#Cargamos los datos.
load("C:/Users/FEBRERO/Downloads/datos_parcial.RData")
print(sat)
## expend ratio salary takers verbal math total
## Alabama 4.405 17.2 31.144 8 491 538 1029
## Alaska 8.963 17.6 47.951 47 445 489 934
## Arizona 4.778 19.3 32.175 27 448 496 944
## Arkansas 4.459 17.1 28.934 6 482 523 1005
## California 4.992 24.0 41.078 45 417 485 902
## Colorado 5.443 18.4 34.571 29 462 518 980
## Connecticut 8.817 14.4 50.045 81 431 477 908
## Delaware 7.030 16.6 39.076 68 429 468 897
## Florida 5.718 19.1 32.588 48 420 469 889
## Georgia 5.193 16.3 32.291 65 406 448 854
## Hawaii 6.078 17.9 38.518 57 407 482 889
## Idaho 4.210 19.1 29.783 15 468 511 979
## Illinois 6.136 17.3 39.431 13 488 560 1048
## Indiana 5.826 17.5 36.785 58 415 467 882
## Iowa 5.483 15.8 31.511 5 516 583 1099
## Kansas 5.817 15.1 34.652 9 503 557 1060
## Kentucky 5.217 17.0 32.257 11 477 522 999
## Louisiana 4.761 16.8 26.461 9 486 535 1021
## Maine 6.428 13.8 31.972 68 427 469 896
## Maryland 7.245 17.0 40.661 64 430 479 909
## Massachusetts 7.287 14.8 40.795 80 430 477 907
## Michigan 6.994 20.1 41.895 11 484 549 1033
## Minnesota 6.000 17.5 35.948 9 506 579 1085
## Mississippi 4.080 17.5 26.818 4 496 540 1036
## Missouri 5.383 15.5 31.189 9 495 550 1045
## Montana 5.692 16.3 28.785 21 473 536 1009
## Nebraska 5.935 14.5 30.922 9 494 556 1050
## Nevada 5.160 18.7 34.836 30 434 483 917
## New Hampshire 5.859 15.6 34.720 70 444 491 935
## New Jersey 9.774 13.8 46.087 70 420 478 898
## New Mexico 4.586 17.2 28.493 11 485 530 1015
## New York 9.623 15.2 47.612 74 419 473 892
## North Carolina 5.077 16.2 30.793 60 411 454 865
## North Dakota 4.775 15.3 26.327 5 515 592 1107
## Ohio 6.162 16.6 36.802 23 460 515 975
## Oklahoma 4.845 15.5 28.172 9 491 536 1027
## Oregon 6.436 19.9 38.555 51 448 499 947
## Pennsylvania 7.109 17.1 44.510 70 419 461 880
## Rhode Island 7.469 14.7 40.729 70 425 463 888
## South Carolina 4.797 16.4 30.279 58 401 443 844
## South Dakota 4.775 14.4 25.994 5 505 563 1068
## Tennessee 4.388 18.6 32.477 12 497 543 1040
## Texas 5.222 15.7 31.223 47 419 474 893
## Utah 3.656 24.3 29.082 4 513 563 1076
## Vermont 6.750 13.8 35.406 68 429 472 901
## Virginia 5.327 14.6 33.987 65 428 468 896
## Washington 5.906 20.2 36.151 48 443 494 937
## West Virginia 6.107 14.8 31.944 17 448 484 932
## Wisconsin 6.930 15.9 37.746 9 501 572 1073
## Wyoming 6.160 14.9 31.285 10 476 525 1001
- Estimar el modelo.
options(scipen = 9999999)
estimacion_modelo<- lm(formula = total~expend+ratio+salary+takers, data =sat)
summary(estimacion_modelo)
##
## Call:
## lm(formula = total ~ expend + ratio + salary + takers, data = sat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -90.531 -20.855 -1.746 15.979 66.571
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1045.9715 52.8698 19.784 < 0.0000000000000002 ***
## expend 4.4626 10.5465 0.423 0.674
## ratio -3.6242 3.2154 -1.127 0.266
## salary 1.6379 2.3872 0.686 0.496
## takers -2.9045 0.2313 -12.559 0.000000000000000261 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 32.7 on 45 degrees of freedom
## Multiple R-squared: 0.8246, Adjusted R-squared: 0.809
## F-statistic: 52.88 on 4 and 45 DF, p-value: < 0.00000000000000022
- Calculamos un intervalo de confianza del 94.78% ´para las variables
“expend” y “salary”.
#Para la variable exped.
confint(object = estimacion_modelo, parm = "expend", level = .9478)
## 2.61 % 97.39 %
## expend -16.57026 25.49545
#Para la variable salary.
confint(object = estimacion_modelo, parm = "salary", level = .9478)
## 2.61 % 97.39 %
## salary -3.122951 6.398786
- ¿El modelo resulta ser estadisticamente significativo? ## p-value:
< 0.00000000000000022 ### El modelo no resulta ser siginifcativo por
que el P value es cero.
- Calcular las matrices A, P y M.
#Calcumalmos Matriz A.
#Formamos matriz x.
matriz_X<- model.matrix(estimacion_modelo)
#Formamos la sigma matriz.
matriz_XX<-t(matriz_X)%*%matriz_X
matriz_A<-solve(matriz_XX)%*%t(matriz_X)
print(matriz_A [1:5,5:1 ])
## California Arkansas Arizona Alaska Alabama
## (Intercept) -0.422174416 0.1780225369 -0.0728991868 -0.471973891 0.2565261764
## expend -0.057183953 -0.0250904587 -0.0045991810 0.058318347 -0.0750342914
## ratio 0.016661935 -0.0062815391 0.0093052725 0.013399464 -0.0177255005
## salary 0.013923827 0.0034232104 -0.0013112799 -0.001220096 0.0154718688
## takers 0.000397894 -0.0006580417 0.0002514394 -0.001016023 -0.0009500899
#Calculamos matriz P.
matriz_P<-matriz_X%*%matriz_A
print(matriz_P[1:5,5:1 ])
## California Arkansas Arizona Alaska Alabama
## Alabama 0.04934236 0.06080472 0.02806512 -0.03073763 0.09537668
## Alaska 0.04489829 -0.02419993 -0.00140838 0.18030612 -0.03073763
## Arizona 0.08491826 0.02928129 0.04931612 -0.00140838 0.02806512
## Arkansas 0.01302079 0.05382878 0.02928129 -0.02419993 0.06080472
## California 0.28211791 0.01302079 0.08491826 0.04489829 0.04934236
#Calculamos matriz M.
n<-nrow(matriz_X)
matriz_M<-diag(n)-matriz_P
print(matriz_M[1:5,5:1 ])
## California Arkansas Arizona Alaska Alabama
## Alabama -0.04934236 -0.06080472 -0.02806512 0.03073763 0.90462332
## Alaska -0.04489829 0.02419993 0.00140838 0.81969388 0.03073763
## Arizona -0.08491826 -0.02928129 0.95068388 0.00140838 -0.02806512
## Arkansas -0.01302079 0.94617122 -0.02928129 0.02419993 -0.06080472
## California 0.71788209 -0.01302079 -0.08491826 -0.04489829 -0.04934236