GASTO DE MANTENIMIENTO
Rodrigo Roque
22 de abril de 2020
Carga de datos
library(readxl)
Ejercicio_regresion <- read_excel("C:/Users/villeda/Desktop/Ejercicio_regresion.xlsx")
head(Ejercicio_regresion,n=6)## # A tibble: 6 x 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 2.2Correr el modelo
library(stargazer)
Ejercicio<-lm(formula = Y~X1+X2+X1*X2,data = Ejercicio_regresion )
# Usando Stargazer
stargazer(Ejercicio,title = "Ejemplo de Regresion Multiple",type = "text",digits = 8)##
## Ejemplo de Regresion Multiple
## ================================================
## Dependent variable:
## ----------------------------
## Y
## ------------------------------------------------
## X1 2.33911700***
## (0.46612250)
##
## X2 -24.96739000**
## (11.24008000)
##
## X1:X2 0.28435440***
## (0.07506235)
##
## Constant 305.73530000***
## (69.92387000)
##
## ------------------------------------------------
## Observations 20
## R2 0.96494280
## Adjusted R2 0.95836960
## Residual Std. Error 66.24833000 (df = 16)
## F Statistic 146.79910000*** (df = 3; 16)
## ================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Matrices A P y M
Mat_x<-model.matrix(Ejercicio)
# Matriz X'X
Mat_xx<-t(Mat_x)%*%Mat_x
print(Mat_xx)## (Intercept) X1 X2 X1:X2
## (Intercept) 20.0 3036.0 118.20 18304.2
## X1 3036.0 574618.0 18304.20 3469532.8
## X2 118.2 18304.2 978.34 149408.7
## X1:X2 18304.2 3469532.8 149408.68 27196881.9# Matriz A
Mat_a<-solve(Mat_xx)%*%t(Mat_x)
print(Mat_a)## 1 2 3 4
## (Intercept) -0.0276842640 2.158537e-01 0.291836335 0.3124221319
## X1 0.0003918313 -1.041498e-03 -0.001463627 -0.0015698882
## X2 0.0390485478 -6.225696e-03 -0.021835104 -0.0263349277
## X1:X2 -0.0002322665 3.172992e-05 0.000119522 0.0001437116
## 5 6 7 8 9
## (Intercept) 0.5183452229 0.386284989 1.949795e-02 9.135614e-02 -0.261133830
## X1 -0.0026979163 -0.001859120 8.194598e-05 -2.466689e-04 0.001192857
## X2 -0.0654785307 -0.044508158 1.823185e-02 4.094045e-03 0.066500674
## X1:X2 0.0003585806 0.000228333 -9.799670e-05 -3.071165e-05 -0.000287323
## 10 11 12 13
## (Intercept) -0.2547733810 7.104915e-02 -0.0595114814 -0.076295534
## X1 0.0006282835 4.344447e-04 0.0012530747 0.001118609
## X2 0.0613008667 -3.526758e-03 0.0127819081 0.010778674
## X1:X2 -0.0001670526 -7.228364e-05 -0.0001707218 -0.000117144
## 14 15 16 17
## (Intercept) -1.640936e-02 -0.2291953094 -0.3326501237 -0.1413146836
## X1 4.092693e-04 0.0024272397 0.0033040996 0.0015130253
## X2 -3.758467e-03 0.0320742161 0.0482576240 0.0126691497
## X1:X2 2.894944e-05 -0.0003046495 -0.0004415541 -0.0001237281
## 18 19 20
## (Intercept) 0.1854125365 0.303238435 0.0036713425
## X1 -0.0014879184 -0.002553991 0.0001659478
## X2 -0.0478403575 -0.069800891 -0.0164286628
## X1:X2 0.0004077643 0.000597656 0.0001291848# Matriz P
Matriz_p<-Mat_x%*%Mat_a
print(Matriz_p)## 1 2 3 4 5
## 1 0.19492794 0.129448747 0.1012983510 0.092222560 0.031583117
## 2 0.12944875 0.137479881 0.1352118632 0.133755179 0.138339500
## 3 0.10129835 0.135211863 0.1424308132 0.143837474 0.171822738
## 4 0.09222256 0.133755179 0.1438374739 0.146122904 0.181113490
## 5 0.03158312 0.138339500 0.1718227379 0.181113490 0.275157947
## 6 0.04845183 0.122478435 0.1453434456 0.151680036 0.217751268
## 7 0.12225213 0.090334996 0.0762932951 0.071686958 0.041210326
## 8 0.09795532 0.090860961 0.0860116614 0.084236925 0.077100906
## 9 0.18430451 0.063577632 0.0173350340 0.002773537 -0.113481154
## 10 0.16845776 0.046005757 -0.0017099765 -0.017162955 -0.141737883
## 11 0.03992843 0.056549983 0.0640879679 0.066904716 0.089105769
## 12 0.03456129 0.025943096 0.0263351113 0.027335311 0.028353615
## 13 0.01605385 0.006297985 0.0065711781 0.007431411 0.004662546
## 14 -0.01304726 -0.006061232 -0.0003435009 0.001829466 0.009364889
## 15 0.01679555 -0.019319870 -0.0256209003 -0.026042154 -0.046241011
## 16 0.02628625 -0.030771044 -0.0429937680 -0.044776966 -0.079760709
## 17 -0.01769112 -0.029955396 -0.0285022289 -0.026984411 -0.031131268
## 18 -0.09212923 -0.027214264 -0.0020354579 0.005283979 0.055159703
## 19 -0.11985502 -0.026561243 0.0074445151 0.016957576 0.087025351
## 20 -0.06180501 -0.036400965 -0.0228176153 -0.018205037 0.004600860
## 6 7 8 9 10
## 1 0.048451827 0.122252134 0.0979553187 0.184304513 0.1684577587
## 2 0.122478435 0.090334996 0.0908609607 0.063577632 0.0460057569
## 3 0.145343446 0.076293295 0.0860116614 0.017335034 -0.0017099765
## 4 0.151680036 0.071686958 0.0842369246 0.002773537 -0.0171629547
## 5 0.217751268 0.041210326 0.0771009064 -0.113481154 -0.1417378825
## 6 0.177110487 0.048648977 0.0745958102 -0.068851138 -0.0985285085
## 7 0.048648977 0.086717782 0.0738494117 0.122530517 0.1202242411
## 8 0.074595810 0.073849412 0.0708327668 0.071652089 0.0609542837
## 9 -0.068851138 0.122530517 0.0716520890 0.319493670 0.3719760955
## 10 -0.098528508 0.120224241 0.0609542837 0.371976096 0.4760816175
## 11 0.085874774 0.039207763 0.0532791324 -0.033060602 -0.0844205911
## 12 0.040562623 0.035764057 0.0424612571 -0.003190585 -0.0509674423
## 13 0.018010743 0.029015344 0.0320353374 0.017899744 -0.0038569927
## 14 0.014104579 0.018472911 0.0218926164 0.023456008 0.0368769932
## 15 -0.014557152 0.024793504 0.0254644114 0.014282309 -0.0371498019
## 16 -0.035203551 0.026475315 0.0242914042 0.019255435 -0.0530855339
## 17 -0.011695038 0.012062196 0.0149080589 0.012468273 -0.0006357297
## 18 0.031715128 -0.012826778 -0.0002983217 -0.005817399 0.0767548162
## 19 0.048066320 -0.022407760 -0.0059512870 -0.015044132 0.1006874688
## 20 0.004440934 -0.004305189 0.0038672579 -0.001559847 0.0312363820
## 11 12 13 14 15
## 1 0.039928428 0.034561293 0.016053855 -0.0130472561 0.016795550
## 2 0.056549983 0.025943096 0.006297985 -0.0060612321 -0.019319870
## 3 0.064087968 0.026335111 0.006571178 -0.0003435009 -0.025620900
## 4 0.066904716 0.027335311 0.007431411 0.0018294658 -0.026042154
## 5 0.089105769 0.028353615 0.004662546 0.0093648889 -0.046241011
## 6 0.085874774 0.040562623 0.018010743 0.0141045790 -0.014557152
## 7 0.039207763 0.035764057 0.029015344 0.0184729113 0.024793504
## 8 0.053279132 0.042461257 0.032035337 0.0218926164 0.025464411
## 9 -0.033060602 -0.003190585 0.017899744 0.0234560082 0.014282309
## 10 -0.084420591 -0.050967442 -0.003856993 0.0368769932 -0.037149802
## 11 0.106040310 0.101514352 0.077230732 0.0462073335 0.106281900
## 12 0.101514352 0.114750680 0.095942043 0.0619643954 0.143239768
## 13 0.077230732 0.095942043 0.091683721 0.0756649826 0.128514663
## 14 0.046207333 0.061964395 0.075664983 0.0880481627 0.086500371
## 15 0.106281900 0.143239768 0.128514663 0.0865003706 0.206032902
## 16 0.125216272 0.173567248 0.150564599 0.0894698349 0.254842212
## 17 0.073269959 0.104338526 0.108858719 0.0990966944 0.155041405
## 18 -0.009794207 -0.008602231 0.040229186 0.1145301521 -0.009600218
## 19 -0.038180509 -0.047746966 0.016497447 0.1203431265 -0.067026142
## 20 0.034756518 0.053873849 0.080692757 0.1116294736 0.083768255
## 16 17 18 19 20
## 1 0.02628625 -0.0176911227 -0.0921292286 -0.119855019 -0.061805013
## 2 -0.03077104 -0.0299553960 -0.0272142641 -0.026561243 -0.036400965
## 3 -0.04299377 -0.0285022289 -0.0020354579 0.007444515 -0.022817615
## 4 -0.04477697 -0.0269844107 0.0052839791 0.016957576 -0.018205037
## 5 -0.07976071 -0.0311312682 0.0551597027 0.087025351 0.004600860
## 6 -0.03520355 -0.0116950377 0.0317151280 0.048066320 0.004440934
## 7 0.02647532 0.0120621962 -0.0128267780 -0.022407760 -0.004305189
## 8 0.02429140 0.0149080589 -0.0002983217 -0.005951287 0.003867258
## 9 0.01925544 0.0124682731 -0.0058173989 -0.015044132 -0.001559847
## 10 -0.05308553 -0.0006357297 0.0767548162 0.100687469 0.031236382
## 11 0.12521627 0.0732699589 -0.0097942070 -0.038180509 0.034756518
## 12 0.17356725 0.1043385263 -0.0086022314 -0.047746966 0.053873849
## 13 0.15056460 0.1088587194 0.0402291862 0.016497447 0.080692757
## 14 0.08946983 0.0990966944 0.1145301521 0.120343127 0.111629474
## 15 0.25484221 0.1550414048 -0.0096002178 -0.067026142 0.083768255
## 16 0.32181689 0.1809499348 -0.0516324790 -0.132991790 0.078480442
## 17 0.18094993 0.1411061996 0.0749555993 0.052223132 0.117316497
## 18 -0.05163248 0.0749555993 0.2832180812 0.357219742 0.180884198
## 19 -0.13299179 0.0522231316 0.3572197419 0.465350583 0.203949588
## 20 0.07848044 0.1173164966 0.1808841976 0.203949588 0.155596657#Matriz M
Matriz_M<-diag(20)-Matriz_p
print(Matriz_M)## 1 2 3 4 5
## 1 0.80507206 -0.129448747 -0.1012983510 -0.092222560 -0.031583117
## 2 -0.12944875 0.862520119 -0.1352118632 -0.133755179 -0.138339500
## 3 -0.10129835 -0.135211863 0.8575691868 -0.143837474 -0.171822738
## 4 -0.09222256 -0.133755179 -0.1438374739 0.853877096 -0.181113490
## 5 -0.03158312 -0.138339500 -0.1718227379 -0.181113490 0.724842053
## 6 -0.04845183 -0.122478435 -0.1453434456 -0.151680036 -0.217751268
## 7 -0.12225213 -0.090334996 -0.0762932951 -0.071686958 -0.041210326
## 8 -0.09795532 -0.090860961 -0.0860116614 -0.084236925 -0.077100906
## 9 -0.18430451 -0.063577632 -0.0173350340 -0.002773537 0.113481154
## 10 -0.16845776 -0.046005757 0.0017099765 0.017162955 0.141737883
## 11 -0.03992843 -0.056549983 -0.0640879679 -0.066904716 -0.089105769
## 12 -0.03456129 -0.025943096 -0.0263351113 -0.027335311 -0.028353615
## 13 -0.01605385 -0.006297985 -0.0065711781 -0.007431411 -0.004662546
## 14 0.01304726 0.006061232 0.0003435009 -0.001829466 -0.009364889
## 15 -0.01679555 0.019319870 0.0256209003 0.026042154 0.046241011
## 16 -0.02628625 0.030771044 0.0429937680 0.044776966 0.079760709
## 17 0.01769112 0.029955396 0.0285022289 0.026984411 0.031131268
## 18 0.09212923 0.027214264 0.0020354579 -0.005283979 -0.055159703
## 19 0.11985502 0.026561243 -0.0074445151 -0.016957576 -0.087025351
## 20 0.06180501 0.036400965 0.0228176153 0.018205037 -0.004600860
## 6 7 8 9 10
## 1 -0.048451827 -0.122252134 -0.0979553187 -0.184304513 -0.1684577587
## 2 -0.122478435 -0.090334996 -0.0908609607 -0.063577632 -0.0460057569
## 3 -0.145343446 -0.076293295 -0.0860116614 -0.017335034 0.0017099765
## 4 -0.151680036 -0.071686958 -0.0842369246 -0.002773537 0.0171629547
## 5 -0.217751268 -0.041210326 -0.0771009064 0.113481154 0.1417378825
## 6 0.822889513 -0.048648977 -0.0745958102 0.068851138 0.0985285085
## 7 -0.048648977 0.913282218 -0.0738494117 -0.122530517 -0.1202242411
## 8 -0.074595810 -0.073849412 0.9291672332 -0.071652089 -0.0609542837
## 9 0.068851138 -0.122530517 -0.0716520890 0.680506330 -0.3719760955
## 10 0.098528508 -0.120224241 -0.0609542837 -0.371976096 0.5239183825
## 11 -0.085874774 -0.039207763 -0.0532791324 0.033060602 0.0844205911
## 12 -0.040562623 -0.035764057 -0.0424612571 0.003190585 0.0509674423
## 13 -0.018010743 -0.029015344 -0.0320353374 -0.017899744 0.0038569927
## 14 -0.014104579 -0.018472911 -0.0218926164 -0.023456008 -0.0368769932
## 15 0.014557152 -0.024793504 -0.0254644114 -0.014282309 0.0371498019
## 16 0.035203551 -0.026475315 -0.0242914042 -0.019255435 0.0530855339
## 17 0.011695038 -0.012062196 -0.0149080589 -0.012468273 0.0006357297
## 18 -0.031715128 0.012826778 0.0002983217 0.005817399 -0.0767548162
## 19 -0.048066320 0.022407760 0.0059512870 0.015044132 -0.1006874688
## 20 -0.004440934 0.004305189 -0.0038672579 0.001559847 -0.0312363820
## 11 12 13 14 15
## 1 -0.039928428 -0.034561293 -0.016053855 0.0130472561 -0.016795550
## 2 -0.056549983 -0.025943096 -0.006297985 0.0060612321 0.019319870
## 3 -0.064087968 -0.026335111 -0.006571178 0.0003435009 0.025620900
## 4 -0.066904716 -0.027335311 -0.007431411 -0.0018294658 0.026042154
## 5 -0.089105769 -0.028353615 -0.004662546 -0.0093648889 0.046241011
## 6 -0.085874774 -0.040562623 -0.018010743 -0.0141045790 0.014557152
## 7 -0.039207763 -0.035764057 -0.029015344 -0.0184729113 -0.024793504
## 8 -0.053279132 -0.042461257 -0.032035337 -0.0218926164 -0.025464411
## 9 0.033060602 0.003190585 -0.017899744 -0.0234560082 -0.014282309
## 10 0.084420591 0.050967442 0.003856993 -0.0368769932 0.037149802
## 11 0.893959690 -0.101514352 -0.077230732 -0.0462073335 -0.106281900
## 12 -0.101514352 0.885249320 -0.095942043 -0.0619643954 -0.143239768
## 13 -0.077230732 -0.095942043 0.908316279 -0.0756649826 -0.128514663
## 14 -0.046207333 -0.061964395 -0.075664983 0.9119518373 -0.086500371
## 15 -0.106281900 -0.143239768 -0.128514663 -0.0865003706 0.793967098
## 16 -0.125216272 -0.173567248 -0.150564599 -0.0894698349 -0.254842212
## 17 -0.073269959 -0.104338526 -0.108858719 -0.0990966944 -0.155041405
## 18 0.009794207 0.008602231 -0.040229186 -0.1145301521 0.009600218
## 19 0.038180509 0.047746966 -0.016497447 -0.1203431265 0.067026142
## 20 -0.034756518 -0.053873849 -0.080692757 -0.1116294736 -0.083768255
## 16 17 18 19 20
## 1 -0.02628625 0.0176911227 0.0921292286 0.119855019 0.061805013
## 2 0.03077104 0.0299553960 0.0272142641 0.026561243 0.036400965
## 3 0.04299377 0.0285022289 0.0020354579 -0.007444515 0.022817615
## 4 0.04477697 0.0269844107 -0.0052839791 -0.016957576 0.018205037
## 5 0.07976071 0.0311312682 -0.0551597027 -0.087025351 -0.004600860
## 6 0.03520355 0.0116950377 -0.0317151280 -0.048066320 -0.004440934
## 7 -0.02647532 -0.0120621962 0.0128267780 0.022407760 0.004305189
## 8 -0.02429140 -0.0149080589 0.0002983217 0.005951287 -0.003867258
## 9 -0.01925544 -0.0124682731 0.0058173989 0.015044132 0.001559847
## 10 0.05308553 0.0006357297 -0.0767548162 -0.100687469 -0.031236382
## 11 -0.12521627 -0.0732699589 0.0097942070 0.038180509 -0.034756518
## 12 -0.17356725 -0.1043385263 0.0086022314 0.047746966 -0.053873849
## 13 -0.15056460 -0.1088587194 -0.0402291862 -0.016497447 -0.080692757
## 14 -0.08946983 -0.0990966944 -0.1145301521 -0.120343127 -0.111629474
## 15 -0.25484221 -0.1550414048 0.0096002178 0.067026142 -0.083768255
## 16 0.67818311 -0.1809499348 0.0516324790 0.132991790 -0.078480442
## 17 -0.18094993 0.8588938004 -0.0749555993 -0.052223132 -0.117316497
## 18 0.05163248 -0.0749555993 0.7167819188 -0.357219742 -0.180884198
## 19 0.13299179 -0.0522231316 -0.3572197419 0.534649417 -0.203949588
## 20 -0.07848044 -0.1173164966 -0.1808841976 -0.203949588 0.844403343Vector de coeficientes estimados
options(scipen = 999)
Ejercicio$coefficients## (Intercept) X1 X2 X1:X2
## 305.7353274 2.3391170 -24.9673923 0.2843544Matriz de varianza-covarianza
var_covar<-vcov(Ejercicio)
print(var_covar)## (Intercept) X1 X2 X1:X2
## (Intercept) 4889.347295 -29.91920102 -691.1337600 4.322975022
## X1 -29.919201 0.21727017 4.3932767 -0.031715864
## X2 -691.133760 4.39327667 126.3393908 -0.789361391
## X1:X2 4.322975 -0.03171586 -0.7893614 0.005634356Intervalo de confianza
confint(object = Ejercicio,level = .95)## 2.5 % 97.5 %
## (Intercept) 157.5033494 453.9673054
## X1 1.3509814 3.3272525
## X2 -48.7952967 -1.1394879
## X1:X2 0.1252294 0.4434795Valores ajustados
plot(Ejercicio$fitted.values,main = "Valores Ajustados",ylab = "Y",xlab = "casos")
# Residuos del modelo
plot(Ejercicio$residuals,main = "Residuos",ylab = "Residuos",xlab = "casos")
library(dplyr)
Ejercicio$residuals %>% matrix()## [,1]
## [1,] -23.143607
## [2,] 70.764175
## [3,] -42.876610
## [4,] 44.407254
## [5,] -39.648685
## [6,] 6.087808
## [7,] 6.076630
## [8,] 64.745346
## [9,] 6.087450
## [10,] -26.598918
## [11,] -3.742989
## [12,] -105.967693
## [13,] -14.361853
## [14,] -111.096309
## [15,] -29.872373
## [16,] 99.010200
## [17,] 69.618669
## [18,] -71.856927
## [19,] 98.872286
## [20,] 3.496145