library(readr)
library(dplyr)
archivo<-"C:/Users/corte/Desktop/datos.csv"
datos<-read.csv(file = archivo)
Y<-datos%>%select(Y) %>% as.matrix()
X<-datos%>% mutate(Cte=1) %>% select("Cte","X") %>% as.matrix()Xt<-t(X)
print(Xt)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## Cte 1 1 1 1 1 1 1 1 1 1 1 1 1
## X 216 283 237 203 259 374 342 301 365 384 404 426 432
## [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
## Cte 1 1 1 1 1 1 1 1 1 1 1
## X 409 553 572 506 528 501 628 677 602 630 652XtX<-t(X)%*%X
print(XtX)## Cte X
## Cte 24 10484
## X 10484 5073858XtX_inv<-solve(XtX)
print(XtX_inv)## Cte X
## Cte 0.4278726796 -8.841038e-04
## X -0.0008841038 2.023893e-06XtY<-t(X)%*%Y
print(XtY)## Y
## Cte 316.0
## X 152715.7B<-XtX_inv%*%XtY
colnames(B)<-c("Parametros")
print(B)## Parametros
## Cte 0.19123503
## X 0.02970339Y_est<-X%*%B
print(Y_est)## Parametros
## [1,] 6.607168
## [2,] 8.597295
## [3,] 7.230939
## [4,] 6.221024
## [5,] 7.884413
## [6,] 11.300304
## [7,] 10.349795
## [8,] 9.131956
## [9,] 11.032973
## [10,] 11.597337
## [11,] 12.191405
## [12,] 12.844880
## [13,] 13.023100
## [14,] 12.339922
## [15,] 16.617211
## [16,] 17.181575
## [17,] 15.221151
## [18,] 15.874626
## [19,] 15.072634
## [20,] 18.844965
## [21,] 20.300431
## [22,] 18.072677
## [23,] 18.904372
## [24,] 19.557846E<-Y-Y_est
print(E)## Y
## [1,] -0.50716765
## [2,] 0.50270510
## [3,] -0.03093888
## [4,] 1.27897644
## [5,] -0.98441350
## [6,] 0.19969645
## [7,] -0.04979501
## [8,] 0.36804405
## [9,] -1.83297302
## [10,] -0.99733747
## [11,] 0.30859470
## [12,] 0.05512008
## [13,] 0.57689973
## [14,] 0.46007774
## [15,] -0.11721068
## [16,] -0.08157512
## [17,] -0.22115126
## [18,] 0.32537412
## [19,] 0.72736569
## [20,] 0.15503494
## [21,] -0.90043126
## [22,] 1.02732313
## [23,] -0.90437184
## [24,] 0.64215354A<-XtX_inv%*%Xt
print(A)## [,1] [,2] [,3] [,4] [,5]
## Cte 0.236906257 0.1776713023 0.2183400774 0.2483996068 0.1988897936
## X -0.000446943 -0.0003113422 -0.0004044412 -0.0004732536 -0.0003599156
## [,6] [,7] [,8] [,9] [,10]
## Cte 0.0972178559 0.1255091777 0.1617574338 0.105174790 0.088376818
## X -0.0001271679 -0.0001919325 -0.0002749121 -0.000145383 -0.000106929
## [,11] [,12] [,13] [,14] [,15]
## Cte 7.069474e-02 0.0512444579 4.593984e-02 6.627422e-02 -0.0610367256
## X -6.645114e-05 -0.0000219255 -9.782148e-06 -5.633168e-05 0.0002351089
## [,16] [,17] [,18] [,19] [,20]
## Cte -0.0778346979 -0.0194838466 -0.0389341304 -0.0150633276 -0.1273445111
## X 0.0002735628 0.0001399859 0.0001845116 0.0001298665 0.0003869008
## [,21] [,22] [,23] [,24]
## Cte -0.1706655976 -0.1043578121 -0.1291127187 -0.1485630024
## X 0.0004860716 0.0003342796 0.0003909486 0.0004354743P<-X%*%XtX_inv%*%Xt
head(P,n=10)## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.14036657 0.11042139 0.13098077 0.14617683 0.12114803 0.06974958
## [2,] 0.11042139 0.08956147 0.10388321 0.11446884 0.09703368 0.06122933
## [3,] 0.13098077 0.10388321 0.12248751 0.13623851 0.11358980 0.06707906
## [4,] 0.14617683 0.11446884 0.13623851 0.15232913 0.12582693 0.07140277
## [5,] 0.12114803 0.09703368 0.11358980 0.12582693 0.10567166 0.06428136
## [6,] 0.06974958 0.06122933 0.06707906 0.07140277 0.06428136 0.04965705
## [7,] 0.08405176 0.07119228 0.08002118 0.08654688 0.07579866 0.05372643
## [8,] 0.10237642 0.08395731 0.09660327 0.10595028 0.09055520 0.05894031
## [9,] 0.07377207 0.06403141 0.07071903 0.07566205 0.06752060 0.05080156
## [10,] 0.06528015 0.05811591 0.06303464 0.06667023 0.06068221 0.04838537
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 0.08405176 0.10237642 0.07377207 0.06528015 0.05634129 0.04650855
## [2,] 0.07119228 0.08395731 0.06403141 0.05811591 0.05188907 0.04503954
## [3,] 0.08002118 0.09660327 0.07071903 0.06303464 0.05494582 0.04604811
## [4,] 0.08654688 0.10595028 0.07566205 0.06667023 0.05720516 0.04679358
## [5,] 0.07579866 0.09055520 0.06752060 0.06068221 0.05348390 0.04556575
## [6,] 0.05372643 0.05894031 0.05080156 0.04838537 0.04584201 0.04304432
## [7,] 0.05986826 0.06773750 0.05545382 0.05180710 0.04796845 0.04374594
## [8,] 0.06773750 0.07900889 0.06141452 0.05619119 0.05069295 0.04464488
## [9,] 0.05545382 0.06141452 0.05211001 0.04934773 0.04644007 0.04324165
## [10,] 0.05180710 0.05619119 0.04934773 0.04731608 0.04517750 0.04282506
## [,13] [,14] [,15] [,16] [,17]
## [1,] 0.04382689 0.05410658 -0.0102532092 -0.0187451258 0.010753111
## [2,] 0.04317149 0.05033236 0.0054990852 -0.0004164159 0.020132167
## [3,] 0.04362147 0.05292361 -0.0053159229 -0.0130003063 0.013692815
## [4,] 0.04395406 0.05483889 -0.0133096246 -0.0223014426 0.008933294
## [5,] 0.04340626 0.05168432 -0.0001435277 -0.0069819239 0.016772505
## [6,] 0.04228131 0.04520617 0.0268939925 0.0244778019 0.032870885
## [7,] 0.04259434 0.04700879 0.0193705086 0.0157237913 0.028391336
## [8,] 0.04299541 0.04931839 0.0097310449 0.0045077151 0.022651913
## [9,] 0.04236935 0.04571316 0.0247780127 0.0220157364 0.031611012
## [10,] 0.04218349 0.04464286 0.0292450813 0.0272134303 0.034270744
## [,18] [,19] [,20] [,21] [,22]
## [1,] 0.0009203652 0.01298783 -0.043773933 -0.065674138 -0.032153415
## [2,] 0.0132826393 0.02168888 -0.017851577 -0.033107343 -0.009756681
## [3,] 0.0047951078 0.01571502 -0.035649015 -0.055466635 -0.025133543
## [4,] -0.0014782850 0.01129956 -0.048803643 -0.071993069 -0.036499050
## [5,] 0.0088543620 0.01857208 -0.027137197 -0.044773061 -0.017779392
## [6,] 0.0300731907 0.03350672 0.017356398 0.011125170 0.020662764
## [7,] 0.0241688210 0.02935100 0.004975572 -0.004429121 0.009965816
## [8,] 0.0166038473 0.02402647 -0.010887362 -0.024358055 -0.003739648
## [9,] 0.0284125867 0.03233793 0.013874291 0.006750526 0.017654248
## [10,] 0.0319183062 0.03480539 0.021225406 0.015985885 0.024005560
## [,23] [,24]
## [1,] -0.044667818 -0.0545005640
## [2,] -0.018474261 -0.0253237891
## [3,] -0.036457898 -0.0453556047
## [4,] -0.049750150 -0.0601617293
## [5,] -0.027857028 -0.0357751712
## [6,] 0.017102062 0.0143043678
## [7,] 0.004591707 0.0003691918
## [8,] -0.011437186 -0.0174852526
## [9,] 0.013583525 0.0103850996
## [10,] 0.021011548 0.0186591104idem=diag(1,nrow = 24)
M=idem-P
head(M,n=10)## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.85963343 -0.11042139 -0.13098077 -0.14617683 -0.12114803
## [2,] -0.11042139 0.91043853 -0.10388321 -0.11446884 -0.09703368
## [3,] -0.13098077 -0.10388321 0.87751249 -0.13623851 -0.11358980
## [4,] -0.14617683 -0.11446884 -0.13623851 0.84767087 -0.12582693
## [5,] -0.12114803 -0.09703368 -0.11358980 -0.12582693 0.89432834
## [6,] -0.06974958 -0.06122933 -0.06707906 -0.07140277 -0.06428136
## [7,] -0.08405176 -0.07119228 -0.08002118 -0.08654688 -0.07579866
## [8,] -0.10237642 -0.08395731 -0.09660327 -0.10595028 -0.09055520
## [9,] -0.07377207 -0.06403141 -0.07071903 -0.07566205 -0.06752060
## [10,] -0.06528015 -0.05811591 -0.06303464 -0.06667023 -0.06068221
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.06974958 -0.08405176 -0.10237642 -0.07377207 -0.06528015
## [2,] -0.06122933 -0.07119228 -0.08395731 -0.06403141 -0.05811591
## [3,] -0.06707906 -0.08002118 -0.09660327 -0.07071903 -0.06303464
## [4,] -0.07140277 -0.08654688 -0.10595028 -0.07566205 -0.06667023
## [5,] -0.06428136 -0.07579866 -0.09055520 -0.06752060 -0.06068221
## [6,] 0.95034295 -0.05372643 -0.05894031 -0.05080156 -0.04838537
## [7,] -0.05372643 0.94013174 -0.06773750 -0.05545382 -0.05180710
## [8,] -0.05894031 -0.06773750 0.92099111 -0.06141452 -0.05619119
## [9,] -0.05080156 -0.05545382 -0.06141452 0.94788999 -0.04934773
## [10,] -0.04838537 -0.05180710 -0.05619119 -0.04934773 0.95268392
## [,11] [,12] [,13] [,14] [,15]
## [1,] -0.05634129 -0.04650855 -0.04382689 -0.05410658 0.0102532092
## [2,] -0.05188907 -0.04503954 -0.04317149 -0.05033236 -0.0054990852
## [3,] -0.05494582 -0.04604811 -0.04362147 -0.05292361 0.0053159229
## [4,] -0.05720516 -0.04679358 -0.04395406 -0.05483889 0.0133096246
## [5,] -0.05348390 -0.04556575 -0.04340626 -0.05168432 0.0001435277
## [6,] -0.04584201 -0.04304432 -0.04228131 -0.04520617 -0.0268939925
## [7,] -0.04796845 -0.04374594 -0.04259434 -0.04700879 -0.0193705086
## [8,] -0.05069295 -0.04464488 -0.04299541 -0.04931839 -0.0097310449
## [9,] -0.04644007 -0.04324165 -0.04236935 -0.04571316 -0.0247780127
## [10,] -0.04517750 -0.04282506 -0.04218349 -0.04464286 -0.0292450813
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.0187451258 -0.010753111 -0.0009203652 -0.01298783 0.043773933
## [2,] 0.0004164159 -0.020132167 -0.0132826393 -0.02168888 0.017851577
## [3,] 0.0130003063 -0.013692815 -0.0047951078 -0.01571502 0.035649015
## [4,] 0.0223014426 -0.008933294 0.0014782850 -0.01129956 0.048803643
## [5,] 0.0069819239 -0.016772505 -0.0088543620 -0.01857208 0.027137197
## [6,] -0.0244778019 -0.032870885 -0.0300731907 -0.03350672 -0.017356398
## [7,] -0.0157237913 -0.028391336 -0.0241688210 -0.02935100 -0.004975572
## [8,] -0.0045077151 -0.022651913 -0.0166038473 -0.02402647 0.010887362
## [9,] -0.0220157364 -0.031611012 -0.0284125867 -0.03233793 -0.013874291
## [10,] -0.0272134303 -0.034270744 -0.0319183062 -0.03480539 -0.021225406
## [,21] [,22] [,23] [,24]
## [1,] 0.065674138 0.032153415 0.044667818 0.0545005640
## [2,] 0.033107343 0.009756681 0.018474261 0.0253237891
## [3,] 0.055466635 0.025133543 0.036457898 0.0453556047
## [4,] 0.071993069 0.036499050 0.049750150 0.0601617293
## [5,] 0.044773061 0.017779392 0.027857028 0.0357751712
## [6,] -0.011125170 -0.020662764 -0.017102062 -0.0143043678
## [7,] 0.004429121 -0.009965816 -0.004591707 -0.0003691918
## [8,] 0.024358055 0.003739648 0.011437186 0.0174852526
## [9,] -0.006750526 -0.017654248 -0.013583525 -0.0103850996
## [10,] -0.015985885 -0.024005560 -0.021011548 -0.0186591104Residuos<-M%*%Y
print(Residuos)## Y
## [1,] -0.50716765
## [2,] 0.50270510
## [3,] -0.03093888
## [4,] 1.27897644
## [5,] -0.98441350
## [6,] 0.19969645
## [7,] -0.04979501
## [8,] 0.36804405
## [9,] -1.83297302
## [10,] -0.99733747
## [11,] 0.30859470
## [12,] 0.05512008
## [13,] 0.57689973
## [14,] 0.46007774
## [15,] -0.11721068
## [16,] -0.08157512
## [17,] -0.22115126
## [18,] 0.32537412
## [19,] 0.72736569
## [20,] 0.15503494
## [21,] -0.90043126
## [22,] 1.02732313
## [23,] -0.90437184
## [24,] 0.64215354library(normtest)
jb.norm.test(Residuos)##
## Jarque-Bera test for normality
##
## data: Residuos
## JB = 1.5606, p-value = 0.22Rechazar Ho si JB > V.c Rechazar Ho si p < a No se rechaza Ho JB < v.C Y P > a, Por lo tanto se concluye que los residuales siguen una distribucion normal.
library(nortest)
lillie.test(Residuos)##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: Residuos
## D = 0.14418, p-value = 0.2209Rechazar Ho si D > v.c Rechazar Ho si p < a D < V.C. por lo que la hipotesis nula no se rechaza, los residuales siguen una distribucion normal.
shapiro.test(Residuos)##
## Shapiro-Wilk normality test
##
## data: Residuos
## W = 0.95746, p-value = 0.3895Rechazar Ho si Wn > V.C Rechazar Ho si p < a Wn < V.C por lo que la hipotesis nula no se rechaza, los residuos siguen una distribucion normal.
d<-c(1,-0.8,0.68,0.74,-0.57,-0.75)
e<-c(-0.8,1,-0.71,-0.87,0.69,0.8)
f<-c(0.68,-0.71,1, 0.81,-0.77, -0.82)
g<-c(0.74,-0.87,0.81,1,-0.80,-0.84)
h<-c(-0.57,0.69,-0.77,-0.80,1,0.64)
i<-c(-0.75,0.8,-0.82,-0.84,0.64,1)
R<-cbind(d,e,f,g,h,i)
print(R)## d e f g h i
## [1,] 1.00 -0.80 0.68 0.74 -0.57 -0.75
## [2,] -0.80 1.00 -0.71 -0.87 0.69 0.80
## [3,] 0.68 -0.71 1.00 0.81 -0.77 -0.82
## [4,] 0.74 -0.87 0.81 1.00 -0.80 -0.84
## [5,] -0.57 0.69 -0.77 -0.80 1.00 0.64
## [6,] -0.75 0.80 -0.82 -0.84 0.64 1.00determinante_R<-det(R)
print(determinante_R)## [1] 0.001684439m<-ncol(R)
n<-nrow(R)
chi_FG<--(n-1-(2*m+5)/6)*log(determinante_R)
print(chi_FG)## [1] 13.83703gl<-m*(m-1)/2
VC<-qchisq(p = 0.95,df = gl)
print(VC)## [1] 24.99579Como el estadistico es menor al Valor Crítico, no se rechaza la Ho, por lo tanto no hay evidencia de colinealidad en los regresores.
library(psych)
FG_test<-cortest.bartlett(R)
print(FG_test)## $chisq
## [1] 614.1513
##
## $p.value
## [1] 3.491034e-121
##
## $df
## [1] 15Matriz de Correlación de los regresores del modelo (Como se obtuvo con anterioridad).
print(R)## d e f g h i
## [1,] 1.00 -0.80 0.68 0.74 -0.57 -0.75
## [2,] -0.80 1.00 -0.71 -0.87 0.69 0.80
## [3,] 0.68 -0.71 1.00 0.81 -0.77 -0.82
## [4,] 0.74 -0.87 0.81 1.00 -0.80 -0.84
## [5,] -0.57 0.69 -0.77 -0.80 1.00 0.64
## [6,] -0.75 0.80 -0.82 -0.84 0.64 1.00Inversa de la matriz de correlación \(R^{-1}\):
Inversa_R<-solve(R)
print(Inversa_R)## [,1] [,2] [,3] [,4] [,5] [,6]
## d 3.12989194 1.8066302 -0.5430948 0.01312674 -0.2872837 0.6516651
## e 1.80663016 5.5207504 -0.8728955 3.04065276 -0.4001754 -0.9671414
## f -0.54309484 -0.8728955 4.6100427 -0.68684569 1.7897206 2.3488587
## g 0.01312674 3.0406528 -0.6868457 7.70048852 2.2224574 2.0601470
## h -0.28728369 -0.4001754 1.7897206 2.22245739 3.5016734 1.1980416
## i 0.65166508 -0.9671414 2.3488587 2.06014702 1.1980416 5.1523030VIF´s para el modelo estimado:
VIFs<-diag(Inversa_R)
print(VIFs)## [1] 3.129892 5.520750 4.610043 7.700489 3.501673 5.152303