load("C:/Users/SANCHEZ/Desktop/GABRIEL2021/Universidad/Ciclo V/Econometria/datos_parcial.RData")
#a) Estime un modelo para explicar los ingresos usando todas las variables del datafrmae
modelo_ingresos<-lm(formula = income ~ sex+status+verbal+gamble,data = teengamb)
summary(modelo_ingresos)##
## Call:
## lm(formula = income ~ sex + status + verbal + gamble, data = teengamb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9561 -1.9072 -0.6399 1.1958 7.1716
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.41097 2.00311 2.202 0.0332 *
## sex 0.09035 1.07210 0.084 0.9332
## status -0.06279 0.03250 -1.932 0.0601 .
## verbal 0.24660 0.26492 0.931 0.3572
## gamble 0.07214 0.01491 4.839 1.79e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.736 on 42 degrees of freedom
## Multiple R-squared: 0.4581, Adjusted R-squared: 0.4065
## F-statistic: 8.877 on 4 and 42 DF, p-value: 2.743e-05#b) Calcule un intervalo de confianza de 92.5% para las variables "verbal" y "gamble" ¿hay evidencia que estas variables tienen una relación con los ingresos? Justifique
#Relación de "verbal"
confint(object = modelo_ingresos,parm = "verbal",level=.925)## 3.75 % 96.25 %
## verbal -0.2370767 0.730284#Relación de "gamble"
confint(object = modelo_ingresos,parm = "gamble",level=.925)## 3.75 % 96.25 %
## gamble 0.04492279 0.09936007#Hay evidencia de que hay una relación de que el aumento en una libra en la variable “gamble” en un 92.5% de las veces aumenta entre un 0.0449 y un 0.0099 libras de ingreso.
#¿Es el modelo estadíticamente significativo? #Respuesta: No, debido a que el modelo solo es capaz de explicar el 40% de las variaciones y hay variables que no tienen relación con la variable endógena, como se vio en el enunciado anterior con la variable “gamble”
#d) Calcule las matrices A, P y M
matriz_X<-model.matrix(modelo_ingresos)
matriz_XX<-t(matriz_X)%*%matriz_X
#Matriz A
matriz_A<-solve(matriz_XX)%*%t(matriz_X)
head(matriz_A, n=5)## 1 2 3 4
## (Intercept) -0.1074542196 -2.196091e-02 0.0166636550 0.1071925261
## sex 0.0809403937 2.485496e-02 0.0546438428 0.0478553863
## status 0.0012534153 -1.991280e-03 0.0004440685 0.0004276380
## verbal 0.0053215827 1.872697e-02 -0.0052703695 -0.0181905266
## gamble 0.0002006996 -7.513551e-05 -0.0001277504 -0.0001794904
## 5 6 7 8
## (Intercept) -0.1997769992 -0.0727522830 0.0110981773 0.0763090842
## sex 0.1347212618 0.1132679914 0.0302292619 0.0407941868
## status 0.0034635069 0.0038310373 -0.0013910482 -0.0003046734
## verbal -0.0012648221 -0.0192505672 0.0094674890 -0.0082880014
## gamble 0.0009505469 0.0001630467 -0.0001123584 -0.0001319919
## 9 10 11 12
## (Intercept) -9.132914e-03 0.0510438018 0.087083036 -0.0167374281
## sex 7.097846e-02 0.0044914027 0.008412608 0.0746863721
## status 1.310899e-03 -0.0028179758 -0.002235133 0.0013552721
## verbal -8.630958e-03 0.0151875447 0.005811670 -0.0083339400
## gamble -5.318337e-06 -0.0002723699 -0.000352645 0.0001045391
## 13 14 15 16
## (Intercept) 0.1122954976 0.0427185721 8.013897e-03 -0.0661198460
## sex 0.0466193386 0.0363050643 5.948747e-02 0.0526471984
## status 0.0006366292 -0.0007824209 6.139250e-04 -0.0005397676
## verbal -0.0198458906 0.0002642055 -5.660552e-03 0.0131714735
## gamble -0.0003366211 -0.0001287975 -4.449864e-05 0.0001457429
## 17 18 19 20
## (Intercept) -2.216644e-02 0.1060634947 -0.1023807059 0.0221131282
## sex 2.495517e-02 0.0206515598 0.0734580723 -0.0765340704
## status -1.990081e-03 -0.0015527499 0.0002687394 -0.0017679247
## verbal 1.873499e-02 -0.0028979217 0.0109476264 0.0186186633
## gamble -7.216639e-05 -0.0001864832 0.0004610514 -0.0007211633
## 21 22 23 24
## (Intercept) 0.0152089834 0.0345152010 0.1958013412 -0.0291030585
## sex -0.0447872567 -0.0850854939 -0.0802570127 0.0408815616
## status 0.0003787218 -0.0023178283 -0.0005639444 -0.0003685991
## verbal 0.0029117935 0.0210463644 -0.0142140679 -0.0017495613
## gamble -0.0006398261 -0.0007335052 -0.0011352375 0.0032214611
## 25 26 27 28
## (Intercept) -0.0592784672 0.1381978266 0.1725078240 0.172387314
## sex 0.0186606021 -0.0982876341 -0.0423970407 -0.093464504
## status 0.0026809592 -0.0024110128 0.0013201849 -0.001817377
## verbal -0.0086993474 0.0076124462 -0.0270967224 -0.001691181
## gamble 0.0005012544 -0.0009752689 -0.0006920167 -0.001028822
## 29 30 31 32
## (Intercept) 9.295843e-02 -0.0024663744 0.2161879565 0.0629101208
## sex -6.809038e-02 -0.0361688693 -0.0413678917 -0.0665863569
## status -5.950436e-04 0.0004818602 -0.0012880897 -0.0029267690
## verbal -8.492182e-05 0.0036021599 -0.0207144383 0.0163772489
## gamble -8.638989e-04 -0.0003844818 0.0009339733 0.0004460091
## 33 34 35 36 37
## (Intercept) -0.042460772 -0.0944339373 0.3669409465 -0.122887833 -0.0592784672
## sex -0.010199698 -0.0286789161 -0.0871197168 0.021921773 0.0186606021
## status -0.001356843 0.0005066856 -0.0001807799 0.001065153 0.0026809592
## verbal 0.014668633 0.0165785096 -0.0418510753 0.009033623 -0.0086993474
## gamble 0.001634588 -0.0003119579 -0.0012205537 0.001396874 0.0005012544
## 38 39 40 41
## (Intercept) 0.0981624593 1.178992e-01 2.680957e-02 0.0190830379
## sex -0.0635335936 -5.875763e-02 -5.578040e-03 -0.0769348096
## status -0.0025781024 5.256039e-05 2.255456e-03 -0.0021083954
## verbal 0.0084881599 -9.027311e-03 -1.566188e-02 0.0209210901
## gamble 0.0004605131 -7.838416e-04 -5.180903e-05 -0.0005522725
## 42 43 44 45
## (Intercept) -0.1583104849 -0.0583931945 -0.0348765429 0.0112423080
## sex 0.0176999260 -0.0007604938 -0.0393553283 0.0001342630
## status 0.0004787128 0.0023601921 0.0003553769 0.0019881420
## verbal 0.0183854152 -0.0036777773 0.0099241877 -0.0128697756
## gamble 0.0014682421 -0.0001187175 -0.0005234561 0.0002981982
## 46 47
## (Intercept) -0.0097463601 -9.169014e-02
## sex -0.0054909255 -8.523074e-03
## status 0.0023919320 1.283812e-03
## verbal -0.0106339789 8.503092e-03
## gamble -0.0002143037 8.876445e-05#Matriz P
matriz_P<-matriz_X%*%matriz_A
head(matriz_P, n=5)## 1 2 3 4 5 6
## 1 0.07998301 0.05115446 0.05179203 0.03133324 0.10146454 0.081894071
## 2 0.05115446 0.09695391 0.04157846 0.02149756 0.02180388 -0.006219786
## 3 0.05179203 0.04157846 0.05611581 0.06172736 0.05550509 0.066760684
## 4 0.03133324 0.02149756 0.06172736 0.09294939 0.03380216 0.071972723
## 5 0.10146454 0.02180388 0.05550509 0.03380216 0.16858435 0.138724307
## 7 8 9 10 11 12
## 1 0.04612389 0.03526092 0.05965372 0.03331880 0.02799721 0.06039630
## 2 0.07811800 0.04226840 0.02950305 0.09813224 0.07940528 0.02922504
## 3 0.04666359 0.05610235 0.05856305 0.04239537 0.04766574 0.05809037
## 4 0.03942783 0.07445687 0.06398805 0.03539376 0.05358429 0.06332394
## 5 0.02444699 0.02840845 0.07790206 -0.01147131 -0.01020649 0.08141908
## 13 14 15 16 17 18 19
## 1 0.03261580 0.04123382 0.05352713 0.06437099 0.05117453 0.02434144 0.07236409
## 2 0.01797333 0.05922950 0.03940685 0.07678565 0.09694640 0.06005469 0.06618308
## 3 0.06339477 0.05165930 0.05625328 0.04558479 0.04156568 0.05187578 0.04670648
## 4 0.09489956 0.05723245 0.06172422 0.02516368 0.02147962 0.07028504 0.02575825
## 5 0.03493084 0.02775549 0.06124991 0.05967081 0.02189893 -0.00105213 0.08516305
## 20 21 22 23 24 25
## 1 0.004364203 0.013030887 -0.000408619 -0.026929380 -0.02101654 0.026516276
## 2 0.045026472 0.004320285 0.052901431 -0.013958659 -0.01253876 -0.035145786
## 3 -0.008122178 0.001905195 -0.010051752 0.009393977 -0.01235703 0.006381542
## 4 -0.034712674 -0.011997619 -0.036638615 0.034610379 0.01797615 0.003310761
## 5 -0.034521545 0.005792400 -0.047234916 -0.057075257 0.03696371 0.073874292
## 26 27 28 29 30 31
## 1 -0.022151892 -0.01933357 -0.027292845 -0.006158543 0.0147569037 -0.056588016
## 2 0.033301403 -0.04969782 0.014506816 0.007527460 0.0036741201 -0.026961953
## 3 -0.003622605 0.01637729 0.001532789 0.002341911 0.0008065417 0.002874116
## 4 -0.004267845 0.05363735 0.013761140 0.001560685 -0.0135412365 0.062713805
## 5 -0.075021342 -0.01441450 -0.072901028 -0.031421573 0.0139671032 -0.056315395
## 32 33 34 35 36 37
## 1 -0.02192347 -0.004510398 0.035356189 -0.06420715 0.025625743 0.026516276
## 2 0.04539222 0.026696992 0.023702420 -0.06004921 0.001127216 -0.035145786
## 3 -0.01370320 -0.014851862 -0.004894429 0.02202592 -0.007353649 0.006381542
## 4 -0.01686091 -0.020045048 -0.044888911 0.09844505 -0.024810093 0.003310761
## 5 -0.05415645 0.008531726 0.036335412 -0.09066092 0.067916626 0.073874292
## 38 39 40 41 42 43
## 1 -0.0289490801 -0.010396348 0.01096476 0.001988784 0.03088712 0.031793891
## 2 0.0303472762 -0.011605237 -0.04091074 0.050481878 0.01987672 -0.022490528
## 3 -0.0098319656 0.006922429 0.01071213 -0.010335861 -0.01258569 0.006106756
## 4 -0.0002436178 0.018781964 0.02135858 -0.037234072 -0.04294677 -0.008646056
## 5 -0.0560164577 -0.025023797 0.04152569 -0.038353292 0.06636664 0.062509717
## 44 45 46 47
## 1 0.023285851 0.009813607 0.021679416 0.033285940
## 2 0.015112183 -0.035913659 -0.033335020 0.003758260
## 3 -0.001537801 0.007719170 0.009460326 -0.001693615
## 4 -0.028405798 0.017742290 0.007636479 -0.029606128
## 5 0.018001387 0.043492278 0.050966113 0.052999093n<-nrow(matriz_X)
#Matriz M
matriz_M<-diag(n)-matriz_P
head(matriz_M, n=5)## 1 2 3 4 5 6
## 1 0.92001699 -0.05115446 -0.05179203 -0.03133324 -0.10146454 -0.081894071
## 2 -0.05115446 0.90304609 -0.04157846 -0.02149756 -0.02180388 0.006219786
## 3 -0.05179203 -0.04157846 0.94388419 -0.06172736 -0.05550509 -0.066760684
## 4 -0.03133324 -0.02149756 -0.06172736 0.90705061 -0.03380216 -0.071972723
## 5 -0.10146454 -0.02180388 -0.05550509 -0.03380216 0.83141565 -0.138724307
## 7 8 9 10 11 12
## 1 -0.04612389 -0.03526092 -0.05965372 -0.03331880 -0.02799721 -0.06039630
## 2 -0.07811800 -0.04226840 -0.02950305 -0.09813224 -0.07940528 -0.02922504
## 3 -0.04666359 -0.05610235 -0.05856305 -0.04239537 -0.04766574 -0.05809037
## 4 -0.03942783 -0.07445687 -0.06398805 -0.03539376 -0.05358429 -0.06332394
## 5 -0.02444699 -0.02840845 -0.07790206 0.01147131 0.01020649 -0.08141908
## 13 14 15 16 17 18
## 1 -0.03261580 -0.04123382 -0.05352713 -0.06437099 -0.05117453 -0.02434144
## 2 -0.01797333 -0.05922950 -0.03940685 -0.07678565 -0.09694640 -0.06005469
## 3 -0.06339477 -0.05165930 -0.05625328 -0.04558479 -0.04156568 -0.05187578
## 4 -0.09489956 -0.05723245 -0.06172422 -0.02516368 -0.02147962 -0.07028504
## 5 -0.03493084 -0.02775549 -0.06124991 -0.05967081 -0.02189893 0.00105213
## 19 20 21 22 23 24
## 1 -0.07236409 -0.004364203 -0.013030887 0.000408619 0.026929380 0.02101654
## 2 -0.06618308 -0.045026472 -0.004320285 -0.052901431 0.013958659 0.01253876
## 3 -0.04670648 0.008122178 -0.001905195 0.010051752 -0.009393977 0.01235703
## 4 -0.02575825 0.034712674 0.011997619 0.036638615 -0.034610379 -0.01797615
## 5 -0.08516305 0.034521545 -0.005792400 0.047234916 0.057075257 -0.03696371
## 25 26 27 28 29 30
## 1 -0.026516276 0.022151892 0.01933357 0.027292845 0.006158543 -0.0147569037
## 2 0.035145786 -0.033301403 0.04969782 -0.014506816 -0.007527460 -0.0036741201
## 3 -0.006381542 0.003622605 -0.01637729 -0.001532789 -0.002341911 -0.0008065417
## 4 -0.003310761 0.004267845 -0.05363735 -0.013761140 -0.001560685 0.0135412365
## 5 -0.073874292 0.075021342 0.01441450 0.072901028 0.031421573 -0.0139671032
## 31 32 33 34 35 36
## 1 0.056588016 0.02192347 0.004510398 -0.035356189 0.06420715 -0.025625743
## 2 0.026961953 -0.04539222 -0.026696992 -0.023702420 0.06004921 -0.001127216
## 3 -0.002874116 0.01370320 0.014851862 0.004894429 -0.02202592 0.007353649
## 4 -0.062713805 0.01686091 0.020045048 0.044888911 -0.09844505 0.024810093
## 5 0.056315395 0.05415645 -0.008531726 -0.036335412 0.09066092 -0.067916626
## 37 38 39 40 41 42
## 1 -0.026516276 0.0289490801 0.010396348 -0.01096476 -0.001988784 -0.03088712
## 2 0.035145786 -0.0303472762 0.011605237 0.04091074 -0.050481878 -0.01987672
## 3 -0.006381542 0.0098319656 -0.006922429 -0.01071213 0.010335861 0.01258569
## 4 -0.003310761 0.0002436178 -0.018781964 -0.02135858 0.037234072 0.04294677
## 5 -0.073874292 0.0560164577 0.025023797 -0.04152569 0.038353292 -0.06636664
## 43 44 45 46 47
## 1 -0.031793891 -0.023285851 -0.009813607 -0.021679416 -0.033285940
## 2 0.022490528 -0.015112183 0.035913659 0.033335020 -0.003758260
## 3 -0.006106756 0.001537801 -0.007719170 -0.009460326 0.001693615
## 4 0.008646056 0.028405798 -0.017742290 -0.007636479 0.029606128
## 5 -0.062509717 -0.018001387 -0.043492278 -0.050966113 -0.052999093