library(stargazer)
load("C:/Users/familia/Downloads/datos_cajas.RData")
Modelo_cajas<- lm(formula = N_cajas~Distancia+Tiempo, data = datos_cajas)
#Usando stargazer
stargazer(Modelo_cajas, title = "Modelo Regresion", type = "text")
##
## Modelo Regresion
## ===============================================
## Dependent variable:
## ---------------------------
## N_cajas
## -----------------------------------------------
## Distancia -0.485***
## (0.132)
##
## Tiempo 0.835***
## (0.146)
##
## Constant 5.797
## (5.503)
##
## -----------------------------------------------
## Observations 15
## R2 0.776
## Adjusted R2 0.739
## Residual Std. Error 3.064 (df = 12)
## F Statistic 20.837*** (df = 2; 12)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
Matrices A & P & M
mat_x<- model.matrix(Modelo_cajas)
# Matriz X'X
mat_xx<- t(mat_x)%*%mat_x
print(mat_xx)
## (Intercept) Distancia Tiempo
## (Intercept) 15 420 463
## Distancia 420 12308 13027
## Tiempo 463 13027 14741
# Matriz A
solve(mat_xx)%*%t(mat_x)->mat_A
print(mat_A)
## 1 2 3 4 5
## (Intercept) 0.407886073 0.439998867 -0.343641239 0.497453174 0.696698048
## Distancia 0.005493401 -0.004559460 0.022741213 -0.018581503 -0.009603898
## Tiempo -0.016037839 -0.007958985 -0.007336265 0.002899425 -0.011699424
## 6 7 8 9 10
## (Intercept) -0.198363444 0.458569098 -0.01768880 1.442399e-02 -0.83672576
## Distancia 0.005009797 -0.002444964 0.01187291 1.820045e-03 0.01457905
## Tiempo 0.004041764 -0.010478730 -0.00803734 4.151462e-05 0.01604251
## 11 12 13 14 15
## (Intercept) 0.284665737 0.25255294 0.4771393294 -0.40940727 -0.723560756
## Distancia -0.015391751 -0.00533889 -0.0003304674 -0.01216598 0.006900499
## Tiempo 0.006899675 -0.00117918 -0.0129984744 0.02645966 0.019341688
# Matriz P
mat_x%*%mat_A -> mat_P
print(mat_P)
## 1 2 3 4 5 6
## 1 0.187779966 0.1121994417 0.162524782 0.0095942757 0.12779492 0.04893281
## 2 0.112199442 0.1111197867 0.026809921 0.1112000666 0.14071614 0.03600912
## 3 0.162524782 0.0268099205 0.353255585 -0.1617236320 -0.02674119 0.11923961
## 4 0.009594276 0.1112000666 -0.161723632 0.2528682890 0.16114573 0.01710760
## 5 0.127794917 0.1407161354 -0.026741188 0.1611457265 0.19292668 0.01289620
## 6 0.048932813 0.0360091200 0.119239606 0.0171075968 0.01289620 0.09031849
## 7 0.133730682 0.1145193116 0.056887399 0.0897191385 0.14281166 0.03697715
## 8 0.145602214 0.0621256639 0.224144572 -0.0531340375 0.04258163 0.08513906
## 9 0.070021689 0.0610460089 0.088429711 0.0484717534 0.05550285 0.07221537
## 10 -0.014333815 -0.0391015467 0.211669292 -0.0769848730 -0.11492374 0.14462786
## 11 -0.011494600 0.0861631777 -0.130913737 0.2215041324 0.11853908 0.03521072
## 12 0.064085924 0.0872428327 0.004801124 0.1198983414 0.10561786 0.04813441
## 13 0.155261923 0.1179188364 0.086964877 0.0682382103 0.14490719 0.03794519
## 14 -0.139354951 0.0008539365 -0.128716486 0.1918544470 -0.01556743 0.08661599
## 15 -0.052345260 -0.0288226922 0.113368174 0.0002405648 -0.08820757 0.12863043
## 7 8 9 10 11 12
## 1 0.13373068 0.14560221 0.07002169 -0.014333815 -0.01149460 0.064085924
## 2 0.11451931 0.06212566 0.06104601 -0.039101547 0.08616318 0.087242833
## 3 0.05688740 0.22414457 0.08842971 0.211669292 -0.13091374 0.004801124
## 4 0.08971914 -0.05313404 0.04847175 -0.076984873 0.22150413 0.119898341
## 5 0.14281166 0.04258163 0.05550285 -0.114923735 0.11853908 0.105617863
## 6 0.03697715 0.08513906 0.07221537 0.144627857 0.03521072 0.048134413
## 7 0.12255308 0.08203591 0.06282454 -0.040565006 0.06387175 0.083083123
## 8 0.08203591 0.16094448 0.07746793 0.108152454 -0.04546291 0.038013644
## 9 0.06282454 0.07746793 0.06849225 0.083384723 0.05219487 0.061170553
## 10 -0.04056501 0.10815245 0.08338472 0.328357261 -0.01574174 0.009025993
## 11 0.06387175 -0.04546291 0.05219487 -0.015741738 0.20451998 0.106862201
## 12 0.08308312 0.03801364 0.06117055 0.009025993 0.10686220 0.083705292
## 13 0.13058684 0.10194616 0.06460307 -0.042028465 0.04158033 0.078923413
## 14 -0.03777170 -0.08218025 0.05802864 0.172378043 0.22044180 0.080232911
## 15 -0.04126388 0.05262349 0.07614606 0.286083558 0.05272494 0.029202372
## 13 14 15
## 1 0.15526192 -0.1393549508 -0.0523452598
## 2 0.11791884 0.0008539365 -0.0288226922
## 3 0.08696488 -0.1287164862 0.1133681745
## 4 0.06823821 0.1918544470 0.0002405648
## 5 0.14490719 -0.0155674320 -0.0882075665
## 6 0.03794519 0.0866159895 0.1286304327
## 7 0.13058684 -0.0377717042 -0.0412638809
## 8 0.10194616 -0.0821802488 0.0526234902
## 9 0.06460307 0.0580286385 0.0761460578
## 10 -0.04202846 0.1723780426 0.2860835577
## 11 0.04158033 0.2204417980 0.0527249398
## 12 0.07892341 0.0802329108 0.0292023722
## 13 0.14325485 -0.0763973449 -0.0537050697
## 14 -0.07639734 0.4220807732 0.2475016310
## 15 -0.05370507 0.2475016310 0.2778232484
# Matriz M
diag(15)-mat_P-> mat_M
print(mat_M)
## 1 2 3 4 5
## 1 0.812220034 -0.1121994417 -0.162524782 -0.0095942757 -0.12779492
## 2 -0.112199442 0.8888802133 -0.026809921 -0.1112000666 -0.14071614
## 3 -0.162524782 -0.0268099205 0.646744415 0.1617236320 0.02674119
## 4 -0.009594276 -0.1112000666 0.161723632 0.7471317110 -0.16114573
## 5 -0.127794917 -0.1407161354 0.026741188 -0.1611457265 0.80707332
## 6 -0.048932813 -0.0360091200 -0.119239606 -0.0171075968 -0.01289620
## 7 -0.133730682 -0.1145193116 -0.056887399 -0.0897191385 -0.14281166
## 8 -0.145602214 -0.0621256639 -0.224144572 0.0531340375 -0.04258163
## 9 -0.070021689 -0.0610460089 -0.088429711 -0.0484717534 -0.05550285
## 10 0.014333815 0.0391015467 -0.211669292 0.0769848730 0.11492374
## 11 0.011494600 -0.0861631777 0.130913737 -0.2215041324 -0.11853908
## 12 -0.064085924 -0.0872428327 -0.004801124 -0.1198983414 -0.10561786
## 13 -0.155261923 -0.1179188364 -0.086964877 -0.0682382103 -0.14490719
## 14 0.139354951 -0.0008539365 0.128716486 -0.1918544470 0.01556743
## 15 0.052345260 0.0288226922 -0.113368174 -0.0002405648 0.08820757
## 6 7 8 9 10 11
## 1 -0.04893281 -0.13373068 -0.14560221 -0.07002169 0.014333815 0.01149460
## 2 -0.03600912 -0.11451931 -0.06212566 -0.06104601 0.039101547 -0.08616318
## 3 -0.11923961 -0.05688740 -0.22414457 -0.08842971 -0.211669292 0.13091374
## 4 -0.01710760 -0.08971914 0.05313404 -0.04847175 0.076984873 -0.22150413
## 5 -0.01289620 -0.14281166 -0.04258163 -0.05550285 0.114923735 -0.11853908
## 6 0.90968151 -0.03697715 -0.08513906 -0.07221537 -0.144627857 -0.03521072
## 7 -0.03697715 0.87744692 -0.08203591 -0.06282454 0.040565006 -0.06387175
## 8 -0.08513906 -0.08203591 0.83905552 -0.07746793 -0.108152454 0.04546291
## 9 -0.07221537 -0.06282454 -0.07746793 0.93150775 -0.083384723 -0.05219487
## 10 -0.14462786 0.04056501 -0.10815245 -0.08338472 0.671642739 0.01574174
## 11 -0.03521072 -0.06387175 0.04546291 -0.05219487 0.015741738 0.79548002
## 12 -0.04813441 -0.08308312 -0.03801364 -0.06117055 -0.009025993 -0.10686220
## 13 -0.03794519 -0.13058684 -0.10194616 -0.06460307 0.042028465 -0.04158033
## 14 -0.08661599 0.03777170 0.08218025 -0.05802864 -0.172378043 -0.22044180
## 15 -0.12863043 0.04126388 -0.05262349 -0.07614606 -0.286083558 -0.05272494
## 12 13 14 15
## 1 -0.064085924 -0.15526192 0.1393549508 0.0523452598
## 2 -0.087242833 -0.11791884 -0.0008539365 0.0288226922
## 3 -0.004801124 -0.08696488 0.1287164862 -0.1133681745
## 4 -0.119898341 -0.06823821 -0.1918544470 -0.0002405648
## 5 -0.105617863 -0.14490719 0.0155674320 0.0882075665
## 6 -0.048134413 -0.03794519 -0.0866159895 -0.1286304327
## 7 -0.083083123 -0.13058684 0.0377717042 0.0412638809
## 8 -0.038013644 -0.10194616 0.0821802488 -0.0526234902
## 9 -0.061170553 -0.06460307 -0.0580286385 -0.0761460578
## 10 -0.009025993 0.04202846 -0.1723780426 -0.2860835577
## 11 -0.106862201 -0.04158033 -0.2204417980 -0.0527249398
## 12 0.916294708 -0.07892341 -0.0802329108 -0.0292023722
## 13 -0.078923413 0.85674515 0.0763973449 0.0537050697
## 14 -0.080232911 0.07639734 0.5779192268 -0.2475016310
## 15 -0.029202372 0.05370507 -0.2475016310 0.7221767516
Matriz de varianza-covarianza de los parametros V[β]
options(scipen = 999)
var_covar<- vcov(Modelo_cajas)
print(var_covar)
## (Intercept) Distancia Tiempo
## (Intercept) 30.2813878 -0.412337558 -0.586714685
## Distancia -0.4123376 0.017415769 -0.002439653
## Tiempo -0.5867147 -0.002439653 0.021221112
Intervalo de confianza
confint(object = Modelo_cajas, level = .95)
## 2.5 % 97.5 %
## (Intercept) -6.1927659 17.7866062
## Distancia -0.7722180 -0.1971473
## Tiempo 0.5176192 1.1524149
library(dplyr)
Modelo_cajas$fitted.values %>% as.matrix()
## [,1]
## 1 11.29685
## 2 16.22532
## 3 10.62511
## 4 22.95816
## 5 16.00933
## 6 18.32732
## 7 14.90562
## 8 12.69819
## 9 17.62665
## 10 20.42933
## 11 23.65883
## 12 18.73037
## 13 13.58592
## 14 29.71994
## 15 23.20308
library(dplyr)
Modelo_cajas$residuals %>% matrix()
## [,1]
## [1,] -1.2968510
## [2,] -1.2253152
## [3,] -0.6251101
## [4,] -2.9581618
## [5,] 8.9906710
## [6,] -0.3273219
## [7,] -2.9056156
## [8,] 1.3018113
## [9,] -1.6266530
## [10,] 1.5706715
## [11,] 0.3411693
## [12,] -1.7303664
## [13,] -0.5859159
## [14,] 0.2800637
## [15,] 0.7969240