numeral 1
load("C:/Users/gusta_000/Desktop/Econometria/Guia/datos_cajas.RData")
modelo_cajas <- lm(formula = Tiempo ~ Distancia + N_cajas, data = datos_cajas)
summary(modelo_cajas)##
## Call:
## lm(formula = Tiempo ~ Distancia + N_cajas, data = datos_cajas)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.2716 -0.5405 0.5212 1.4051 2.9381
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.3112 5.8573 0.395 0.70007
## Distancia 0.4559 0.1468 3.107 0.00908 **
## N_cajas 0.8772 0.1530 5.732 9.43e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.141 on 12 degrees of freedom
## Multiple R-squared: 0.7368, Adjusted R-squared: 0.6929
## F-statistic: 16.8 on 2 and 12 DF, p-value: 0.0003325numeral 2
matriz_x <- model.matrix(modelo_cajas)
matriz_xx <- t(matriz_x)%*%matriz_x
#Calculando Matriz A
matriz_A <- solve(matriz_xx)%*%t(matriz_x)
print(matriz_A)## 1 2 3 4 5
## (Intercept) 0.459747079 0.505626389 -0.317731768 0.707001469 0.053149816
## Distancia -0.003015297 -0.009318829 0.018819615 -0.019989342 -0.006641453
## N_cajas -0.017147338 -0.009890695 -0.007919488 -0.004479623 0.011082085
## 6 7 8 9 10
## (Intercept) -0.166576988 0.633594572 -0.125532551 0.1260628274 -0.90735239
## Distancia 0.006550474 -0.009903692 0.009409808 0.0003379213 0.02334256
## N_cajas 0.002768355 -0.016090251 -0.003959744 -0.0038254420 0.01780152
## 11 12 13 14 15
## (Intercept) 0.277217608 0.368482344 0.487274665 -0.3674581822 -0.73350489
## Distancia -0.011931220 -0.007473259 -0.006797416 0.0001559637 0.01645417
## N_cajas 0.006862401 -0.005142468 -0.012793352 0.0238754370 0.01885861#Calculando Matriz P
matriz_P <- matriz_x%*%matriz_A
print(matriz_P)## 1 2 3 4 5 6
## 1 0.19781478 0.127154573 0.16766180 0.062524965 -0.03527291 0.057620774
## 2 0.12715457 0.124295239 0.03396629 0.140073563 0.05334477 0.038710181
## 3 0.16766180 0.033966286 0.35585795 -0.137368460 -0.10168744 0.123125512
## 4 0.06252497 0.140073563 -0.13736846 0.257600846 0.15524536 0.006698639
## 5 -0.03527291 0.053344771 -0.10168744 0.155245361 0.18408997 0.046742309
## 6 0.05762077 0.038710181 0.12312551 0.006698639 0.04674231 0.086318088
## 7 0.17558129 0.144648497 0.07654437 0.133523089 0.01345706 0.036955589
## 8 0.11716423 0.050316476 0.21126231 -0.035350897 -0.01751039 0.094896089
## 9 0.09794605 0.077129229 0.10132526 0.055636570 0.03786105 0.067680430
## 10 -0.02906036 -0.056765574 0.20436525 -0.131155907 0.05122193 0.136694350
## 11 -0.01209498 0.081873124 -0.13140718 0.199703669 0.18629079 0.030873007
## 12 0.09285990 0.104513848 0.01812731 0.131114317 0.07550894 0.044246890
## 13 0.15541865 0.125438973 0.08744449 0.109054124 0.01789770 0.046274418
## 14 -0.12402490 -0.005427535 -0.12246527 0.112857904 0.23285894 0.067134558
## 15 -0.05129385 -0.039271650 0.11324781 -0.060157783 0.09995191 0.116029165
## 7 8 9 10 11 12
## 1 0.17558129 0.11716423 0.09794605 -0.02906036 -0.01209498 0.092859897
## 2 0.14464850 0.05031648 0.07712923 -0.05676557 0.08187312 0.104513848
## 3 0.07654437 0.21126231 0.10132526 0.20436525 -0.13140718 0.018127310
## 4 0.13352309 -0.03535090 0.05563657 -0.13115591 0.19970367 0.131114317
## 5 0.01345706 -0.01751039 0.03786105 0.05122193 0.18629079 0.075508940
## 6 0.03695559 0.09489609 0.06768043 0.13669435 0.03087301 0.044246890
## 7 0.18301556 0.07160552 0.08894348 -0.08682757 0.04935470 0.112467995
## 8 0.07160552 0.13896449 0.08399596 0.13551596 -0.03237026 0.042396988
## 9 0.08894348 0.08399596 0.07465547 0.05440619 0.04101064 0.069478345
## 10 -0.08682757 0.13551596 0.05440619 0.34795579 -0.01326471 -0.021162536
## 11 0.04935470 -0.03237026 0.04101064 -0.01326471 0.20329083 0.095597926
## 12 0.11246799 0.04239699 0.06947834 -0.02116254 0.09559793 0.094228911
## 13 0.15702161 0.07705558 0.08545596 -0.04568349 0.04428588 0.099852268
## 14 -0.07689788 -0.02789930 0.01907176 0.16357209 0.20867158 0.042323339
## 15 -0.07939330 0.08995724 0.04540362 0.29018859 0.04818497 -0.001554438
## 13 14 15
## 1 0.15541865 -0.124024902 -0.051293849
## 2 0.12543897 -0.005427535 -0.039271650
## 3 0.08744449 -0.122465266 0.113247813
## 4 0.10905412 0.112857904 -0.060157783
## 5 0.01789770 0.232858944 0.099951911
## 6 0.04627442 0.067134558 0.116029165
## 7 0.15702161 -0.076897883 -0.079393301
## 8 0.07705558 -0.027899299 0.089957240
## 9 0.08545596 0.019071756 0.045403621
## 10 -0.04568349 0.163572088 0.290188586
## 11 0.04428588 0.208671580 0.048184973
## 12 0.09985227 0.042323339 -0.001554438
## 13 0.13743085 -0.052866482 -0.044080529
## 14 -0.05286648 0.352392093 0.210699107
## 15 -0.04408053 0.210699107 0.262089133#Calculando Matriz M
n <- nrow(matriz_x)
matriz_M <- diag(n)-matriz_P
print(matriz_M)## 1 2 3 4 5 6
## 1 0.80218522 -0.127154573 -0.16766180 -0.062524965 0.03527291 -0.057620774
## 2 -0.12715457 0.875704761 -0.03396629 -0.140073563 -0.05334477 -0.038710181
## 3 -0.16766180 -0.033966286 0.64414205 0.137368460 0.10168744 -0.123125512
## 4 -0.06252497 -0.140073563 0.13736846 0.742399154 -0.15524536 -0.006698639
## 5 0.03527291 -0.053344771 0.10168744 -0.155245361 0.81591003 -0.046742309
## 6 -0.05762077 -0.038710181 -0.12312551 -0.006698639 -0.04674231 0.913681912
## 7 -0.17558129 -0.144648497 -0.07654437 -0.133523089 -0.01345706 -0.036955589
## 8 -0.11716423 -0.050316476 -0.21126231 0.035350897 0.01751039 -0.094896089
## 9 -0.09794605 -0.077129229 -0.10132526 -0.055636570 -0.03786105 -0.067680430
## 10 0.02906036 0.056765574 -0.20436525 0.131155907 -0.05122193 -0.136694350
## 11 0.01209498 -0.081873124 0.13140718 -0.199703669 -0.18629079 -0.030873007
## 12 -0.09285990 -0.104513848 -0.01812731 -0.131114317 -0.07550894 -0.044246890
## 13 -0.15541865 -0.125438973 -0.08744449 -0.109054124 -0.01789770 -0.046274418
## 14 0.12402490 0.005427535 0.12246527 -0.112857904 -0.23285894 -0.067134558
## 15 0.05129385 0.039271650 -0.11324781 0.060157783 -0.09995191 -0.116029165
## 7 8 9 10 11 12
## 1 -0.17558129 -0.11716423 -0.09794605 0.02906036 0.01209498 -0.092859897
## 2 -0.14464850 -0.05031648 -0.07712923 0.05676557 -0.08187312 -0.104513848
## 3 -0.07654437 -0.21126231 -0.10132526 -0.20436525 0.13140718 -0.018127310
## 4 -0.13352309 0.03535090 -0.05563657 0.13115591 -0.19970367 -0.131114317
## 5 -0.01345706 0.01751039 -0.03786105 -0.05122193 -0.18629079 -0.075508940
## 6 -0.03695559 -0.09489609 -0.06768043 -0.13669435 -0.03087301 -0.044246890
## 7 0.81698444 -0.07160552 -0.08894348 0.08682757 -0.04935470 -0.112467995
## 8 -0.07160552 0.86103551 -0.08399596 -0.13551596 0.03237026 -0.042396988
## 9 -0.08894348 -0.08399596 0.92534453 -0.05440619 -0.04101064 -0.069478345
## 10 0.08682757 -0.13551596 -0.05440619 0.65204421 0.01326471 0.021162536
## 11 -0.04935470 0.03237026 -0.04101064 0.01326471 0.79670917 -0.095597926
## 12 -0.11246799 -0.04239699 -0.06947834 0.02116254 -0.09559793 0.905771089
## 13 -0.15702161 -0.07705558 -0.08545596 0.04568349 -0.04428588 -0.099852268
## 14 0.07689788 0.02789930 -0.01907176 -0.16357209 -0.20867158 -0.042323339
## 15 0.07939330 -0.08995724 -0.04540362 -0.29018859 -0.04818497 0.001554438
## 13 14 15
## 1 -0.15541865 0.124024902 0.051293849
## 2 -0.12543897 0.005427535 0.039271650
## 3 -0.08744449 0.122465266 -0.113247813
## 4 -0.10905412 -0.112857904 0.060157783
## 5 -0.01789770 -0.232858944 -0.099951911
## 6 -0.04627442 -0.067134558 -0.116029165
## 7 -0.15702161 0.076897883 0.079393301
## 8 -0.07705558 0.027899299 -0.089957240
## 9 -0.08545596 -0.019071756 -0.045403621
## 10 0.04568349 -0.163572088 -0.290188586
## 11 -0.04428588 -0.208671580 -0.048184973
## 12 -0.09985227 -0.042323339 0.001554438
## 13 0.86256915 0.052866482 0.044080529
## 14 0.05286648 0.647607907 -0.210699107
## 15 0.04408053 -0.210699107 0.737910867numeral 3
library(magrittr)
residuos_modelo_cajas <- modelo_cajas$residuals
residuos_matrices <- matriz_M%*%datos_cajas$Tiempo
cbind(residuos_matrices,residuos_modelo_cajas,residuos_matrices-residuos_modelo_cajas)%>%round(digits = 2)%>%as.data.frame() -> comparacion
names(comparacion) <- c("Por matrices", "en el modelo", "Diferencia")
print(comparacion)## Por matrices en el modelo Diferencia
## 1 -0.76 -0.76 0
## 2 0.13 0.13 0
## 3 -0.32 -0.32 0
## 4 2.94 2.94 0
## 5 -9.27 -9.27 0
## 6 0.77 0.77 0
## 7 1.31 1.31 0
## 8 -2.09 -2.09 0
## 9 1.43 1.43 0
## 10 0.52 0.52 0
## 11 0.52 0.52 0
## 12 1.38 1.38 0
## 13 -1.02 -1.02 0
## 14 2.89 2.89 0
## 15 1.59 1.59 0numeral 4
options(scipen = 999999)
descomposicion <- eigen(x = matriz_xx,symmetric = TRUE)
auto_valores <- descomposicion$values
print(auto_valores)## [1] 16976.7781334 709.9345923 0.2872743print(auto_valores>0)## [1] TRUE TRUE TRUE