Practica_RLM_Ej.2
Jairo Mendez
2023-04-05
#datos
library(readxl)
coste_de_mantenimiento_xlsx <- read_excel("C:/Users/mende/OneDrive/Escritorio/Econometria/practicas/coste de mantenimiento.xlsx.xlsx")
head(coste_de_mantenimiento_xlsx,n = 8)## # A tibble: 8 × 3
## Y X1 X2
## <dbl> <dbl> <dbl>
## 1 320 50 7.4
## 2 450 53 5.1
## 3 370 60 4.2
## 4 470 63 3.9
## 5 420 69 1.4
## 6 500 82 2.2
## 7 570 100 7
## 8 640 104 5.7Regresion lineal
library(stargazer)
modelo_reglin<-lm(formula = Y~X1+X2+(X1*X2),data = coste_de_mantenimiento_xlsx)
#summary
summary(modelo_reglin)##
## Call:
## lm(formula = Y ~ X1 + X2 + (X1 * X2), data = coste_de_mantenimiento_xlsx)
##
## Residuals:
## Min 1Q Median 3Q Max
## -108.527 -37.595 -2.745 52.292 102.808
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 303.50401 71.54695 4.242 0.000621 ***
## X1 2.32927 0.47698 4.883 0.000166 ***
## X2 -25.07113 11.48487 -2.183 0.044283 *
## X1:X2 0.28617 0.07681 3.726 0.001840 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 67.68 on 16 degrees of freedom
## Multiple R-squared: 0.9634, Adjusted R-squared: 0.9566
## F-statistic: 140.4 on 3 and 16 DF, p-value: 1.054e-11#stargazer
stargazer(modelo_reglin,title = "regrecion de coste",type = "text",digits = 6)##
## regrecion de coste
## ===============================================
## Dependent variable:
## ---------------------------
## Y
## -----------------------------------------------
## X1 2.329275***
## (0.476982)
##
## X2 -25.071130**
## (11.484870)
##
## X1:X2 0.286169***
## (0.076813)
##
## Constant 303.504000***
## (71.546950)
##
## -----------------------------------------------
## Observations 20
## R2 0.963414
## Adjusted R2 0.956554
## Residual Std. Error 67.677750 (df = 16)
## F Statistic 140.440600*** (df = 3; 16)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Vector de Coeficientes estimados βˆ
options(scipen = 9999)
modelo_reglin$coefficients## (Intercept) X1 X2 X1:X2
## 303.5040143 2.3292746 -25.0711288 0.2861686Matriz de Varianza - Covarianza de los parametros V[β]
var_covar<-vcov(modelo_reglin)
print(var_covar)## (Intercept) X1 X2 X1:X2
## (Intercept) 5118.96645 -31.10997447 -722.8989902 4.493190281
## X1 -31.10997 0.22751204 4.5755139 -0.033223456
## X2 -722.89899 4.57551391 131.9021598 -0.822206343
## X1:X2 4.49319 -0.03322346 -0.8222063 0.005900226Intervalos de confianza
confint(object = modelo_reglin,level = .90)## 5 % 95 %
## (Intercept) 178.5913573 428.416671
## X1 1.4965192 3.162030
## X2 -45.1223698 -5.019888
## X1:X2 0.1520621 0.420275Valores Ajustados Yˆ
plot(modelo_reglin$fitted.values,main ="valores ajustados",ylab = "Y",xlab = "casos")
modelo_reglin$fitted.values## 1 2 3 4 5 6 7 8
## 340.3238 376.4442 410.0762 422.7825 456.7683 490.9729 561.2516 572.4839
## 9 10 11 12 13 14 15 16
## 661.8956 805.2546 743.9514 802.6063 921.3246 1038.5268 966.3846 967.1923
## 17 18 19 20
## 1087.4101 1280.2249 1349.9604 1214.1649Residuos del Modelo ϵˆ
plot(modelo_reglin$residuals,main = "Residuos", ylab = "Residuos",xlab = "casos")
modelo_reglin$residuals## 1 2 3 4 5 6
## -20.323767 73.555820 -40.076233 47.217467 -36.768268 9.027138
## 7 8 9 10 11 12
## 8.748419 67.516125 8.104393 -25.254613 -53.951414 -102.606335
## 13 14 15 16 17 18
## -11.324647 -108.526815 -26.384626 102.807683 72.589856 -70.224936
## 19 20
## 100.039646 5.835106matrices A & P & M
matriz_x<-model.matrix(modelo_reglin)
#Matriz X'x
matriz_xx<-t(matriz_x)%*%matriz_x
print(matriz_xx)## (Intercept) X1 X2 X1:X2
## (Intercept) 20.0 3036.0 121.20 18754.2
## X1 3036.0 574618.0 18754.20 3537032.8
## X2 121.2 18754.2 999.94 152648.7
## X1:X2 18754.2 3537032.8 152648.68 27682881.9#Matriz A
solve(matriz_xx)%*%t(matriz_x)->matriz_A
print(matriz_A)## 1 2 3 4
## (Intercept) -0.0269643876 0.21786063243 0.294409235 0.3152011324
## X1 0.0003999215 -0.00102548702 -0.001444105 -0.0015490795
## X2 0.0388047049 -0.00653630884 -0.022176619 -0.0266881805
## X1:X2 -0.0002334413 0.00002923967 0.000116450 0.0001404267
## 5 6 7 8
## (Intercept) 0.5227546767 0.3904003745 0.02028463523 0.09313147605
## X1 -0.0026669364 -0.0018298820 0.00009025813 -0.00023211650
## X2 -0.0659240840 -0.0449422757 0.01799521280 0.00379733432
## X1:X2 0.0003536128 0.0002236575 -0.00009921704 -0.00003296119
## 9 10 11 12
## (Intercept) -0.2653043830 -0.2622967332 0.0443152123 -0.0545535472
## X1 0.0011696748 0.0005835039 0.0002043562 0.0012880664
## X2 0.0665768143 0.0616052800 0.0015591322 0.0122720018
## X1:X2 -0.0002833581 -0.0001595452 -0.0000370955 -0.0001763267
## 13 14 15 16
## (Intercept) -0.072917817 -0.01500641231 -0.2239786763 -0.3262481783
## X1 0.001143413 0.00042125956 0.0024639940 0.0033485820
## X2 0.010376875 -0.00402060621 0.0315412720 0.0476387398
## X1:X2 -0.000121078 0.00002711295 -0.0003105392 -0.0004487073
## 17 18 19 20
## (Intercept) -0.1381839072 0.1833273040 0.2993764155 0.0043929480
## X1 0.0015362166 -0.0014987044 -0.0025763624 0.0001734280
## X2 0.0122853632 -0.0478476959 -0.0696793809 -0.0166375793
## X1:X2 -0.0001273987 0.0004096502 0.0006014359 0.0001280827#matriz P
matriz_x%*%matriz_A->matriz_P
print(matriz_P)## 1 2 3 4 5
## 1 0.19381324 0.129036273 0.1011834639 0.092212497 0.032406355
## 2 0.12903627 0.138078127 0.1362473103 0.134947532 0.140775748
## 3 0.10118346 0.136247310 0.1439664947 0.145553529 0.174967755
## 4 0.09221250 0.134947532 0.1455535292 0.148028057 0.184516411
## 5 0.03240635 0.140775748 0.1749677551 0.184516411 0.280601341
## 6 0.04908672 0.124665653 0.1482115949 0.154795589 0.222824650
## 7 0.12125181 0.090025536 0.0762773231 0.071774601 0.042121378
## 8 0.09743028 0.091286297 0.0868470703 0.085219176 0.079247655
## 9 0.18100528 0.059638434 0.0130924780 -0.001586386 -0.118761676
## 10 0.16372580 0.039690827 -0.0087497204 -0.024475658 -0.151199641
## 11 0.05234526 0.053070750 0.0537768719 0.054155902 0.057015148
## 12 0.03542173 0.028640088 0.0298385285 0.031131985 0.034470683
## 13 0.01624282 0.007877722 0.0087581517 0.009838119 0.008809143
## 14 -0.01366413 -0.005856117 0.0002150787 0.002514228 0.011050760
## 15 0.01772693 -0.016465255 -0.0219215745 -0.022035577 -0.039803397
## 16 0.02768589 -0.027101345 -0.0383247931 -0.039743813 -0.071846910
## 17 -0.01759892 -0.028544954 -0.0265168679 -0.024791215 -0.027292170
## 18 -0.09411030 -0.029398837 -0.0043234403 0.002953959 0.052502132
## 19 -0.12253784 -0.029967514 0.0037031147 0.013088796 0.082154982
## 20 -0.06266315 -0.036646273 -0.0228023690 -0.018097732 0.005439657
## 6 7 8 9 10 11
## 1 0.049086720 0.12125181 0.097430285 0.181005277 0.163725800 0.05234526
## 2 0.124665653 0.09002554 0.091286297 0.059638434 0.039690827 0.05307075
## 3 0.148211595 0.07627732 0.086847070 0.013092478 -0.008749720 0.05377687
## 4 0.154795589 0.07177460 0.085219176 -0.001586386 -0.024475658 0.05415590
## 5 0.222824650 0.04212138 0.079247655 -0.118761676 -0.151199641 0.05701515
## 6 0.181824864 0.04937652 0.076505860 -0.074039863 -0.107699756 0.05781048
## 7 0.049376516 0.08582501 0.073428333 0.119350110 0.115608957 0.04969791
## 8 0.076505860 0.07342833 0.071096772 0.067854942 0.054959357 0.05246510
## 9 -0.074039863 0.11935011 0.067854942 0.319570105 0.374493574 0.03291963
## 10 -0.107699756 0.11560896 0.054959357 0.374493574 0.483734939 0.01736368
## 11 0.057810481 0.04969791 0.052465096 0.032919625 0.017363681 0.05454216
## 12 0.046256974 0.03672845 0.044829330 -0.009255161 -0.061772505 0.06635373
## 13 0.021828668 0.02930695 0.033370226 0.012993057 -0.012231797 0.05889144
## 14 0.015582714 0.01795437 0.021959684 0.020061277 0.031624199 0.04841884
## 15 -0.008561643 0.02583218 0.027974307 0.007952119 -0.048452187 0.06891842
## 16 -0.027806025 0.02798608 0.027551473 0.011987645 -0.066301176 0.07573560
## 17 -0.008169078 0.01225618 0.016087216 0.007758466 -0.008609916 0.05744390
## 18 0.029069502 -0.01472189 -0.002429200 -0.006425960 0.077167686 0.02788077
## 19 0.043319093 -0.02501037 -0.009206552 -0.014246880 0.103968771 0.01765567
## 20 0.005117486 -0.00506943 0.003522672 -0.004361183 0.027154564 0.04353875
## 12 13 14 15 16
## 1 0.035421725 0.016242817 -0.0136641286 0.017726930 0.02768589
## 2 0.028640088 0.007877722 -0.0058561168 -0.016465255 -0.02710135
## 3 0.029838529 0.008758152 0.0002150787 -0.021921574 -0.03832479
## 4 0.031131985 0.009838119 0.0025142276 -0.022035577 -0.03974381
## 5 0.034470683 0.008809143 0.0110507595 -0.039803397 -0.07184691
## 6 0.046256974 0.021828668 0.0155827141 -0.008561643 -0.02780602
## 7 0.036728450 0.029306947 0.0179543655 0.025832182 0.02798608
## 8 0.044829330 0.033370226 0.0219596835 0.027974307 0.02755147
## 9 -0.009255161 0.012993057 0.0200612774 0.007952119 0.01198764
## 10 -0.061772505 -0.012231797 0.0316241994 -0.048452187 -0.06630118
## 11 0.066353735 0.058891445 0.0484188370 0.068918416 0.07573560
## 12 0.121621418 0.100578949 0.0638133975 0.150471895 0.18247104
## 13 0.100578949 0.094687541 0.0766409627 0.133403695 0.15666477
## 14 0.063813397 0.076640963 0.0879569172 0.088464457 0.09206349
## 15 0.150471895 0.133403695 0.0884644569 0.213644887 0.26420835
## 16 0.182471043 0.156664770 0.0920634863 0.264208351 0.33328907
## 17 0.108627255 0.111610526 0.0999420803 0.159565062 0.18661128
## 18 -0.011671138 0.037646387 0.1125960736 -0.012796988 -0.05523773
## 19 -0.053321689 0.012099216 0.1174654547 -0.072852378 -0.13975401
## 20 0.054765037 0.080983456 0.1111962734 0.084726697 0.07986110
## 17 18 19 20
## 1 -0.017598924 -0.094110303 -0.122537845 -0.062663147
## 2 -0.028544954 -0.029398837 -0.029967514 -0.036646273
## 3 -0.026516868 -0.004323440 0.003703115 -0.022802369
## 4 -0.024791215 0.002953959 0.013088796 -0.018097732
## 5 -0.027292170 0.052502132 0.082154982 0.005439657
## 6 -0.008169078 0.029069502 0.043319093 0.005117486
## 7 0.012256176 -0.014721888 -0.025010370 -0.005069430
## 8 0.016087216 -0.002429200 -0.009206552 0.003522672
## 9 0.007758466 -0.006425960 -0.014246880 -0.004361183
## 10 -0.008609916 0.077167686 0.103968771 0.027154564
## 11 0.057443899 0.027880775 0.017655665 0.043538746
## 12 0.108627255 -0.011671138 -0.053321689 0.054765037
## 13 0.111610526 0.037646387 0.012099216 0.080983456
## 14 0.099942080 0.112596074 0.117465455 0.111196273
## 15 0.159565062 -0.012796988 -0.072852378 0.084726697
## 16 0.186611278 -0.055237727 -0.139754007 0.079861104
## 17 0.143621327 0.072458882 0.048021095 0.117519864
## 18 0.072458882 0.282503205 0.357117396 0.179219484
## 19 0.048021095 0.357117396 0.466651545 0.201652106
## 20 0.117519864 0.179219484 0.201652106 0.154942988#Matriz M
diag(20)-matriz_P->matriz_M
print(matriz_M)## 1 2 3 4 5
## 1 0.80618676 -0.129036273 -0.1011834639 -0.092212497 -0.032406355
## 2 -0.12903627 0.861921873 -0.1362473103 -0.134947532 -0.140775748
## 3 -0.10118346 -0.136247310 0.8560335053 -0.145553529 -0.174967755
## 4 -0.09221250 -0.134947532 -0.1455535292 0.851971943 -0.184516411
## 5 -0.03240635 -0.140775748 -0.1749677551 -0.184516411 0.719398659
## 6 -0.04908672 -0.124665653 -0.1482115949 -0.154795589 -0.222824650
## 7 -0.12125181 -0.090025536 -0.0762773231 -0.071774601 -0.042121378
## 8 -0.09743028 -0.091286297 -0.0868470703 -0.085219176 -0.079247655
## 9 -0.18100528 -0.059638434 -0.0130924780 0.001586386 0.118761676
## 10 -0.16372580 -0.039690827 0.0087497204 0.024475658 0.151199641
## 11 -0.05234526 -0.053070750 -0.0537768719 -0.054155902 -0.057015148
## 12 -0.03542173 -0.028640088 -0.0298385285 -0.031131985 -0.034470683
## 13 -0.01624282 -0.007877722 -0.0087581517 -0.009838119 -0.008809143
## 14 0.01366413 0.005856117 -0.0002150787 -0.002514228 -0.011050760
## 15 -0.01772693 0.016465255 0.0219215745 0.022035577 0.039803397
## 16 -0.02768589 0.027101345 0.0383247931 0.039743813 0.071846910
## 17 0.01759892 0.028544954 0.0265168679 0.024791215 0.027292170
## 18 0.09411030 0.029398837 0.0043234403 -0.002953959 -0.052502132
## 19 0.12253784 0.029967514 -0.0037031147 -0.013088796 -0.082154982
## 20 0.06266315 0.036646273 0.0228023690 0.018097732 -0.005439657
## 6 7 8 9 10 11
## 1 -0.049086720 -0.12125181 -0.097430285 -0.181005277 -0.163725800 -0.05234526
## 2 -0.124665653 -0.09002554 -0.091286297 -0.059638434 -0.039690827 -0.05307075
## 3 -0.148211595 -0.07627732 -0.086847070 -0.013092478 0.008749720 -0.05377687
## 4 -0.154795589 -0.07177460 -0.085219176 0.001586386 0.024475658 -0.05415590
## 5 -0.222824650 -0.04212138 -0.079247655 0.118761676 0.151199641 -0.05701515
## 6 0.818175136 -0.04937652 -0.076505860 0.074039863 0.107699756 -0.05781048
## 7 -0.049376516 0.91417499 -0.073428333 -0.119350110 -0.115608957 -0.04969791
## 8 -0.076505860 -0.07342833 0.928903228 -0.067854942 -0.054959357 -0.05246510
## 9 0.074039863 -0.11935011 -0.067854942 0.680429895 -0.374493574 -0.03291963
## 10 0.107699756 -0.11560896 -0.054959357 -0.374493574 0.516265061 -0.01736368
## 11 -0.057810481 -0.04969791 -0.052465096 -0.032919625 -0.017363681 0.94545784
## 12 -0.046256974 -0.03672845 -0.044829330 0.009255161 0.061772505 -0.06635373
## 13 -0.021828668 -0.02930695 -0.033370226 -0.012993057 0.012231797 -0.05889144
## 14 -0.015582714 -0.01795437 -0.021959684 -0.020061277 -0.031624199 -0.04841884
## 15 0.008561643 -0.02583218 -0.027974307 -0.007952119 0.048452187 -0.06891842
## 16 0.027806025 -0.02798608 -0.027551473 -0.011987645 0.066301176 -0.07573560
## 17 0.008169078 -0.01225618 -0.016087216 -0.007758466 0.008609916 -0.05744390
## 18 -0.029069502 0.01472189 0.002429200 0.006425960 -0.077167686 -0.02788077
## 19 -0.043319093 0.02501037 0.009206552 0.014246880 -0.103968771 -0.01765567
## 20 -0.005117486 0.00506943 -0.003522672 0.004361183 -0.027154564 -0.04353875
## 12 13 14 15 16
## 1 -0.035421725 -0.016242817 0.0136641286 -0.017726930 -0.02768589
## 2 -0.028640088 -0.007877722 0.0058561168 0.016465255 0.02710135
## 3 -0.029838529 -0.008758152 -0.0002150787 0.021921574 0.03832479
## 4 -0.031131985 -0.009838119 -0.0025142276 0.022035577 0.03974381
## 5 -0.034470683 -0.008809143 -0.0110507595 0.039803397 0.07184691
## 6 -0.046256974 -0.021828668 -0.0155827141 0.008561643 0.02780602
## 7 -0.036728450 -0.029306947 -0.0179543655 -0.025832182 -0.02798608
## 8 -0.044829330 -0.033370226 -0.0219596835 -0.027974307 -0.02755147
## 9 0.009255161 -0.012993057 -0.0200612774 -0.007952119 -0.01198764
## 10 0.061772505 0.012231797 -0.0316241994 0.048452187 0.06630118
## 11 -0.066353735 -0.058891445 -0.0484188370 -0.068918416 -0.07573560
## 12 0.878378582 -0.100578949 -0.0638133975 -0.150471895 -0.18247104
## 13 -0.100578949 0.905312459 -0.0766409627 -0.133403695 -0.15666477
## 14 -0.063813397 -0.076640963 0.9120430828 -0.088464457 -0.09206349
## 15 -0.150471895 -0.133403695 -0.0884644569 0.786355113 -0.26420835
## 16 -0.182471043 -0.156664770 -0.0920634863 -0.264208351 0.66671093
## 17 -0.108627255 -0.111610526 -0.0999420803 -0.159565062 -0.18661128
## 18 0.011671138 -0.037646387 -0.1125960736 0.012796988 0.05523773
## 19 0.053321689 -0.012099216 -0.1174654547 0.072852378 0.13975401
## 20 -0.054765037 -0.080983456 -0.1111962734 -0.084726697 -0.07986110
## 17 18 19 20
## 1 0.017598924 0.094110303 0.122537845 0.062663147
## 2 0.028544954 0.029398837 0.029967514 0.036646273
## 3 0.026516868 0.004323440 -0.003703115 0.022802369
## 4 0.024791215 -0.002953959 -0.013088796 0.018097732
## 5 0.027292170 -0.052502132 -0.082154982 -0.005439657
## 6 0.008169078 -0.029069502 -0.043319093 -0.005117486
## 7 -0.012256176 0.014721888 0.025010370 0.005069430
## 8 -0.016087216 0.002429200 0.009206552 -0.003522672
## 9 -0.007758466 0.006425960 0.014246880 0.004361183
## 10 0.008609916 -0.077167686 -0.103968771 -0.027154564
## 11 -0.057443899 -0.027880775 -0.017655665 -0.043538746
## 12 -0.108627255 0.011671138 0.053321689 -0.054765037
## 13 -0.111610526 -0.037646387 -0.012099216 -0.080983456
## 14 -0.099942080 -0.112596074 -0.117465455 -0.111196273
## 15 -0.159565062 0.012796988 0.072852378 -0.084726697
## 16 -0.186611278 0.055237727 0.139754007 -0.079861104
## 17 0.856378673 -0.072458882 -0.048021095 -0.117519864
## 18 -0.072458882 0.717496795 -0.357117396 -0.179219484
## 19 -0.048021095 -0.357117396 0.533348455 -0.201652106
## 20 -0.117519864 -0.179219484 -0.201652106 0.845057012#Matriz y
library(dplyr)
coste_de_mantenimiento_xlsx$Y %>% as.matrix(modelo_reglin)->matriz_Y
print(matriz_Y)## [,1]
## [1,] 320
## [2,] 450
## [3,] 370
## [4,] 470
## [5,] 420
## [6,] 500
## [7,] 570
## [8,] 640
## [9,] 670
## [10,] 780
## [11,] 690
## [12,] 700
## [13,] 910
## [14,] 930
## [15,] 940
## [16,] 1070
## [17,] 1160
## [18,] 1210
## [19,] 1450
## [20,] 1220#Vector de Coeficientes estimados βˆ
matriz_A%*%matriz_Y## [,1]
## (Intercept) 303.5040143
## X1 2.3292746
## X2 -25.0711288
## X1:X2 0.2861686#Valores Ajustados Yˆ
t(matriz_P%*%matriz_Y)## 1 2 3 4 5 6 7 8
## [1,] 340.3238 376.4442 410.0762 422.7825 456.7683 490.9729 561.2516 572.4839
## 9 10 11 12 13 14 15 16
## [1,] 661.8956 805.2546 743.9514 802.6063 921.3246 1038.527 966.3846 967.1923
## 17 18 19 20
## [1,] 1087.41 1280.225 1349.96 1214.165#Residuos del Modelo ϵˆ
t(matriz_M%*%matriz_Y)## 1 2 3 4 5 6 7 8
## [1,] -20.32377 73.55582 -40.07623 47.21747 -36.76827 9.027138 8.748419 67.51613
## 9 10 11 12 13 14 15
## [1,] 8.104393 -25.25461 -53.95141 -102.6063 -11.32465 -108.5268 -26.38463
## 16 17 18 19 20
## [1,] 102.8077 72.58986 -70.22494 100.0396 5.835106