Carga de datos
library(wooldridge)
data("hprice1")
head(force(hprice1),n=5)## price assess bdrms lotsize sqrft colonial lprice lassess llotsize lsqrft
## 1 300 349.1 4 6126 2438 1 5.703783 5.855359 8.720297 7.798934
## 2 370 351.5 3 9903 2076 1 5.913503 5.862210 9.200593 7.638198
## 3 191 217.7 3 5200 1374 0 5.252274 5.383118 8.556414 7.225482
## 4 195 231.8 3 4600 1448 1 5.273000 5.445875 8.433811 7.277938
## 5 373 319.1 4 6095 2514 1 5.921578 5.765504 8.715224 7.829630Estimación del modelo
library(stargazer)
modelo_estimado<-lm(formula = price~lotsize+sqrft+bdrms,data = hprice1)
stargazer(modelo_estimado,type = "text",title = "Modelo Estimado")##
## Modelo Estimado
## ===============================================
## Dependent variable:
## ---------------------------
## price
## -----------------------------------------------
## lotsize 0.002***
## (0.001)
##
## sqrft 0.123***
## (0.013)
##
## bdrms 13.853
## (9.010)
##
## Constant -21.770
## (29.475)
##
## -----------------------------------------------
## Observations 88
## R2 0.672
## Adjusted R2 0.661
## Residual Std. Error 59.833 (df = 84)
## F Statistic 57.460*** (df = 3; 84)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Prueba de Durbin Watson
library(lmtest)
dwtest(modelo_estimado,alternative = "two.sided",iterations = 1000)##
## Durbin-Watson test
##
## data: modelo_estimado
## DW = 2.1098, p-value = 0.6218
## alternative hypothesis: true autocorrelation is not 0library(car)
durbinWatsonTest(modelo_estimado,simulate = TRUE,reps = 1000)## lag Autocorrelation D-W Statistic p-value
## 1 -0.05900522 2.109796 0.666
## Alternative hypothesis: rho != 0En ambos casos, se puede rechazar la presencia de autocorrelación (No se rechaza la Ho), ya que el Pvalue > 0.05
Prueba del Multiplicador de Lagrange [Breusch-Godfrey]
library(dplyr)
library(tidyr)
library(kableExtra)
residuos<-modelo_estimado$residuals
cbind(residuos,hprice1) %>%
as.data.frame() %>%
mutate(Lag1=dplyr::lag(residuos,1),
Lag2=dplyr::lag(residuos,2))%>%
replace_na(list(Lag1=0,Lag2=0))-> DATA_PRUEBA_BG
print(DATA_PRUEBA_BG)## residuos price assess bdrms lotsize sqrft colonial lprice lassess
## 1 -45.639765 300.000 349.1 4 6126 2438 1 5.703783 5.855359
## 2 74.848732 370.000 351.5 3 9903 2076 1 5.913503 5.862210
## 3 -8.236558 191.000 217.7 3 5200 1374 0 5.252274 5.383118
## 4 -12.081520 195.000 231.8 3 4600 1448 1 5.273000 5.445875
## 5 18.093192 373.000 319.1 4 6095 2514 1 5.921578 5.765504
## 6 62.939597 466.275 414.5 5 8566 2754 1 6.144775 6.027073
## 7 40.320875 332.500 367.8 3 9000 2067 1 5.806640 5.907539
## 8 69.843246 315.000 300.2 3 6210 1731 1 5.752573 5.704449
## 9 -43.142550 206.000 236.1 3 6000 1767 0 5.327876 5.464255
## 10 -17.817835 240.000 256.3 3 2892 1890 0 5.480639 5.546349
## 11 -47.855859 285.000 314.0 4 6000 2336 1 5.652489 5.749393
## 12 -85.461169 300.000 416.5 5 7047 2634 1 5.703783 6.031887
## 13 -54.466158 405.000 434.0 3 12237 3375 1 6.003887 6.073044
## 14 -54.300415 212.000 279.3 3 6460 1899 0 5.356586 5.632287
## 15 -52.129801 265.000 287.5 3 6519 2312 1 5.579730 5.661223
## 16 -29.766931 227.400 232.9 4 3597 1760 1 5.426711 5.450609
## 17 -51.441108 240.000 303.8 4 5922 2000 0 5.480639 5.716370
## 18 32.675968 285.000 305.6 3 7123 1774 1 5.652489 5.722277
## 19 67.603959 268.000 266.7 3 5642 1376 1 5.590987 5.586124
## 20 33.275839 310.000 326.0 4 8602 1835 1 5.736572 5.786897
## 21 -16.596960 266.000 294.3 3 5494 2048 1 5.583496 5.684599
## 22 -26.696234 270.000 318.8 3 7800 2124 1 5.598422 5.764564
## 23 -24.271531 225.000 294.2 3 6003 1768 0 5.416101 5.684260
## 24 -107.080889 150.000 208.0 4 5218 1732 0 5.010635 5.337538
## 25 30.924022 247.000 239.7 3 9425 1440 1 5.509388 5.479388
## 26 5.363331 275.000 294.1 3 6114 1932 0 5.616771 5.683920
## 27 -40.869022 230.000 267.4 3 6710 1932 0 5.438079 5.588746
## 28 46.907165 343.000 359.9 3 8577 2106 1 5.837730 5.885826
## 29 -48.350295 477.500 478.1 7 8400 3529 1 6.168564 6.169820
## 30 44.334467 350.000 355.3 4 9773 2051 1 5.857933 5.872962
## 31 -6.707262 230.000 217.8 4 4806 1573 1 5.438079 5.383577
## 32 -77.172687 335.000 385.0 4 15086 2829 0 5.814130 5.953243
## 33 19.168108 251.000 224.3 3 5763 1630 1 5.525453 5.412984
## 34 -37.749811 235.000 251.9 4 6383 1840 1 5.459586 5.529032
## 35 55.091131 361.000 354.9 4 9000 2066 1 5.888878 5.871836
## 36 -59.845223 190.000 212.5 4 3500 1702 0 5.247024 5.358942
## 37 -33.801248 360.000 452.4 4 10892 2750 1 5.886104 6.114567
## 38 18.801816 575.000 518.1 5 15634 3880 1 6.354370 6.250168
## 39 -65.502849 209.001 289.4 4 6400 1854 1 5.342339 5.667810
## 40 26.236229 225.000 268.1 2 8880 1421 0 5.416101 5.591360
## 41 9.099900 246.000 278.5 3 6314 1662 1 5.505332 5.629418
## 42 198.660139 713.500 655.4 5 28231 3331 1 6.570182 6.485246
## 43 -3.537785 248.000 273.3 4 7050 1656 1 5.513429 5.610570
## 44 55.470305 230.000 212.1 3 5305 1171 0 5.438079 5.357058
## 45 32.253952 375.000 354.0 5 6637 2293 1 5.926926 5.869297
## 46 12.433611 265.000 252.1 3 7834 1764 1 5.579730 5.529826
## 47 -48.704980 313.000 324.0 3 1000 2768 0 5.746203 5.780744
## 48 -91.243980 417.500 475.5 4 8112 3733 0 6.034285 6.164367
## 49 32.529367 253.000 256.8 3 5850 1536 1 5.533390 5.548297
## 50 66.478628 315.000 279.2 4 6660 1638 1 5.752573 5.631928
## 51 -11.629207 264.000 313.9 3 6637 1972 1 5.575949 5.749074
## 52 36.031430 255.000 279.8 2 15267 1478 0 5.541264 5.634075
## 53 6.700640 210.000 198.7 3 5146 1408 1 5.347107 5.291796
## 54 -74.702719 180.000 221.5 3 6017 1812 1 5.192957 5.400423
## 55 1.399296 250.000 268.4 3 8410 1722 1 5.521461 5.592478
## 56 -13.815798 250.000 282.3 4 5625 1780 1 5.521461 5.642970
## 57 -41.749618 209.000 230.7 4 5600 1674 1 5.342334 5.441118
## 58 -16.271207 258.000 287.0 4 6525 1850 1 5.552959 5.659482
## 59 20.334434 289.000 298.7 3 6060 1925 1 5.666427 5.699440
## 60 -16.762094 316.000 314.6 4 5539 2343 0 5.755742 5.751302
## 61 -2.824941 225.000 291.0 3 7566 1567 0 5.416101 5.673323
## 62 16.718018 266.000 286.4 4 5484 1664 1 5.583496 5.657390
## 63 67.426518 310.000 253.6 6 5348 1386 1 5.736572 5.535758
## 64 69.707122 471.250 482.0 5 15834 2617 1 6.155389 6.177944
## 65 -0.195089 335.000 384.3 4 8022 2321 1 5.814130 5.951424
## 66 112.729191 495.000 543.6 4 11966 2638 1 6.204558 6.298213
## 67 -6.752801 279.500 336.5 4 8460 1915 1 5.633002 5.818598
## 68 -2.745208 380.000 515.1 4 15105 2589 1 5.940171 6.244361
## 69 -63.699108 325.000 437.0 4 10859 2709 0 5.783825 6.079933
## 70 -7.662789 220.000 263.4 3 6300 1587 1 5.393628 5.573674
## 71 -36.663785 215.000 300.4 3 11554 1694 0 5.370638 5.705115
## 72 19.219211 240.000 250.7 3 6000 1536 1 5.480639 5.524257
## 73 163.795081 725.000 708.6 5 31000 3662 0 6.586172 6.563291
## 74 -11.312669 230.000 276.3 3 4054 1736 1 5.438079 5.621487
## 75 -13.462160 306.000 388.6 2 20700 2205 0 5.723585 5.962551
## 76 209.375830 425.000 252.5 3 5525 1502 0 6.052089 5.531411
## 77 -115.508697 318.000 295.2 4 92681 1696 1 5.762052 5.687653
## 78 24.909926 330.000 359.5 3 8178 2186 1 5.799093 5.884714
## 79 -36.646568 246.000 276.2 4 5944 1928 1 5.505332 5.621125
## 80 7.386314 225.000 249.8 3 18838 1294 0 5.416101 5.520660
## 81 -120.026447 111.000 202.4 4 4315 1535 1 4.709530 5.310246
## 82 -5.446904 268.125 254.0 3 5167 1980 1 5.591453 5.537334
## 83 -62.566594 244.000 306.8 4 7893 2090 1 5.497168 5.726196
## 84 37.147186 295.000 318.3 3 6056 1837 1 5.686975 5.762994
## 85 -6.402439 236.000 259.4 3 5828 1715 0 5.463832 5.558371
## 86 -23.651448 202.500 258.1 3 6341 1574 0 5.310740 5.553347
## 87 54.418366 219.000 232.0 2 6362 1185 0 5.389072 5.446737
## 88 -19.683427 242.000 252.0 4 4950 1774 1 5.488938 5.529429
## llotsize lsqrft Lag1 Lag2
## 1 8.720297 7.798934 0.000000 0.000000
## 2 9.200593 7.638198 -45.639765 0.000000
## 3 8.556414 7.225482 74.848732 -45.639765
## 4 8.433811 7.277938 -8.236558 74.848732
## 5 8.715224 7.829630 -12.081520 -8.236558
## 6 9.055556 7.920810 18.093192 -12.081520
## 7 9.104980 7.633853 62.939597 18.093192
## 8 8.733916 7.456455 40.320875 62.939597
## 9 8.699514 7.477038 69.843246 40.320875
## 10 7.969704 7.544332 -43.142550 69.843246
## 11 8.699514 7.756196 -17.817835 -43.142550
## 12 8.860357 7.876259 -47.855859 -17.817835
## 13 9.412219 8.124150 -85.461169 -47.855859
## 14 8.773385 7.549083 -54.466158 -85.461169
## 15 8.782476 7.745868 -54.300415 -54.466158
## 16 8.187856 7.473069 -52.129801 -54.300415
## 17 8.686430 7.600903 -29.766931 -52.129801
## 18 8.871084 7.480992 -51.441108 -29.766931
## 19 8.637994 7.226936 32.675968 -51.441108
## 20 9.059750 7.514800 67.603959 32.675968
## 21 8.611412 7.624619 33.275839 67.603959
## 22 8.961879 7.661057 -16.596960 33.275839
## 23 8.700015 7.477604 -26.696234 -16.596960
## 24 8.559870 7.457032 -24.271531 -26.696234
## 25 9.151121 7.272398 -107.080889 -24.271531
## 26 8.718336 7.566311 30.924022 -107.080889
## 27 8.811355 7.566311 5.363331 30.924022
## 28 9.056840 7.652546 -40.869022 5.363331
## 29 9.035987 8.168770 46.907165 -40.869022
## 30 9.187379 7.626083 -48.350295 46.907165
## 31 8.477620 7.360740 44.334467 -48.350295
## 32 9.621523 7.947679 -6.707262 44.334467
## 33 8.659213 7.396335 -77.172687 -6.707262
## 34 8.761394 7.517521 19.168108 -77.172687
## 35 9.104980 7.633369 -37.749811 19.168108
## 36 8.160519 7.439559 55.091131 -37.749811
## 37 9.295784 7.919356 -59.845223 55.091131
## 38 9.657204 8.263591 -33.801248 -59.845223
## 39 8.764053 7.525101 18.801816 -33.801248
## 40 9.091557 7.259116 -65.502849 18.801816
## 41 8.750525 7.415777 26.236229 -65.502849
## 42 10.248176 8.111028 9.099900 26.236229
## 43 8.860783 7.412160 198.660139 9.099900
## 44 8.576406 7.065613 -3.537785 198.660139
## 45 8.800415 7.737616 55.470305 -3.537785
## 46 8.966228 7.475339 32.253952 55.470305
## 47 6.907755 7.925880 12.433611 32.253952
## 48 9.001100 8.224967 -48.704980 12.433611
## 49 8.674197 7.336937 -91.243980 -48.704980
## 50 8.803875 7.401231 32.529367 -91.243980
## 51 8.800415 7.586803 66.478628 32.529367
## 52 9.633449 7.298445 -11.629207 66.478628
## 53 8.545975 7.249926 36.031430 -11.629207
## 54 8.702344 7.502186 6.700640 36.031430
## 55 9.037177 7.451241 -74.702719 6.700640
## 56 8.634976 7.484369 1.399296 -74.702719
## 57 8.630522 7.422971 -13.815798 1.399296
## 58 8.783396 7.522941 -41.749618 -13.815798
## 59 8.709465 7.562681 -16.271207 -41.749618
## 60 8.619569 7.759187 20.334434 -16.271207
## 61 8.931419 7.356918 -16.762094 20.334434
## 62 8.609590 7.416980 -2.824941 -16.762094
## 63 8.584478 7.234177 16.718018 -2.824941
## 64 9.669915 7.869784 67.426518 16.718018
## 65 8.989944 7.749753 69.707122 67.426518
## 66 9.389825 7.877776 -0.195089 69.707122
## 67 9.043104 7.557473 112.729191 -0.195089
## 68 9.622781 7.859027 -6.752801 112.729191
## 69 9.292749 7.904335 -2.745208 -6.752801
## 70 8.748305 7.369601 -63.699108 -2.745208
## 71 9.354787 7.434848 -7.662789 -63.699108
## 72 8.699514 7.336937 -36.663785 -7.662789
## 73 10.341743 8.205765 19.219211 -36.663785
## 74 8.307459 7.459339 163.795081 19.219211
## 75 9.937889 7.698483 -11.312669 163.795081
## 76 8.617039 7.314553 -13.462160 -11.312669
## 77 11.436919 7.436028 209.375830 -13.462160
## 78 9.009203 7.689829 -115.508697 209.375830
## 79 8.690138 7.564239 24.909926 -115.508697
## 80 9.843632 7.165493 -36.646568 24.909926
## 81 8.369853 7.336286 7.386314 -36.646568
## 82 8.550048 7.590852 -120.026447 7.386314
## 83 8.973732 7.644919 -5.446904 -120.026447
## 84 8.708805 7.515889 -62.566594 -5.446904
## 85 8.670429 7.447168 37.147186 -62.566594
## 86 8.754792 7.361375 -6.402439 37.147186
## 87 8.758098 7.077498 -23.651448 -6.402439
## 88 8.507143 7.480992 54.418366 -23.651448Prueba del Multiplicador de Lagrange [Breusch-Godfrey]
library(lmtest)
bgtest(modelo_estimado,order = 1)##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: modelo_estimado
## LM test = 0.39362, df = 1, p-value = 0.5304bgtest(modelo_estimado,order = 2)##
## Breusch-Godfrey test for serial correlation of order up to 2
##
## data: modelo_estimado
## LM test = 3.0334, df = 2, p-value = 0.2194En ambos casos (primer y segundo orden) no se rechaza la Ho debido a que Pvalue > 0.05, por o tanto puede concluirse que los residuos del modelo no siguen autocorrelación.