2242.75  
##                                                                        
##       wfir              wser               wmfg            wfed      
##  Min.   :  3.516   Min.   :   1.844   Min.   :101.8   Min.   :255.4  
##  1st Qu.:235.705   1st Qu.: 191.319   1st Qu.:234.0   1st Qu.:361.5  
##  Median :264.423   Median : 216.475   Median :271.6   Median :404.0  
##  Mean   :272.059   Mean   : 224.671   Mean   :285.2   Mean   :403.9  
##  3rd Qu.:302.440   3rd Qu.: 247.155   3rd Qu.:320.0   3rd Qu.:444.6  
##  Max.   :509.466   Max.   :2177.068   Max.   :646.9   Max.   :598.0  
##                                                                      
##       wsta            wloc            mix              pctymle       
##  Min.   :173.0   Min.   :163.6   Min.   :0.002457   Min.   :0.06216  
##  1st Qu.:258.2   1st Qu.:226.8   1st Qu.:0.075324   1st Qu.:0.07859  
##  Median :289.4   Median :253.1   Median :0.102089   Median :0.08316  
##  Mean   :296.9   Mean   :258.0   Mean   :0.139396   Mean   :0.08897  
##  3rd Qu.:331.5   3rd Qu.:289.3   3rd Qu.:0.149009   3rd Qu.:0.08919  
##  Max.   :548.0   Max.   :388.1   Max.   :4.000000   Max.   :0.27436  
##                                                                      
##       d82              d83              d84              d85        
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.1429   Mean   :0.1429   Mean   :0.1429   Mean   :0.1429  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##                                                                     
##       d86              d87            lcrmrte          lprbarr      
##  Min.   :0.0000   Min.   :0.0000   Min.   :-6.314   Min.   :-2.833  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:-3.998   1st Qu.:-1.524  
##  Median :0.0000   Median :0.0000   Median :-3.560   Median :-1.279  
##  Mean   :0.1429   Mean   :0.1429   Mean   :-3.609   Mean   :-1.274  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:-3.260   3rd Qu.:-1.043  
##  Max.   :1.0000   Max.   :1.0000   Max.   :-1.809   Max.   : 1.012  
##                                                                     
##     lprbconv          lprbpris          lavgsen          lpolpc      
##  Min.   :-2.6827   Min.   :-1.9042   Min.   :1.440   Min.   :-7.688  
##  1st Qu.:-1.0564   1st Qu.:-0.9824   1st Qu.:1.969   1st Qu.:-6.733  
##  Median :-0.7458   Median :-0.8473   Median :2.139   Median :-6.536  
##  Mean   :-0.6929   Mean   :-0.8786   Mean   :2.153   Mean   :-6.491  
##  3rd Qu.:-0.4532   3rd Qu.:-0.7273   3rd Qu.:2.322   3rd Qu.:-6.318  
##  Max.   : 3.6109   Max.   :-0.3878   Max.   :3.252   Max.   :-3.336  
##                                                                      
##     ldensity            ltaxpc          lwcon           lwtuc      
##  Min.   :-1.62091   Min.   :2.660   Min.   :4.184   Min.   :3.362  
##  1st Qu.:-0.62934   1st Qu.:3.154   1st Qu.:5.307   1st Qu.:5.761  
##  Median :-0.04857   Median :3.325   Median :5.466   Median :5.881  
##  Mean   :-0.01593   Mean   :3.356   Mean   :5.463   Mean   :5.916  
##  3rd Qu.: 0.41066   3rd Qu.:3.505   3rd Qu.:5.597   3rd Qu.:6.019  
##  Max.   : 2.17789   Max.   :4.786   Max.   :7.751   Max.   :8.020  
##                                                                    
##      lwtrd           lwfir           lwser            lwmfg      
##  Min.   :2.826   Min.   :1.257   Min.   :0.6118   Min.   :4.623  
##  1st Qu.:5.124   1st Qu.:5.463   1st Qu.:5.2539   1st Qu.:5.455  
##  Median :5.223   Median :5.578   Median :5.3775   Median :5.604  
##  Mean   :5.232   Mean   :5.579   Mean   :5.3646   Mean   :5.615  
##  3rd Qu.:5.322   3rd Qu.:5.712   3rd Qu.:5.5100   3rd Qu.:5.768  
##  Max.   :7.715   Max.   :6.233   Max.   :7.6857   Max.   :6.472  
##                                                                  
##      lwfed           lwsta           lwloc            lmix       
##  Min.   :5.543   Min.   :5.153   Min.   :5.097   Min.   :-6.009  
##  1st Qu.:5.890   1st Qu.:5.554   1st Qu.:5.424   1st Qu.:-2.586  
##  Median :6.001   Median :5.668   Median :5.534   Median :-2.282  
##  Mean   :5.989   Mean   :5.678   Mean   :5.540   Mean   :-2.234  
##  3rd Qu.:6.097   3rd Qu.:5.804   3rd Qu.:5.667   3rd Qu.:-1.904  
##  Max.   :6.394   Max.   :6.306   Max.   :5.961   Max.   : 1.386  
##                                                                  
##     lpctymle         lpctmin          clcrmrte           clprbarr       
##  Min.   :-2.778   Min.   :0.2497   Min.   :-1.65011   Min.   :-1.58045  
##  1st Qu.:-2.543   1st Qu.:2.3030   1st Qu.:-0.09075   1st Qu.:-0.10829  
##  Median :-2.487   Median :3.2127   Median : 0.00244   Median :-0.01083  
##  Mean   :-2.443   Mean   :2.9134   Mean   : 0.00200   Mean   :-0.00202  
##  3rd Qu.:-2.417   3rd Qu.:3.6434   3rd Qu.: 0.09144   3rd Qu.: 0.10956  
##  Max.   :-1.293   Max.   :4.1643   Max.   : 1.22130   Max.   : 1.23470  
##                                    NA's   :90         NA's   :90        
##     clprbcon           clprbpri           clavgsen           clpolpc        
##  Min.   :-3.04558   Min.   :-1.23561   Min.   :-1.27884   Min.   :-3.13172  
##  1st Qu.:-0.16320   1st Qu.:-0.14009   1st Qu.:-0.20212   1st Qu.:-0.02428  
##  Median : 0.01169   Median :-0.01864   Median :-0.01591   Median : 0.01332  
##  Mean   :-0.00262   Mean   :-0.00942   Mean   :-0.01409   Mean   : 0.01292  
##  3rd Qu.: 0.18252   3rd Qu.: 0.11168   3rd Qu.: 0.17459   3rd Qu.: 0.05990  
##  Max.   : 2.19564   Max.   : 1.13105   Max.   : 1.20779   Max.   : 2.42342  
##  NA's   :90         NA's   :90         NA's   :90         NA's   :90        
##     cltaxpc             clmix         
##  Min.   :-0.70896   Min.   :-2.90690  
##  1st Qu.: 0.02723   1st Qu.:-0.16300  
##  Median : 0.07361   Median : 0.00147  
##  Mean   : 0.07730   Mean   :-0.00368  
##  3rd Qu.: 0.12487   3rd Qu.: 0.18899  
##  Max.   : 0.93222   Max.   : 2.72867  
##  NA's   :90         NA's   :90
mymodel <- pdata.frame(crime4, index = c("county", "year") )
pdim(mymodel)
## Balanced Panel: n = 90, T = 7, N = 630
model1 <- plm(log(crmrte) ~ polpc, data = crime4, model = "within")
summary(model1)
## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = log(crmrte) ~ polpc, data = crime4, model = "within")
## 
## Balanced Panel: n = 90, T = 7, N = 630
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -0.784786 -0.086367 -0.005256  0.087046  0.646375 
## 
## Coefficients:
##       Estimate Std. Error t-value  Pr(>|t|)    
## polpc  30.9904     4.0779  7.5995 1.326e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    17.991
## Residual Sum of Squares: 16.25
## R-Squared:      0.096779
## Adj. R-Squared: -0.054038
## F-statistic: 57.7529 on 1 and 539 DF, p-value: 1.3256e-13
model1 <- lm(log(crmrte) ~ 0 + polpc, data = crime4)
summary(model1)
## 
## Call:
## lm(formula = log(crmrte) ~ 0 + polpc, data = crime4)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -4.822 -3.148 -2.623 -2.156 19.421 
## 
## Coefficients:
##       Estimate Std. Error t value Pr(>|t|)    
## polpc  -624.50      35.85  -17.42   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.004 on 629 degrees of freedom
## Multiple R-squared:  0.3254, Adjusted R-squared:  0.3243 
## F-statistic: 303.4 on 1 and 629 DF,  p-value: < 2.2e-16