1 Viết function để làm việc với dữ liệu (Chạy hồi quy, kiểm định khuyết tật, Dự báo)

library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.3.1
library(AER)
data("TravelMode")
data <- TravelMode
names(data) <-  c("I","M","C","W","V","T","G","IN","S")


handle <- function(data,a,b,c) {
  
  result <- list() # Tạo một list để chứa các kết quả
  var <- lm({{a}} ~ {{b}} + {{c}},data = data) # Hồi quy
    result$lm <- summary(var) 
    white_test <- ncvTest({{var}}) # Kiểm định phương sai sai số thay đổi
    result$white <- print(white_test)
    vif <- vif({{var}}) #Kiểm tra đa cộng tuyến
    result$vif <- print(vif)
    predict <- predict({{var}}) #Dự báo 
    result$predict <- print(predict)
    return(result) #Xem kết quả
   
}
handle(data, data$V, data$G, data$IN)
## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 65.37911, Df = 1, p = 6.1791e-16
## {\n    {\n        b\n    }\n} {\n    {\n        c\n    }\n} 
##                      1.009896                      1.009896 
##         1         2         3         4         5         6         7         8 
##  33.37546  33.72778  33.37546  19.28271  32.47797  38.11507  38.46738  26.13623 
##         9        10        11        12        13        14        15        16 
##  54.35512  77.60815  61.40149  44.49019  30.84993  37.89630  38.60094  21.33732 
##        17        18        19        20        21        22        23        24 
##  37.98899  41.86450  42.21681  43.97841  32.79690  28.21675  28.56907  23.28429 
##        25        26        27        28        29        30        31        32 
##  65.46985  84.14274  67.93608  53.13870  56.09368  60.32151  59.26455  55.38905 
##        33        34        35        36        37        38        39        40 
##  33.56831  33.92063  33.56831  22.99875  32.96384  34.37312  34.02080  20.63269 
##        41        42        43        44        45        46        47        48 
##  31.89940  32.60404  33.66100  20.62521  36.54633  40.42183  40.77415  24.21517 
##        49        50        51        52        53        54        55        56 
##  31.48779  37.82953  38.53416  23.73678  34.27295  38.85309  39.20541  29.34049 
##        57        58        59        60        61        62        63        64 
##  46.76875  83.76222  74.95425  78.47744  34.08528  27.74354  33.73296  26.68658 
##        65        66        67        68        69        70        71        72 
##  32.67600  31.61905  32.32368  24.92499  34.37082  26.61981  29.79067  26.26749 
##        73        74        75        76        77        78        79        80 
##  34.55849  26.10284  30.33066  29.97835  35.50721  36.56417  37.62113  30.22243 
##        81        82        83        84        85        86        87        88 
##  31.90459  26.61981  28.02908  24.15357  42.27611  48.61785  46.85626  42.27611 
##        89        90        91        92        93        94        95        96 
##  63.19647  57.20705  43.11431  43.11431  55.79778  56.85474  42.76199  43.11431 
##        97        98        99       100       101       102       103       104 
##  40.47077  27.43497  27.78729  22.50251  47.02320  91.06304  74.85638  88.24449 
##       105       106       107       108       109       110       111       112 
##  39.75058  58.42348  44.33073  45.03536  45.40323  57.02975  55.62047  46.46018 
##       113       114       115       116       117       118       119       120 
##  43.25593  39.73274  33.74332  28.10622  32.25690  22.39198  28.02908  23.09662 
##       121       122       123       124       125       126       127       128 
##  32.79690  25.75052  32.79690  23.98893  34.81812  32.70421  34.81812  28.12407 
##       129       130       131       132       133       134       135       136 
##  34.72544  35.78239  40.36253  30.14529  32.17976  29.71353  29.36121  25.13339 
##       137       138       139       140       141       142       143       144 
##  35.32991  26.52194  32.51136  25.11266  34.43241  29.14763  33.72778  26.32908 
##       145       146       147       148       149       150       151       152 
##  40.61469  36.73918  43.43324  35.68222  28.65658  32.53208  33.23672  26.19034 
##       153       154       155       156       157       158       159       160 
##  32.95636  36.12723  37.53650  28.02390  64.03237  67.90787  54.16744  42.18861 
##       161       162       163       164       165       166       167       168 
##  56.63367  55.92904  41.83629  39.01774  67.13876  58.68311  44.59036  41.06717 
##       169       170       171       172       173       174       175       176 
##  57.97847  60.09238  45.99963  44.23804  49.96783  67.23144  53.13870  46.09232 
##       177       178       179       180       181       182       183       184 
##  50.65462  53.47317  51.71158  42.90361  54.80760  60.44470  46.70427  48.11355 
##       185       186       187       188       189       190       191       192 
##  45.35948  64.73701  50.64426  43.95020  30.43083  33.95402  33.60170  26.55533 
##       193       194       195       196       197       198       199       200 
##  36.63901  31.70655  33.11583  26.06945  48.68463  68.06216  54.32173  42.69521 
##       201       202       203       204       205       206       207       208 
##  40.68146  72.03783  57.94508  50.19407  50.09390  63.48201  56.08332  42.69521 
##       209       210       211       212       213       214       215       216 
##  34.23956  31.06869  33.53492  25.78391  34.65866  35.36329  40.29576  30.43083 
##       217       218       219       220       221       222       223       224 
##  27.32444  30.84763  33.31386  26.26749  52.91245  52.91245  57.84491  59.95883 
##       225       226       227       228       229       230       231       232 
##  56.09368  49.75195  61.02615  59.26455  56.66706  68.64590  72.87373  61.24721 
##       233       234       235       236       237       238       239       240 
##  55.37868  59.60651  59.25419  55.73100  46.05893  77.76762  68.60733  60.15168 
##       241       242       243       244       245       246       247       248 
##  51.98675  56.91922  58.32849  61.14704  67.48878  63.96559  73.47820  70.30733 
##       249       250       251       252       253       254       255       256 
##  51.71158  67.21360  73.20302  61.92882  49.16820  45.99733  54.10067  52.69139 
##       257       258       259       260       261       262       263       264 
##  57.50296  75.82353  71.24339  61.37846  49.74158  75.10853  49.38926  59.95883 
##       265       266       267       268       269       270       271       272 
##  59.44704 103.48688  86.92790  69.31197  53.45762  76.00602  54.86690  60.15168 
##       273       274       275       276       277       278       279       280 
##  50.89871  77.67493  75.20870  62.87754  60.05899  76.97029  73.79942  64.28682 
##       281       282       283       284       285       286       287       288 
##  56.44600  37.77311  74.76658  65.25397  50.73176  47.56089  58.48277  56.72118 
##       289       290       291       292       293       294       295       296 
##  53.90263  47.56089  64.47219  59.53973  52.33389  48.10607  55.50476  57.61867 
##       297       298       299       300       301       302       303       304 
##  59.89205  82.08813  74.33712  61.65364  51.71158  78.13548  70.38447  73.20302 
##       305       306       307       308       309       310       311       312 
##  49.38926  67.35752  55.73100  55.02636  56.40225  76.83674  75.42746  55.69761 
##       313       314       315       316       317       318       319       320 
##  44.59036  81.58383  74.18513  90.39179  52.17443  74.01819  53.23138  53.93602 
##       321       322       323       324       325       326       327       328 
##  61.82059  81.90275  67.10537  61.46827  30.84993  37.54398  36.48703  21.33732 
##       329       330       331       332       333       334       335       336 
##  31.98173  23.87840  27.75390  26.34463  33.88724  42.69521  33.53492  24.02232 
##       337       338       339       340       341       342       343       344 
##  40.36253  66.43412  52.34137  46.70427  33.28277  33.63509  35.04436  26.94103 
##       345       346       347       348       349       350       351       352 
##  35.26313  32.79690  32.09226  22.57965  32.25172  25.90999  32.60404  24.85303 
##       353       354       355       356       357       358       359       360 
##  35.64883  38.46738  36.70579  24.72695  33.38064  36.55151  38.31310  28.80050 
##       361       362       363       364       365       366       367       368 
##  29.14763  34.78473  34.08009  27.03372  32.84065  31.43137  32.84065  26.85123 
##       369       370       371       372       373       374       375       376 
##  45.29500  66.43412  52.34137  34.72544  64.95807  38.53416  38.88648  29.72619 
##       377       378       379       380       381       382       383       384 
##  56.82135  90.99626  74.43728  63.16308  46.35195  62.55861  48.46587  43.18108 
##       385       386       387       388       389       390       391       392 
##  34.87742  29.24032  30.29728  25.71713  77.77280  77.42048  61.21382  56.28136 
##       393       394       395       396       397       398       399       400 
##  54.74082  87.85878  80.10777  64.25343  53.39833  88.63020  77.00368  57.62615 
##       401       402       403       404       405       406       407       408 
##  33.53492  33.88724  31.06869  30.01174  44.17126  80.10777  72.70908  52.27459 
##       409       410       411       412       413       414       415       416 
##  32.09226  27.51211  28.21675  24.34125  55.45582  87.16451  70.95785  67.43466 
##       417       418       419       420       421       422       423       424 
##  56.31993  89.79021  73.58354  92.25644  51.85550  77.22244  48.68463  57.14028 
##       425       426       427       428       429       430       431       432 
##  53.80994  74.59675  58.39009  48.17284  44.13787  80.42670  71.61873  59.28758 
##       433       434       435       436       437       438       439       440 
##  38.56755  42.44306  42.79538  26.94103  45.89947  82.18830  73.38033  51.53657 
##       441       442       443       444       445       446       447       448 
##  37.89630  37.54398  37.19167  23.45124  59.03543  92.50571  75.94673  55.15992 
##       449       450       451       452       453       454       455       456 
##  50.79854  38.11507  38.46738  27.89782  34.08009  47.11589  47.46821  33.02314 
##       457       458       459       460       461       462       463       464 
##  38.21523  39.62451  39.27219  24.47480  36.22740  34.11348  33.76117  28.12407 
##       465       466       467       468       469       470       471       472 
##  31.99957  33.40885  24.95320  26.01015  60.09008  66.78414  57.97617  55.15762 
##       473       474       475       476       477       478       479       480 
##  65.47503  76.74923  60.54257  53.49620  36.32008  33.50153  33.14921  27.51211 
##       481       482       483       484       485       486       487       488 
##  39.84327  32.09226  33.50153  26.10284  56.98599  76.36352  60.15686  55.57672 
##       489       490       491       492       493       494       495       496 
##  48.99838  75.77460  59.56794  63.79576  49.59766  73.20302  72.14606  61.57650 
##       497       498       499       500       501       502       503       504 
##  51.93264  78.00422  47.70481  56.86510  54.54797  87.31361  62.65130  63.70826 
##       505       506       507       508       509       510       511       512 
##  48.55855  87.31361  76.03941  60.18507  53.81513  85.87613  62.62309  61.56614 
##       513       514       515       516       517       518       519       520 
##  34.69205  34.69205  34.33973  25.88408  34.87742  40.16220  35.22974  29.94496 
##       521       522       523       524       525       526       527       528 
##  55.25261  87.31361  71.10695  45.03536  47.72784  82.60739  71.33319  50.54639 
##       529       530       531       532       533       534       535       536 
##  55.12653  78.73189  57.59276  57.59276  49.59766  57.70099  44.31288  54.53013 
##       537       538       539       540       541       542       543       544 
##  54.42189  93.88159  77.32261  56.88813  56.44600  84.27918  82.86991  52.92282 
##       545       546       547       548       549       550       551       552 
##  52.43406  76.03941  59.83275  50.32015  55.79778  77.64154  64.60575  64.60575 
##       553       554       555       556       557       558       559       560 
##  48.17803  72.48802  51.34889  52.40585  44.29734  80.93848  69.66429  45.00198 
##       561       562       563       564       565       566       567       568 
##  51.86586  59.26455  58.20760  59.61687  57.26635  63.60809  59.38026  57.61867 
##       569       570       571       572       573       574       575       576 
##  49.04731  68.07252  75.82353  60.67383  50.63907  73.18747  73.18747  61.20864 
##       577       578       579       580       581       582       583       584 
##  53.81513  46.41643  57.69063  57.69063  50.22516  45.99733  54.80530  53.74835 
##       585       586       587       588       589       590       591       592 
##  51.20497  48.03411  56.84207  56.84207  54.00280  62.45845  73.38033  63.51540 
##       593       594       595       596       597       598       599       600 
##  68.09555  82.18830  81.48366  75.14192  53.01262  76.61797  60.41131  60.41131 
##       601       602       603       604       605       606       607       608 
##  60.36526  62.47917  61.42222  57.89903  54.74082  86.80183  69.18589  61.43488 
##       609       610       611       612       613       614       615       616 
##  76.61797  92.12000  75.56102  68.16232  56.92151  78.06064  61.85398  60.09238 
##       617       618       619       620       621       622       623       624 
##  41.67164  38.85309  39.20541  29.34049  38.66024  37.25096  37.60328  27.03372 
##       625       626       627       628       629       630       631       632 
##  77.32261  95.99550  77.67493  69.57160  49.13711  82.95971  66.75305  65.69609 
##       633       634       635       636       637       638       639       640 
##  40.64808  40.64808  41.00039  29.37388  42.72860  42.72860  43.43324  26.16962 
##       641       642       643       644       645       646       647       648 
##  41.03378  33.98741  33.63509  25.88408  44.77573  33.85385  33.50153  25.04588 
##       649       650       651       652       653       654       655       656 
##  42.05735  72.35676  62.49184  38.18184  40.71485  65.02485  57.62615  42.82877 
##       657       658       659       660       661       662       663       664 
##  41.35271  63.19647  53.68387  39.23880  42.18861  60.15686  46.06411  42.89324 
##       665       666       667       668       669       670       671       672 
##  40.45522  60.88971  53.13870  40.80754  37.28435  60.18507  54.54797  35.87508 
##       673       674       675       676       677       678       679       680 
##  40.58130  56.43564  42.34289  36.00115  41.67164  64.92468  55.05975  44.13787 
##       681       682       683       684       685       686       687       688 
##  46.63749  75.17531  61.08256  39.94344  33.02314  33.72778  26.68140  25.62445 
##       689       690       691       692       693       694       695       696 
##  34.74616  34.74616  25.23356  26.99515  43.25593  56.29172  48.89303  43.25593 
##       697       698       699       700       701       702       703       704 
##  33.88724  34.94420  34.59188  21.55609  58.27437  81.52741  53.69423  61.79756 
##       705       706       707       708       709       710       711       712 
##  32.32368  33.02832  27.03890  24.22035  33.99777  34.70241  25.54212  26.24676 
##       713       714       715       716       717       718       719       720 
##  34.65866  66.71966  52.62691  49.10372  46.70427  39.65790  40.01022  29.79297 
##       721       722       723       724       725       726       727       728 
##  33.53492  36.70579  36.35347  24.37464  33.73296  34.08528  33.73296  23.51571 
##       729       730       731       732       733       734       735       736 
##  30.91441  48.53034  37.60846  28.09586  42.23236  44.69859  33.77671  28.49193 
##       737       738       739       740       741       742       743       744 
##  33.02314  31.96618  37.95560  28.09068  40.64808  62.84415  54.38851  44.52358 
##       745       746       747       748       749       750       751       752 
##  27.95194  26.89498  27.24730  24.07643  34.23956  35.64883  36.35347  26.84087 
##       753       754       755       756       757       758       759       760 
##  33.76117  34.11348  33.76117  21.78233  32.93045  32.93045  31.16886  25.17944 
##       761       762       763       764       765       766       767       768 
##  36.40759  31.47513  30.77049  22.31484  44.45680  33.88724  33.53492  24.72695 
##       769       770       771       772       773       774       775       776 
##  39.97683  34.33973  33.98741  26.23640  52.96657  61.06990  47.32947  45.92019 
##       777       778       779       780       781       782       783       784 
##  28.49193  29.19657  33.77671  26.73034  33.30868  35.42259  30.84245  26.96694 
##       785       786       787       788       789       790       791       792 
##  32.67600  33.02832  32.32368  22.10644  51.88888  56.82135  42.72860  40.61469 
##       793       794       795       796       797       798       799       800 
##  36.83935  39.30558  39.65790  28.03138  34.81812  37.63667  38.34131  28.12407 
##       801       802       803       804       805       806       807       808 
##  52.40585  79.18207  65.08932  56.63367  45.35429  59.79936  46.05893  39.71719 
##       809       810       811       812       813       814       815       816 
##  32.88440  27.59962  26.54266  26.19034  31.73994  33.50153  30.68298  24.34125 
##       817       818       819       820       821       822       823       824 
##  52.43406  73.92550  51.02478  55.25261  42.02396  56.46903  42.37628  46.95642 
##       825       826       827       828       829       830       831       832 
##  58.58294  56.46903  42.37628  42.37628  31.39798  26.46552  27.52248  23.64697 
##       833       834       835       836       837       838       839       840 
##  41.25255  43.36646  41.95718  37.02472  40.71485  65.02485  57.27383  43.18108
## $lm
## 
## Call:
## lm(formula = {
##     {
##         a
##     }
## } ~ {
##     {
##         b
##     }
## } + {
##     {
##         c
##     }
## }, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -80.392 -17.299  -8.853  19.017 102.227 
## 
## Coefficients:
##                               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    7.36317    2.80798   2.622  0.00889 ** 
## {\n    {\n        b\n    }\n}  0.35232    0.01995  17.663  < 2e-16 ***
## {\n    {\n        c\n    }\n}  0.03857    0.04864   0.793  0.42798    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27.58 on 837 degrees of freedom
## Multiple R-squared:  0.2757, Adjusted R-squared:  0.2739 
## F-statistic: 159.3 on 2 and 837 DF,  p-value: < 2.2e-16
## 
## 
## $white
## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 65.37911, Df = 1, p = 6.1791e-16
## 
## $vif
## {\n    {\n        b\n    }\n} {\n    {\n        c\n    }\n} 
##                      1.009896                      1.009896 
## 
## $predict
##         1         2         3         4         5         6         7         8 
##  33.37546  33.72778  33.37546  19.28271  32.47797  38.11507  38.46738  26.13623 
##         9        10        11        12        13        14        15        16 
##  54.35512  77.60815  61.40149  44.49019  30.84993  37.89630  38.60094  21.33732 
##        17        18        19        20        21        22        23        24 
##  37.98899  41.86450  42.21681  43.97841  32.79690  28.21675  28.56907  23.28429 
##        25        26        27        28        29        30        31        32 
##  65.46985  84.14274  67.93608  53.13870  56.09368  60.32151  59.26455  55.38905 
##        33        34        35        36        37        38        39        40 
##  33.56831  33.92063  33.56831  22.99875  32.96384  34.37312  34.02080  20.63269 
##        41        42        43        44        45        46        47        48 
##  31.89940  32.60404  33.66100  20.62521  36.54633  40.42183  40.77415  24.21517 
##        49        50        51        52        53        54        55        56 
##  31.48779  37.82953  38.53416  23.73678  34.27295  38.85309  39.20541  29.34049 
##        57        58        59        60        61        62        63        64 
##  46.76875  83.76222  74.95425  78.47744  34.08528  27.74354  33.73296  26.68658 
##        65        66        67        68        69        70        71        72 
##  32.67600  31.61905  32.32368  24.92499  34.37082  26.61981  29.79067  26.26749 
##        73        74        75        76        77        78        79        80 
##  34.55849  26.10284  30.33066  29.97835  35.50721  36.56417  37.62113  30.22243 
##        81        82        83        84        85        86        87        88 
##  31.90459  26.61981  28.02908  24.15357  42.27611  48.61785  46.85626  42.27611 
##        89        90        91        92        93        94        95        96 
##  63.19647  57.20705  43.11431  43.11431  55.79778  56.85474  42.76199  43.11431 
##        97        98        99       100       101       102       103       104 
##  40.47077  27.43497  27.78729  22.50251  47.02320  91.06304  74.85638  88.24449 
##       105       106       107       108       109       110       111       112 
##  39.75058  58.42348  44.33073  45.03536  45.40323  57.02975  55.62047  46.46018 
##       113       114       115       116       117       118       119       120 
##  43.25593  39.73274  33.74332  28.10622  32.25690  22.39198  28.02908  23.09662 
##       121       122       123       124       125       126       127       128 
##  32.79690  25.75052  32.79690  23.98893  34.81812  32.70421  34.81812  28.12407 
##       129       130       131       132       133       134       135       136 
##  34.72544  35.78239  40.36253  30.14529  32.17976  29.71353  29.36121  25.13339 
##       137       138       139       140       141       142       143       144 
##  35.32991  26.52194  32.51136  25.11266  34.43241  29.14763  33.72778  26.32908 
##       145       146       147       148       149       150       151       152 
##  40.61469  36.73918  43.43324  35.68222  28.65658  32.53208  33.23672  26.19034 
##       153       154       155       156       157       158       159       160 
##  32.95636  36.12723  37.53650  28.02390  64.03237  67.90787  54.16744  42.18861 
##       161       162       163       164       165       166       167       168 
##  56.63367  55.92904  41.83629  39.01774  67.13876  58.68311  44.59036  41.06717 
##       169       170       171       172       173       174       175       176 
##  57.97847  60.09238  45.99963  44.23804  49.96783  67.23144  53.13870  46.09232 
##       177       178       179       180       181       182       183       184 
##  50.65462  53.47317  51.71158  42.90361  54.80760  60.44470  46.70427  48.11355 
##       185       186       187       188       189       190       191       192 
##  45.35948  64.73701  50.64426  43.95020  30.43083  33.95402  33.60170  26.55533 
##       193       194       195       196       197       198       199       200 
##  36.63901  31.70655  33.11583  26.06945  48.68463  68.06216  54.32173  42.69521 
##       201       202       203       204       205       206       207       208 
##  40.68146  72.03783  57.94508  50.19407  50.09390  63.48201  56.08332  42.69521 
##       209       210       211       212       213       214       215       216 
##  34.23956  31.06869  33.53492  25.78391  34.65866  35.36329  40.29576  30.43083 
##       217       218       219       220       221       222       223       224 
##  27.32444  30.84763  33.31386  26.26749  52.91245  52.91245  57.84491  59.95883 
##       225       226       227       228       229       230       231       232 
##  56.09368  49.75195  61.02615  59.26455  56.66706  68.64590  72.87373  61.24721 
##       233       234       235       236       237       238       239       240 
##  55.37868  59.60651  59.25419  55.73100  46.05893  77.76762  68.60733  60.15168 
##       241       242       243       244       245       246       247       248 
##  51.98675  56.91922  58.32849  61.14704  67.48878  63.96559  73.47820  70.30733 
##       249       250       251       252       253       254       255       256 
##  51.71158  67.21360  73.20302  61.92882  49.16820  45.99733  54.10067  52.69139 
##       257       258       259       260       261       262       263       264 
##  57.50296  75.82353  71.24339  61.37846  49.74158  75.10853  49.38926  59.95883 
##       265       266       267       268       269       270       271       272 
##  59.44704 103.48688  86.92790  69.31197  53.45762  76.00602  54.86690  60.15168 
##       273       274       275       276       277       278       279       280 
##  50.89871  77.67493  75.20870  62.87754  60.05899  76.97029  73.79942  64.28682 
##       281       282       283       284       285       286       287       288 
##  56.44600  37.77311  74.76658  65.25397  50.73176  47.56089  58.48277  56.72118 
##       289       290       291       292       293       294       295       296 
##  53.90263  47.56089  64.47219  59.53973  52.33389  48.10607  55.50476  57.61867 
##       297       298       299       300       301       302       303       304 
##  59.89205  82.08813  74.33712  61.65364  51.71158  78.13548  70.38447  73.20302 
##       305       306       307       308       309       310       311       312 
##  49.38926  67.35752  55.73100  55.02636  56.40225  76.83674  75.42746  55.69761 
##       313       314       315       316       317       318       319       320 
##  44.59036  81.58383  74.18513  90.39179  52.17443  74.01819  53.23138  53.93602 
##       321       322       323       324       325       326       327       328 
##  61.82059  81.90275  67.10537  61.46827  30.84993  37.54398  36.48703  21.33732 
##       329       330       331       332       333       334       335       336 
##  31.98173  23.87840  27.75390  26.34463  33.88724  42.69521  33.53492  24.02232 
##       337       338       339       340       341       342       343       344 
##  40.36253  66.43412  52.34137  46.70427  33.28277  33.63509  35.04436  26.94103 
##       345       346       347       348       349       350       351       352 
##  35.26313  32.79690  32.09226  22.57965  32.25172  25.90999  32.60404  24.85303 
##       353       354       355       356       357       358       359       360 
##  35.64883  38.46738  36.70579  24.72695  33.38064  36.55151  38.31310  28.80050 
##       361       362       363       364       365       366       367       368 
##  29.14763  34.78473  34.08009  27.03372  32.84065  31.43137  32.84065  26.85123 
##       369       370       371       372       373       374       375       376 
##  45.29500  66.43412  52.34137  34.72544  64.95807  38.53416  38.88648  29.72619 
##       377       378       379       380       381       382       383       384 
##  56.82135  90.99626  74.43728  63.16308  46.35195  62.55861  48.46587  43.18108 
##       385       386       387       388       389       390       391       392 
##  34.87742  29.24032  30.29728  25.71713  77.77280  77.42048  61.21382  56.28136 
##       393       394       395       396       397       398       399       400 
##  54.74082  87.85878  80.10777  64.25343  53.39833  88.63020  77.00368  57.62615 
##       401       402       403       404       405       406       407       408 
##  33.53492  33.88724  31.06869  30.01174  44.17126  80.10777  72.70908  52.27459 
##       409       410       411       412       413       414       415       416 
##  32.09226  27.51211  28.21675  24.34125  55.45582  87.16451  70.95785  67.43466 
##       417       418       419       420       421       422       423       424 
##  56.31993  89.79021  73.58354  92.25644  51.85550  77.22244  48.68463  57.14028 
##       425       426       427       428       429       430       431       432 
##  53.80994  74.59675  58.39009  48.17284  44.13787  80.42670  71.61873  59.28758 
##       433       434       435       436       437       438       439       440 
##  38.56755  42.44306  42.79538  26.94103  45.89947  82.18830  73.38033  51.53657 
##       441       442       443       444       445       446       447       448 
##  37.89630  37.54398  37.19167  23.45124  59.03543  92.50571  75.94673  55.15992 
##       449       450       451       452       453       454       455       456 
##  50.79854  38.11507  38.46738  27.89782  34.08009  47.11589  47.46821  33.02314 
##       457       458       459       460       461       462       463       464 
##  38.21523  39.62451  39.27219  24.47480  36.22740  34.11348  33.76117  28.12407 
##       465       466       467       468       469       470       471       472 
##  31.99957  33.40885  24.95320  26.01015  60.09008  66.78414  57.97617  55.15762 
##       473       474       475       476       477       478       479       480 
##  65.47503  76.74923  60.54257  53.49620  36.32008  33.50153  33.14921  27.51211 
##       481       482       483       484       485       486       487       488 
##  39.84327  32.09226  33.50153  26.10284  56.98599  76.36352  60.15686  55.57672 
##       489       490       491       492       493       494       495       496 
##  48.99838  75.77460  59.56794  63.79576  49.59766  73.20302  72.14606  61.57650 
##       497       498       499       500       501       502       503       504 
##  51.93264  78.00422  47.70481  56.86510  54.54797  87.31361  62.65130  63.70826 
##       505       506       507       508       509       510       511       512 
##  48.55855  87.31361  76.03941  60.18507  53.81513  85.87613  62.62309  61.56614 
##       513       514       515       516       517       518       519       520 
##  34.69205  34.69205  34.33973  25.88408  34.87742  40.16220  35.22974  29.94496 
##       521       522       523       524       525       526       527       528 
##  55.25261  87.31361  71.10695  45.03536  47.72784  82.60739  71.33319  50.54639 
##       529       530       531       532       533       534       535       536 
##  55.12653  78.73189  57.59276  57.59276  49.59766  57.70099  44.31288  54.53013 
##       537       538       539       540       541       542       543       544 
##  54.42189  93.88159  77.32261  56.88813  56.44600  84.27918  82.86991  52.92282 
##       545       546       547       548       549       550       551       552 
##  52.43406  76.03941  59.83275  50.32015  55.79778  77.64154  64.60575  64.60575 
##       553       554       555       556       557       558       559       560 
##  48.17803  72.48802  51.34889  52.40585  44.29734  80.93848  69.66429  45.00198 
##       561       562       563       564       565       566       567       568 
##  51.86586  59.26455  58.20760  59.61687  57.26635  63.60809  59.38026  57.61867 
##       569       570       571       572       573       574       575       576 
##  49.04731  68.07252  75.82353  60.67383  50.63907  73.18747  73.18747  61.20864 
##       577       578       579       580       581       582       583       584 
##  53.81513  46.41643  57.69063  57.69063  50.22516  45.99733  54.80530  53.74835 
##       585       586       587       588       589       590       591       592 
##  51.20497  48.03411  56.84207  56.84207  54.00280  62.45845  73.38033  63.51540 
##       593       594       595       596       597       598       599       600 
##  68.09555  82.18830  81.48366  75.14192  53.01262  76.61797  60.41131  60.41131 
##       601       602       603       604       605       606       607       608 
##  60.36526  62.47917  61.42222  57.89903  54.74082  86.80183  69.18589  61.43488 
##       609       610       611       612       613       614       615       616 
##  76.61797  92.12000  75.56102  68.16232  56.92151  78.06064  61.85398  60.09238 
##       617       618       619       620       621       622       623       624 
##  41.67164  38.85309  39.20541  29.34049  38.66024  37.25096  37.60328  27.03372 
##       625       626       627       628       629       630       631       632 
##  77.32261  95.99550  77.67493  69.57160  49.13711  82.95971  66.75305  65.69609 
##       633       634       635       636       637       638       639       640 
##  40.64808  40.64808  41.00039  29.37388  42.72860  42.72860  43.43324  26.16962 
##       641       642       643       644       645       646       647       648 
##  41.03378  33.98741  33.63509  25.88408  44.77573  33.85385  33.50153  25.04588 
##       649       650       651       652       653       654       655       656 
##  42.05735  72.35676  62.49184  38.18184  40.71485  65.02485  57.62615  42.82877 
##       657       658       659       660       661       662       663       664 
##  41.35271  63.19647  53.68387  39.23880  42.18861  60.15686  46.06411  42.89324 
##       665       666       667       668       669       670       671       672 
##  40.45522  60.88971  53.13870  40.80754  37.28435  60.18507  54.54797  35.87508 
##       673       674       675       676       677       678       679       680 
##  40.58130  56.43564  42.34289  36.00115  41.67164  64.92468  55.05975  44.13787 
##       681       682       683       684       685       686       687       688 
##  46.63749  75.17531  61.08256  39.94344  33.02314  33.72778  26.68140  25.62445 
##       689       690       691       692       693       694       695       696 
##  34.74616  34.74616  25.23356  26.99515  43.25593  56.29172  48.89303  43.25593 
##       697       698       699       700       701       702       703       704 
##  33.88724  34.94420  34.59188  21.55609  58.27437  81.52741  53.69423  61.79756 
##       705       706       707       708       709       710       711       712 
##  32.32368  33.02832  27.03890  24.22035  33.99777  34.70241  25.54212  26.24676 
##       713       714       715       716       717       718       719       720 
##  34.65866  66.71966  52.62691  49.10372  46.70427  39.65790  40.01022  29.79297 
##       721       722       723       724       725       726       727       728 
##  33.53492  36.70579  36.35347  24.37464  33.73296  34.08528  33.73296  23.51571 
##       729       730       731       732       733       734       735       736 
##  30.91441  48.53034  37.60846  28.09586  42.23236  44.69859  33.77671  28.49193 
##       737       738       739       740       741       742       743       744 
##  33.02314  31.96618  37.95560  28.09068  40.64808  62.84415  54.38851  44.52358 
##       745       746       747       748       749       750       751       752 
##  27.95194  26.89498  27.24730  24.07643  34.23956  35.64883  36.35347  26.84087 
##       753       754       755       756       757       758       759       760 
##  33.76117  34.11348  33.76117  21.78233  32.93045  32.93045  31.16886  25.17944 
##       761       762       763       764       765       766       767       768 
##  36.40759  31.47513  30.77049  22.31484  44.45680  33.88724  33.53492  24.72695 
##       769       770       771       772       773       774       775       776 
##  39.97683  34.33973  33.98741  26.23640  52.96657  61.06990  47.32947  45.92019 
##       777       778       779       780       781       782       783       784 
##  28.49193  29.19657  33.77671  26.73034  33.30868  35.42259  30.84245  26.96694 
##       785       786       787       788       789       790       791       792 
##  32.67600  33.02832  32.32368  22.10644  51.88888  56.82135  42.72860  40.61469 
##       793       794       795       796       797       798       799       800 
##  36.83935  39.30558  39.65790  28.03138  34.81812  37.63667  38.34131  28.12407 
##       801       802       803       804       805       806       807       808 
##  52.40585  79.18207  65.08932  56.63367  45.35429  59.79936  46.05893  39.71719 
##       809       810       811       812       813       814       815       816 
##  32.88440  27.59962  26.54266  26.19034  31.73994  33.50153  30.68298  24.34125 
##       817       818       819       820       821       822       823       824 
##  52.43406  73.92550  51.02478  55.25261  42.02396  56.46903  42.37628  46.95642 
##       825       826       827       828       829       830       831       832 
##  58.58294  56.46903  42.37628  42.37628  31.39798  26.46552  27.52248  23.64697 
##       833       834       835       836       837       838       839       840 
##  41.25255  43.36646  41.95718  37.02472  40.71485  65.02485  57.27383  43.18108
handle(data, data$W, data$V, data$T)
## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 0.7953846, Df = 1, p = 0.37248
## {\n    {\n        b\n    }\n} {\n    {\n        c\n    }\n} 
##                      1.026274                      1.026274 
##          1          2          3          4          5          6          7 
## 47.1245047 29.9198193 26.5031096 25.0643032 47.3578206 30.2856374 26.8689277 
##          8          9         10         11         12         13         14 
## 23.9570886 69.9699592 47.2925779 28.7295765 19.5111169 43.6045738 28.2005003 
##         15         16         17         18         19         20         21 
## 25.2008180 22.9791662 46.6473101 29.6865034 26.2697937 15.6944929 47.1245047 
##         22         23         24         25         26         27         28 
## 25.8812449 21.4987806 23.7847424 83.9350962 51.6368032 33.0738018 22.8798273 
##         29         30         31         32         33         34         35 
## 71.9233966 28.1702865 27.5394639 29.5514634 47.1245047 29.9198193 26.5031096 
##         36         37         38         39         40         41         42 
## 27.3737983 47.3578206 30.2246677 26.8079580 23.2035242 47.3578206 23.9692565 
##         43         44         45         46         47         48         49 
## 21.8036290 21.9524419 48.2130011 31.2115480 27.7948383 21.9735677 41.0015957 
##         50         51         52         53         54         55         56 
## 26.8786880 23.8790057 21.7597725 46.8294167 30.1636980 26.7469883 25.0155014 
##         57         58         59         60         61         62         63 
## 55.7308600 34.4777095 25.0893113  7.2538033 46.9928050 25.8706820 26.1372915 
##         64         65         66         67         68         69         70 
## 23.2774642 48.4869635 35.2168288 27.4891874 23.5717498 50.7452492 27.2128175 
##         71         72         73         74         75         76         77 
## 24.3667632 24.9959807 46.1489898 25.8601191 21.1232022 22.5466306 46.8497399 
##         78         79         80         81         82         83         84 
## 30.0303933 27.9460587 21.8833169 48.5072867 27.1112014 22.7799464 23.5920730 
##         85         86         87         88         89         90         91 
## 45.6319513 33.8681430 18.9803054 18.6128823 81.6361640 42.0485130 25.9063832 
##         92         93         94         95         96         97         98 
## 26.5876125 72.3599447 41.6314855 25.4893557 26.5876125 58.6785304 23.4709362 
##         99        100        101        102        103        104        105 
## 21.3053087 22.2897815 57.1542884 43.2247224 24.6617210 42.0850166 53.5937111 
##        106        107        108        109        110        111        112 
## 40.7779100 24.6357802 29.0084841 57.1542884 27.3216562 25.7754859 20.4443803 
##        113        114        115        116        117        118        119 
## 51.7743810 35.9809561 26.2982723 21.7817008 47.1245047 23.3473918 21.4987806 
##        120        121        122        123        124        125        126 
## 24.2017698 47.1041815 25.5447079 26.4421399 23.9375679 49.4128741 31.2920384 
##        127        128        129        130        131        132        133 
## 28.4150980 25.4130081 47.6732319 30.7522691 27.3672480 21.9239634 49.0665767 
##        134        135        136        137        138        139        140 
## 31.4847078 24.4074096 25.4024453 46.8911889 24.1009562 27.8143590 23.2766617 
##        141        142        143        144        145        146        147 
## 47.1960373 27.5387917 26.3405238 25.4024453 46.6684359 27.2445061 26.7990001 
##        148        149        150        151        152        153        154 
## 20.4614935 44.0419245 32.0944046 22.4035655 20.7948205 41.4397489 27.6615335 
##        155        156        157        158        159        160        161 
## 21.0012628 19.0868669 83.8229172 50.8076937 34.6655639 23.4456676 74.4450818 
##        162        163        164        165        166        167        168 
## 41.6314855 25.4893557 22.8343658 86.0096704 42.8012749 26.6591451 22.6311335 
##        169        170        171        172        173        174        175 
## 69.2692091 40.8087961 24.6666663 23.8626951 64.1210126 41.1030816 24.9609518 
##        176        177        178        179        180        181        182 
## 19.9151739 66.0029174 26.5071221 24.9609518 17.8300368 64.8957027 41.1851771 
##        183        184        185        186        187        188        189 
## 25.0430473 30.8700657 60.0523546 41.2144581 25.0723283 18.2470642 42.2323547 
##        190        191        192        193        194        195        196 
## 30.0620819 26.6453722 24.9650946 51.5996273 24.2334584 22.0678310 19.8185031 
##        197        198        199        200        201        202        203 
## 63.0942883 50.8076937 34.6655639 23.8626951 48.0918643 41.6330906 25.4909608 
##        204        205        206        207        208        209        210 
## 20.1094483 66.6126142 34.3907991 25.7551627 15.9586949 47.0740979 27.1428900 
##        211        212        213        214        215        216        217 
## 26.2389076 23.2262549 46.9107096 26.8169158 26.5031096 21.5174988 41.8348481 
##        218        219        220        221        222        223        224 
## 27.8330772 21.9458916 20.2558537 66.1362221 19.6972360 24.8747136 27.4378478 
##        225        226        227        228        229        230        231 
## 65.3647420 15.6391408 24.7438164 20.2792567 69.7057573 26.0331376 27.7426962 
##        232        233        234        235        236        237        238 
## 14.5400815 70.3569031 33.1014779 26.5834697 22.4538421 58.8321584 41.3298472 
##        239        240        241        242        243        244        245 
## 25.4128779 13.8482893 64.3567360 24.2951004 24.2243704 26.4013632 67.8278650 
##        246        247        248        249        250        251        252 
## 18.5477699 28.1499633 21.6815594 64.5388425 21.7823730 23.3195855 14.4490283 
##        253        254        255        256        257        258        259 
## 64.7014283 17.4682313 25.7990192 22.3717466 69.5943808 47.7462392 26.3696746 
##        260        261        262        263        264        265        266 
## 14.7132302 64.8843374 42.4516372 21.0076829 27.3768781 65.3338559 44.2351359 
##        267        268        269        270        271        272        273 
## 25.6721346 15.8846246 65.9939595 44.4855650 23.5415360 28.6580439 59.6466925 
##        274        275        276        277        278        279        280 
## 38.8992152 25.0381020 13.1979460 70.9064327 40.2819972 28.1597236 14.2254728 
##        281        282        283        284        285        286        287 
## 66.1467850 26.4519003 24.4080819 17.5820153 68.6473444 21.6173797 27.7833427 
##        288        289        290        291        292        293        294 
## 26.9996946 62.9235472 17.2755619 21.6132369 21.7742177 63.8584156 17.1739457 
##        295        296        297        298        299        300        301 
## 25.2909385 22.3936749 73.0118930 41.4737148 28.9230484 14.4693515 64.5591657 
##        302        303        304        305        306        307        308 
## 37.9237003 24.3560701 27.2346155 64.9656303 41.6558213 24.9145576 22.9009531 
##        309        310        311        312        313        314        315 
## 68.3636218 26.5541887 25.9233661 20.7621991 53.2587791 32.1682145 24.4479259 
##        316        317        318        319        320        321        322 
## -0.5429631 66.2784847 43.2751292 26.5306554 21.2840527 73.5923088 51.9611723 
##        323        324        325        326        327        328        329 
## 25.4063276 27.2752620 40.8690935 27.8444426 25.5560732 22.9791662 47.1651512 
##        330        331        332        333        334        335        336 
## 22.6360788 21.5800735 24.8943646 46.8399795 42.7249273 26.3811702 21.0801482 
##        337        338        339        340        341        342        343 
## 48.8137401 41.2144581 25.0723283 19.4981465 48.2121986 34.1901046 28.0996867 
##        344        345        346        347        348        349        350 
## 23.8871611 46.7586866 24.5488697 23.0945552 21.7597725 48.5276099 25.8601191 
##        351        352        353        354        355        356        357 
## 27.7639522 22.8092275 46.7586866 30.8042809 28.0988842 21.6687193 48.0699360 
##        358        359        360        361        362        363        364 
## 35.9086210 27.4891874 22.3206675 41.0113561 31.1489733 25.4438942 19.7981798 
##        365        366        367        368        369        370        371 
## 46.2197198 30.1531352 26.2998773 22.9929391 57.3876043 41.6314855 25.4893557 
##        372        373        374        375        376        377        378 
## 23.4912594 83.1920946 30.5091929 27.0924832 23.9578911 72.9802044 44.0994237 
##        379        380        381        382        383        384        385 
## 25.5364223 14.9067021 55.9243319 40.2096621 24.0675323 22.6725825 47.0236911 
##        386        387        388        389        390        391        392 
## 23.3294761 31.3830917 22.8604368 96.3654282 41.6492710 23.0862696 22.6066675 
##        393        394        395        396        397        398        399 
## 59.0581214 38.2106330 15.3383050 10.8290863 58.7931170 37.1326995 24.4080819 
##        400        401        402        403        404        405        406 
## 15.7895588 46.9009492 29.8385264 27.6615335 27.0103878 52.7198123 32.9510600 
##        407        408        409        410        411        412        413 
## 25.2307714 15.3408427 46.7278005 23.7863474 21.6207200 23.8765982 67.3157718 
##        414        415        416        417        418        419        420 
## 44.7392041 26.1762027 13.7994875 65.7907272 43.1434295 24.5804281  3.6273110 
##        421        422        423        424        425        426        427 
## 64.2852034 41.7915336 20.0720119 22.8611091 65.9329898 43.3564221 24.7934207 
##        428        429        430        431        432        433        434 
## 24.0984184 54.1131571 33.7241451 24.3357469 11.4583038 46.6473101 29.6865034 
##        435        436        437        438        439        440        441 
## 26.2697937 22.4011579 53.5237835 33.5517989 24.1634007 14.9238153 50.2981382 
##        442        443        444        445        446        447        448 
## 32.8796576 29.4629479 24.6789644 65.5265253 42.8995507 24.3365494 17.8430072 
##        449        450        451        452        453        454        455 
## 67.9653126 30.9058971 27.4891874 21.0695853 46.9107096 27.6135343 24.1968245 
##        456        457        458        459        460        461        462 
## 19.7184919 50.9899304 34.5176837 31.1009740 24.5269415 49.9420805 29.9198193 
##        463        464        465        466        467        468        469 
## 26.5031096 25.4130081 46.9611164 30.2653142 27.0795128 23.4701337 74.5889494 
##        470        471        472        473        474        475        476 
## 33.5314757 30.4066440 22.2302866 85.5926430 46.3975534 27.8345520 21.9953657 
##        477        478        479        480        481        482        483 
## 52.0166547 31.5976893 28.1809796 27.4875823 53.7969433 23.7351381 21.5695106 
##        484        485        486        487        488        489        490 
## 21.5776660 65.1411865 43.9368378 25.3738365 26.7346902 59.7897576 42.5028465 
##        491        492        493        494        495        496        497 
## 23.9398452 30.2050168 61.0197141 24.4178423 23.7870197 16.6658651 64.3055266 
##        498        499        500        501        502        503        504 
## 41.5070084 26.6810733 22.5253746 64.0510850 43.1832734 23.4992845 13.6661828 
##        505        506        507        508        509        510        511 
## 57.0225887 36.0750892 23.3504716 12.2923587 66.7662422 44.5660554 23.7130796 
##        512        513        514        515        516        517        518 
## 14.2758796 47.0025654 29.9198193 26.5031096 23.8765982 46.2197198 31.4253431 
##        519        520        521        522        523        524        525 
## 21.2955483 20.4907746 66.0646896 43.7832099 25.2202085 11.9729348 57.5103461 
##        526        527        528        529        530        531        532 
## 37.5277987 24.8031811 17.8113186 65.6078182 42.8491439 20.1459520 22.0473775 
##        533        534        535        536        537        538        539 
## 64.4778728 25.1901249 20.1419394 22.0571379 64.2543173 41.6086245 23.0456232 
##        540        541        542        543        544        545        546 
## 25.3178121 68.8212956 28.6206075 27.9897850 17.8430072 66.1256592 43.9262750 
##        547        548        549        550        551        552        553 
## 25.3632736 24.3227765 70.9771628 46.2146443 34.3842487 33.7843123 65.0363603 
##        554        555        556        557        558        559        560 
## 43.1523873 22.8895877 22.3815070 57.9468943 37.3140035 24.5893859 17.3626026 
##        561        562        563        564        565        566        567 
## 65.9630734 34.1387650 25.0072159 29.7359775 66.7174404 35.3199197 26.8379113 
##        568        569        570        571        572        573        574 
## 26.5119372 55.2130189 21.9961682 24.1032335 10.0047918 60.4401009 37.5660376 
##        575        576        577        578        579        580        581 
## 25.9632101 13.3605318 67.9872408 17.1121736 25.5152965 26.8371088 64.1323779 
##        582        583        584        585        586        587        588 
## 16.2277119 25.4941708 21.1417901 66.0850128 22.9700781 24.9763298 27.3963988 
##        589        590        591        592        593        594        595 
## 64.1730244 26.8143781 23.6854036 14.2254728 80.8134745 42.3988229 35.5345174 
##        596        597        598        599        600        601        602 
## 26.8891207 58.2655156 43.8856285 25.3226271 27.2646991 79.7648220 31.6894149 
##        603        604        605        606        607        608        609 
## 31.0585923 26.1054726 62.0081994 50.9970228 33.1453344 22.7505351 82.3409266 
##        610        611        612        613        614        615        616 
## 43.3775478 24.8145465 13.8198107 66.6759914 46.9568434 28.3938420 27.6101940 
##        617        618        619        620        621        622        623 
## 51.8134224 30.1636980 26.7469883 20.6631208 53.9896127 28.0582377 25.0585554 
##        624        625        626        627        628        629        630 
## 19.8185031 89.7035525 45.7683358 27.9166474 16.1488265 59.7791948 43.6539177 
##        631        632        633        634        635        636        637 
## 25.0909163 27.4191296 51.8239853 29.6556173 26.2389076 20.7240904 54.3050240 
##        638        639        640        641        642        643        644 
## 29.8190057 26.8193234 20.7232879 56.9088046 30.9668668 27.5501570 23.7343356 
##        645        646        647        648        649        650        651 
## 61.8220804 30.8554903 27.4387805 24.0091004 50.5330591 34.1794114 23.0416106 
##        652        653        654        655        656        657        658 
## 19.5875947 48.7121240 33.3738352 24.7381988 16.5074220 51.4581672 36.4548104 
##        659        660        661        662        663        664        665 
## 25.3170096 17.5235834 55.5065020 39.9755438 23.8334140 26.1201783 48.5292149 
##        666        667        668        669        670        671        672 
## 34.0339388 25.3983025 17.4325301 45.7319624 31.4407211 24.8902218 17.0854302 
##        673        674        675        676        677        678        679 
## 56.4007240 41.3469604 25.2048306 28.1208124 51.2142885 35.7841439 24.6463431 
##        680        681        682        683        684        685        686 
## 16.7317800 55.5170648 38.6138875 22.4717578 20.0151850 48.5072867 31.2009851 
##        687        688        689        690        691        692        693 
## 30.7815502 24.0091004 46.8708656 29.4117386 28.4322112 23.2571410 55.7097342 
##        694        695        696        697        698        699        700 
## 25.3893446 25.9974364 17.6064813 46.7790099 29.8287660 26.4120563 27.9834951 
##        701        702        703        704        705        706        707 
## 65.2330423 42.0573406 21.6701940 21.5815483 47.3683834 29.7263474 27.3144337 
##        708        709        710        711        712        713        714 
## 23.8969214 46.8399795 29.5743244 28.3712415 23.1856085 45.1515466 42.3436010 
##        715        716        717        718        719        720        721 
## 26.2014712 22.5904871 58.5980400 30.4075767 26.9908670 20.9679692 48.8633444 
##        722        723        724        725        726        727        728 
## 33.1544225 29.7377128 23.4595708 46.6977169 29.6352941 26.2185844 24.9033224 
##        729        730        731        732        733        734        735 
## 43.9915177 42.8777527 25.4959061 20.4086792 46.8724706 33.1145785 22.9831787 
##        736        737        738        739        740        741        742 
## 21.7817008 47.2358812 27.3144337 26.6551325 21.0695853 51.7426924 36.2003688 
##        743        744        745        746        747        748        749 
## 26.6493847 17.2301004 43.8793387 23.4709362 21.3053087 23.5717498 48.3650241 
##        750        751        752        753        754        755        756 
## 27.4477384 24.4480561 19.8388263 47.1245047 29.9198193 26.5031096 25.7056887 
##        757        758        759        760        761        762        763 
## 47.2562044 30.8953342 28.1899374 27.1811289 46.6684359 23.2489857 21.7946712 
##        764        765        766        767        768        769        770 
## 27.4859773 61.6082852 30.8961367 27.4794270 23.7140124 54.3155869 31.3229245 
##        771        772        773        774        775        776        777 
## 27.9062148 23.5717498 62.3935382 31.2074052 35.8305382 17.6072838 43.2891626 
##        778        779        780        781        782        783        784 
## 28.1273627 21.9052452 19.6355940 46.8497399 30.6612158 22.9417297 20.6322347 
##        785        786        787        788        789        790        791 
## 47.2464441 29.7263474 26.3096377 23.2352128 68.7083141 42.0485130 25.9063832 
##        792        793        794        795        796        797        798 
## 24.0854480 49.6161063 29.9905493 26.5738396 21.5573428 47.8463805 26.8583648 
##        799        800        801        802        803        804        805 
## 23.8586825 18.9543646 61.1831025 39.4796310 23.9374376 14.4880697 60.1238871 
##        806        807        808        809        810        811        812 
## 43.8596877 27.7175579 25.6714623 46.8399795 23.5424687 22.8709997 24.8333949 
##        813        814        815        816        817        818        819 
## 48.2325219 31.5773661 34.9014175 23.7343356 66.2475986 43.8035331 23.3976684 
##        820        821        822        823        824        825        826 
## 22.3416630 55.8113504 41.0315491 24.8894193 22.4303088 74.3540285 41.6314855 
##        827        828        829        830        831        832        833 
## 25.4893557 26.1705851 47.4090299 23.4912594 31.2603498 23.8765982 55.8113504 
##        834        835        836        837        838        839        840 
## 26.8526170 25.3064467 25.4471043 49.2307675 33.4551281 24.8194918 18.5819962
## $lm
## 
## Call:
## lm(formula = {
##     {
##         a
##     }
## } ~ {
##     {
##         b
##     }
## } + {
##     {
##         c
##     }
## }, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -53.823 -18.331   3.104  14.198  77.004 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                   24.552210   1.733244   14.16   <2e-16 ***
## {\n    {\n        b\n    }\n}  0.417027   0.020981   19.88   <2e-16 ***
## {\n    {\n        c\n    }\n} -0.020323   0.002253   -9.02   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 19.42 on 837 degrees of freedom
## Multiple R-squared:  0.3956, Adjusted R-squared:  0.3942 
## F-statistic: 273.9 on 2 and 837 DF,  p-value: < 2.2e-16
## 
## 
## $white
## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 0.7953846, Df = 1, p = 0.37248
## 
## $vif
## {\n    {\n        b\n    }\n} {\n    {\n        c\n    }\n} 
##                      1.026274                      1.026274 
## 
## $predict
##          1          2          3          4          5          6          7 
## 47.1245047 29.9198193 26.5031096 25.0643032 47.3578206 30.2856374 26.8689277 
##          8          9         10         11         12         13         14 
## 23.9570886 69.9699592 47.2925779 28.7295765 19.5111169 43.6045738 28.2005003 
##         15         16         17         18         19         20         21 
## 25.2008180 22.9791662 46.6473101 29.6865034 26.2697937 15.6944929 47.1245047 
##         22         23         24         25         26         27         28 
## 25.8812449 21.4987806 23.7847424 83.9350962 51.6368032 33.0738018 22.8798273 
##         29         30         31         32         33         34         35 
## 71.9233966 28.1702865 27.5394639 29.5514634 47.1245047 29.9198193 26.5031096 
##         36         37         38         39         40         41         42 
## 27.3737983 47.3578206 30.2246677 26.8079580 23.2035242 47.3578206 23.9692565 
##         43         44         45         46         47         48         49 
## 21.8036290 21.9524419 48.2130011 31.2115480 27.7948383 21.9735677 41.0015957 
##         50         51         52         53         54         55         56 
## 26.8786880 23.8790057 21.7597725 46.8294167 30.1636980 26.7469883 25.0155014 
##         57         58         59         60         61         62         63 
## 55.7308600 34.4777095 25.0893113  7.2538033 46.9928050 25.8706820 26.1372915 
##         64         65         66         67         68         69         70 
## 23.2774642 48.4869635 35.2168288 27.4891874 23.5717498 50.7452492 27.2128175 
##         71         72         73         74         75         76         77 
## 24.3667632 24.9959807 46.1489898 25.8601191 21.1232022 22.5466306 46.8497399 
##         78         79         80         81         82         83         84 
## 30.0303933 27.9460587 21.8833169 48.5072867 27.1112014 22.7799464 23.5920730 
##         85         86         87         88         89         90         91 
## 45.6319513 33.8681430 18.9803054 18.6128823 81.6361640 42.0485130 25.9063832 
##         92         93         94         95         96         97         98 
## 26.5876125 72.3599447 41.6314855 25.4893557 26.5876125 58.6785304 23.4709362 
##         99        100        101        102        103        104        105 
## 21.3053087 22.2897815 57.1542884 43.2247224 24.6617210 42.0850166 53.5937111 
##        106        107        108        109        110        111        112 
## 40.7779100 24.6357802 29.0084841 57.1542884 27.3216562 25.7754859 20.4443803 
##        113        114        115        116        117        118        119 
## 51.7743810 35.9809561 26.2982723 21.7817008 47.1245047 23.3473918 21.4987806 
##        120        121        122        123        124        125        126 
## 24.2017698 47.1041815 25.5447079 26.4421399 23.9375679 49.4128741 31.2920384 
##        127        128        129        130        131        132        133 
## 28.4150980 25.4130081 47.6732319 30.7522691 27.3672480 21.9239634 49.0665767 
##        134        135        136        137        138        139        140 
## 31.4847078 24.4074096 25.4024453 46.8911889 24.1009562 27.8143590 23.2766617 
##        141        142        143        144        145        146        147 
## 47.1960373 27.5387917 26.3405238 25.4024453 46.6684359 27.2445061 26.7990001 
##        148        149        150        151        152        153        154 
## 20.4614935 44.0419245 32.0944046 22.4035655 20.7948205 41.4397489 27.6615335 
##        155        156        157        158        159        160        161 
## 21.0012628 19.0868669 83.8229172 50.8076937 34.6655639 23.4456676 74.4450818 
##        162        163        164        165        166        167        168 
## 41.6314855 25.4893557 22.8343658 86.0096704 42.8012749 26.6591451 22.6311335 
##        169        170        171        172        173        174        175 
## 69.2692091 40.8087961 24.6666663 23.8626951 64.1210126 41.1030816 24.9609518 
##        176        177        178        179        180        181        182 
## 19.9151739 66.0029174 26.5071221 24.9609518 17.8300368 64.8957027 41.1851771 
##        183        184        185        186        187        188        189 
## 25.0430473 30.8700657 60.0523546 41.2144581 25.0723283 18.2470642 42.2323547 
##        190        191        192        193        194        195        196 
## 30.0620819 26.6453722 24.9650946 51.5996273 24.2334584 22.0678310 19.8185031 
##        197        198        199        200        201        202        203 
## 63.0942883 50.8076937 34.6655639 23.8626951 48.0918643 41.6330906 25.4909608 
##        204        205        206        207        208        209        210 
## 20.1094483 66.6126142 34.3907991 25.7551627 15.9586949 47.0740979 27.1428900 
##        211        212        213        214        215        216        217 
## 26.2389076 23.2262549 46.9107096 26.8169158 26.5031096 21.5174988 41.8348481 
##        218        219        220        221        222        223        224 
## 27.8330772 21.9458916 20.2558537 66.1362221 19.6972360 24.8747136 27.4378478 
##        225        226        227        228        229        230        231 
## 65.3647420 15.6391408 24.7438164 20.2792567 69.7057573 26.0331376 27.7426962 
##        232        233        234        235        236        237        238 
## 14.5400815 70.3569031 33.1014779 26.5834697 22.4538421 58.8321584 41.3298472 
##        239        240        241        242        243        244        245 
## 25.4128779 13.8482893 64.3567360 24.2951004 24.2243704 26.4013632 67.8278650 
##        246        247        248        249        250        251        252 
## 18.5477699 28.1499633 21.6815594 64.5388425 21.7823730 23.3195855 14.4490283 
##        253        254        255        256        257        258        259 
## 64.7014283 17.4682313 25.7990192 22.3717466 69.5943808 47.7462392 26.3696746 
##        260        261        262        263        264        265        266 
## 14.7132302 64.8843374 42.4516372 21.0076829 27.3768781 65.3338559 44.2351359 
##        267        268        269        270        271        272        273 
## 25.6721346 15.8846246 65.9939595 44.4855650 23.5415360 28.6580439 59.6466925 
##        274        275        276        277        278        279        280 
## 38.8992152 25.0381020 13.1979460 70.9064327 40.2819972 28.1597236 14.2254728 
##        281        282        283        284        285        286        287 
## 66.1467850 26.4519003 24.4080819 17.5820153 68.6473444 21.6173797 27.7833427 
##        288        289        290        291        292        293        294 
## 26.9996946 62.9235472 17.2755619 21.6132369 21.7742177 63.8584156 17.1739457 
##        295        296        297        298        299        300        301 
## 25.2909385 22.3936749 73.0118930 41.4737148 28.9230484 14.4693515 64.5591657 
##        302        303        304        305        306        307        308 
## 37.9237003 24.3560701 27.2346155 64.9656303 41.6558213 24.9145576 22.9009531 
##        309        310        311        312        313        314        315 
## 68.3636218 26.5541887 25.9233661 20.7621991 53.2587791 32.1682145 24.4479259 
##        316        317        318        319        320        321        322 
## -0.5429631 66.2784847 43.2751292 26.5306554 21.2840527 73.5923088 51.9611723 
##        323        324        325        326        327        328        329 
## 25.4063276 27.2752620 40.8690935 27.8444426 25.5560732 22.9791662 47.1651512 
##        330        331        332        333        334        335        336 
## 22.6360788 21.5800735 24.8943646 46.8399795 42.7249273 26.3811702 21.0801482 
##        337        338        339        340        341        342        343 
## 48.8137401 41.2144581 25.0723283 19.4981465 48.2121986 34.1901046 28.0996867 
##        344        345        346        347        348        349        350 
## 23.8871611 46.7586866 24.5488697 23.0945552 21.7597725 48.5276099 25.8601191 
##        351        352        353        354        355        356        357 
## 27.7639522 22.8092275 46.7586866 30.8042809 28.0988842 21.6687193 48.0699360 
##        358        359        360        361        362        363        364 
## 35.9086210 27.4891874 22.3206675 41.0113561 31.1489733 25.4438942 19.7981798 
##        365        366        367        368        369        370        371 
## 46.2197198 30.1531352 26.2998773 22.9929391 57.3876043 41.6314855 25.4893557 
##        372        373        374        375        376        377        378 
## 23.4912594 83.1920946 30.5091929 27.0924832 23.9578911 72.9802044 44.0994237 
##        379        380        381        382        383        384        385 
## 25.5364223 14.9067021 55.9243319 40.2096621 24.0675323 22.6725825 47.0236911 
##        386        387        388        389        390        391        392 
## 23.3294761 31.3830917 22.8604368 96.3654282 41.6492710 23.0862696 22.6066675 
##        393        394        395        396        397        398        399 
## 59.0581214 38.2106330 15.3383050 10.8290863 58.7931170 37.1326995 24.4080819 
##        400        401        402        403        404        405        406 
## 15.7895588 46.9009492 29.8385264 27.6615335 27.0103878 52.7198123 32.9510600 
##        407        408        409        410        411        412        413 
## 25.2307714 15.3408427 46.7278005 23.7863474 21.6207200 23.8765982 67.3157718 
##        414        415        416        417        418        419        420 
## 44.7392041 26.1762027 13.7994875 65.7907272 43.1434295 24.5804281  3.6273110 
##        421        422        423        424        425        426        427 
## 64.2852034 41.7915336 20.0720119 22.8611091 65.9329898 43.3564221 24.7934207 
##        428        429        430        431        432        433        434 
## 24.0984184 54.1131571 33.7241451 24.3357469 11.4583038 46.6473101 29.6865034 
##        435        436        437        438        439        440        441 
## 26.2697937 22.4011579 53.5237835 33.5517989 24.1634007 14.9238153 50.2981382 
##        442        443        444        445        446        447        448 
## 32.8796576 29.4629479 24.6789644 65.5265253 42.8995507 24.3365494 17.8430072 
##        449        450        451        452        453        454        455 
## 67.9653126 30.9058971 27.4891874 21.0695853 46.9107096 27.6135343 24.1968245 
##        456        457        458        459        460        461        462 
## 19.7184919 50.9899304 34.5176837 31.1009740 24.5269415 49.9420805 29.9198193 
##        463        464        465        466        467        468        469 
## 26.5031096 25.4130081 46.9611164 30.2653142 27.0795128 23.4701337 74.5889494 
##        470        471        472        473        474        475        476 
## 33.5314757 30.4066440 22.2302866 85.5926430 46.3975534 27.8345520 21.9953657 
##        477        478        479        480        481        482        483 
## 52.0166547 31.5976893 28.1809796 27.4875823 53.7969433 23.7351381 21.5695106 
##        484        485        486        487        488        489        490 
## 21.5776660 65.1411865 43.9368378 25.3738365 26.7346902 59.7897576 42.5028465 
##        491        492        493        494        495        496        497 
## 23.9398452 30.2050168 61.0197141 24.4178423 23.7870197 16.6658651 64.3055266 
##        498        499        500        501        502        503        504 
## 41.5070084 26.6810733 22.5253746 64.0510850 43.1832734 23.4992845 13.6661828 
##        505        506        507        508        509        510        511 
## 57.0225887 36.0750892 23.3504716 12.2923587 66.7662422 44.5660554 23.7130796 
##        512        513        514        515        516        517        518 
## 14.2758796 47.0025654 29.9198193 26.5031096 23.8765982 46.2197198 31.4253431 
##        519        520        521        522        523        524        525 
## 21.2955483 20.4907746 66.0646896 43.7832099 25.2202085 11.9729348 57.5103461 
##        526        527        528        529        530        531        532 
## 37.5277987 24.8031811 17.8113186 65.6078182 42.8491439 20.1459520 22.0473775 
##        533        534        535        536        537        538        539 
## 64.4778728 25.1901249 20.1419394 22.0571379 64.2543173 41.6086245 23.0456232 
##        540        541        542        543        544        545        546 
## 25.3178121 68.8212956 28.6206075 27.9897850 17.8430072 66.1256592 43.9262750 
##        547        548        549        550        551        552        553 
## 25.3632736 24.3227765 70.9771628 46.2146443 34.3842487 33.7843123 65.0363603 
##        554        555        556        557        558        559        560 
## 43.1523873 22.8895877 22.3815070 57.9468943 37.3140035 24.5893859 17.3626026 
##        561        562        563        564        565        566        567 
## 65.9630734 34.1387650 25.0072159 29.7359775 66.7174404 35.3199197 26.8379113 
##        568        569        570        571        572        573        574 
## 26.5119372 55.2130189 21.9961682 24.1032335 10.0047918 60.4401009 37.5660376 
##        575        576        577        578        579        580        581 
## 25.9632101 13.3605318 67.9872408 17.1121736 25.5152965 26.8371088 64.1323779 
##        582        583        584        585        586        587        588 
## 16.2277119 25.4941708 21.1417901 66.0850128 22.9700781 24.9763298 27.3963988 
##        589        590        591        592        593        594        595 
## 64.1730244 26.8143781 23.6854036 14.2254728 80.8134745 42.3988229 35.5345174 
##        596        597        598        599        600        601        602 
## 26.8891207 58.2655156 43.8856285 25.3226271 27.2646991 79.7648220 31.6894149 
##        603        604        605        606        607        608        609 
## 31.0585923 26.1054726 62.0081994 50.9970228 33.1453344 22.7505351 82.3409266 
##        610        611        612        613        614        615        616 
## 43.3775478 24.8145465 13.8198107 66.6759914 46.9568434 28.3938420 27.6101940 
##        617        618        619        620        621        622        623 
## 51.8134224 30.1636980 26.7469883 20.6631208 53.9896127 28.0582377 25.0585554 
##        624        625        626        627        628        629        630 
## 19.8185031 89.7035525 45.7683358 27.9166474 16.1488265 59.7791948 43.6539177 
##        631        632        633        634        635        636        637 
## 25.0909163 27.4191296 51.8239853 29.6556173 26.2389076 20.7240904 54.3050240 
##        638        639        640        641        642        643        644 
## 29.8190057 26.8193234 20.7232879 56.9088046 30.9668668 27.5501570 23.7343356 
##        645        646        647        648        649        650        651 
## 61.8220804 30.8554903 27.4387805 24.0091004 50.5330591 34.1794114 23.0416106 
##        652        653        654        655        656        657        658 
## 19.5875947 48.7121240 33.3738352 24.7381988 16.5074220 51.4581672 36.4548104 
##        659        660        661        662        663        664        665 
## 25.3170096 17.5235834 55.5065020 39.9755438 23.8334140 26.1201783 48.5292149 
##        666        667        668        669        670        671        672 
## 34.0339388 25.3983025 17.4325301 45.7319624 31.4407211 24.8902218 17.0854302 
##        673        674        675        676        677        678        679 
## 56.4007240 41.3469604 25.2048306 28.1208124 51.2142885 35.7841439 24.6463431 
##        680        681        682        683        684        685        686 
## 16.7317800 55.5170648 38.6138875 22.4717578 20.0151850 48.5072867 31.2009851 
##        687        688        689        690        691        692        693 
## 30.7815502 24.0091004 46.8708656 29.4117386 28.4322112 23.2571410 55.7097342 
##        694        695        696        697        698        699        700 
## 25.3893446 25.9974364 17.6064813 46.7790099 29.8287660 26.4120563 27.9834951 
##        701        702        703        704        705        706        707 
## 65.2330423 42.0573406 21.6701940 21.5815483 47.3683834 29.7263474 27.3144337 
##        708        709        710        711        712        713        714 
## 23.8969214 46.8399795 29.5743244 28.3712415 23.1856085 45.1515466 42.3436010 
##        715        716        717        718        719        720        721 
## 26.2014712 22.5904871 58.5980400 30.4075767 26.9908670 20.9679692 48.8633444 
##        722        723        724        725        726        727        728 
## 33.1544225 29.7377128 23.4595708 46.6977169 29.6352941 26.2185844 24.9033224 
##        729        730        731        732        733        734        735 
## 43.9915177 42.8777527 25.4959061 20.4086792 46.8724706 33.1145785 22.9831787 
##        736        737        738        739        740        741        742 
## 21.7817008 47.2358812 27.3144337 26.6551325 21.0695853 51.7426924 36.2003688 
##        743        744        745        746        747        748        749 
## 26.6493847 17.2301004 43.8793387 23.4709362 21.3053087 23.5717498 48.3650241 
##        750        751        752        753        754        755        756 
## 27.4477384 24.4480561 19.8388263 47.1245047 29.9198193 26.5031096 25.7056887 
##        757        758        759        760        761        762        763 
## 47.2562044 30.8953342 28.1899374 27.1811289 46.6684359 23.2489857 21.7946712 
##        764        765        766        767        768        769        770 
## 27.4859773 61.6082852 30.8961367 27.4794270 23.7140124 54.3155869 31.3229245 
##        771        772        773        774        775        776        777 
## 27.9062148 23.5717498 62.3935382 31.2074052 35.8305382 17.6072838 43.2891626 
##        778        779        780        781        782        783        784 
## 28.1273627 21.9052452 19.6355940 46.8497399 30.6612158 22.9417297 20.6322347 
##        785        786        787        788        789        790        791 
## 47.2464441 29.7263474 26.3096377 23.2352128 68.7083141 42.0485130 25.9063832 
##        792        793        794        795        796        797        798 
## 24.0854480 49.6161063 29.9905493 26.5738396 21.5573428 47.8463805 26.8583648 
##        799        800        801        802        803        804        805 
## 23.8586825 18.9543646 61.1831025 39.4796310 23.9374376 14.4880697 60.1238871 
##        806        807        808        809        810        811        812 
## 43.8596877 27.7175579 25.6714623 46.8399795 23.5424687 22.8709997 24.8333949 
##        813        814        815        816        817        818        819 
## 48.2325219 31.5773661 34.9014175 23.7343356 66.2475986 43.8035331 23.3976684 
##        820        821        822        823        824        825        826 
## 22.3416630 55.8113504 41.0315491 24.8894193 22.4303088 74.3540285 41.6314855 
##        827        828        829        830        831        832        833 
## 25.4893557 26.1705851 47.4090299 23.4912594 31.2603498 23.8765982 55.8113504 
##        834        835        836        837        838        839        840 
## 26.8526170 25.3064467 25.4471043 49.2307675 33.4551281 24.8194918 18.5819962
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