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R version 2.9.0 (2009-04-17)
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ISBN 3-900051-07-0
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> pdf("rpd4_11r.pdf")
>
>
> alldata <- matrix(
+ c(44,89.47,44.609,11.37,62,178,182,
+ 40,75.07,45.313,10.07,62,185,185,
+ 44,85.84,54.297,8.65,45,156,184,
+ 42,68.15,59.571,8.17,40,166,172,
+ 38,89.02,49.874,9.22,55,178,180,
+ 47,77.45,44.811,11.63,58,176,176,
+ 40,75.98,45.681,11.95,70,176,180,
+ 43,81.19,49.091,10.85,64,162,170,
+ 44,81.42,39.442,13.08,63,174,176,
+ 38,81.87,60.055,8.63,48,170,186,
+ 44,73.03,50.541,10.13,45,168,168,
+ 45,87.66,37.388,14.03,56,186,192,
+ 45,66.45,44.754,11.12,51,176,176,
+ 47,79.15,47.273,10.6,47,162,164,
+ 54,83.12,51.855,10.33,50,166,170,
+ 49,81.42,49.156,8.95,44,180,185,
+ 51,69.63,40.836,10.95,57,168,172,
+ 51,77.91,46.672,10,48,162,168,
+ 48,91.63,46.774,10.25,48,162,164,
+ 49,73.37,50.388,10.08,67,168,168,
+ 57,73.37,39.407,12.63,58,174,176,
+ 54,79.38,46.08,11.17,62,156,176,
+ 52,76.32,45.441,9.63,48,164,166,
+ 50,70.87,54.625,8.92,48,146,186,
+ 51,67.25,45.118,11.08,48,172,172,
+ 54,91.63,39.203,12.88,44,168,172,
+ 51,73.71,45.79,10.47,59,186,188,
+ 57,59.08,50.545,9.93,49,148,160,
+ 49,76.32,48.673,9.4,56,186,188,
+ 48,61.24,47.92,11.5,52,170,176,
+ 52,82.78,47.467,10.5,53,170,172),byrow=T,ncol=7)
>
> Y <- alldata[,3]
> X <- alldata[,4:7]
>
> X <- cbind(rep(1,nrow(X)),X)
>
> XPXINV <- solve(t(X) %*% X)
>
> BETAHAT <- XPXINV %*% t(X) %*% Y
>
> BETAHAT
[,1]
[1,] 84.26901669
[2,] -3.06981406
[3,] 0.00799404
[4,] -0.11670572
[5,] 0.08518177
> XPXINV
[,1] [,2] [,3] [,4] [,5]
[1,] 17.423094927 -0.1596195144 7.267501e-03 -1.404500e-02 -7.796573e-02
[2,] -0.159619514 0.0236857375 -1.696658e-03 -9.852195e-04 9.482363e-04
[3,] 0.007267501 -0.0016966578 7.775643e-04 -9.345606e-05 -8.540163e-05
[4,] -0.014044998 -0.0009852195 -9.345606e-05 5.428172e-04 -3.561660e-04
[5,] -0.077965727 0.0009482363 -8.540163e-05 -3.561660e-04 7.560261e-04
>
> ix <- diag(1,ncol=nrow(X),nrow=nrow(X))
> jx <- matrix(rep(1,nrow(X)*nrow(X)),ncol=nrow(X))
>
> SSRESID <- t(Y) %*% (ix - X %*% XPXINV %*% t(X)) %*% Y
> DFRESID <- nrow(X)-ncol(X)
> S2 <- SSRESID/DFRESID
>
> S2BETA <- S2[1,1]*XPXINV
>
> DHAT <- sqrt(diag(S2BETA))
>
>
> BETALO <- BETAHAT - qt(.975,DFRESID) * DHAT
> BETAHI <- BETAHAT + qt(.975,DFRESID) * DHAT
>
> S2BETA
[,1] [,2] [,3] [,4] [,5]
[1,] 129.41189701 -1.185590979 0.0539801409 -0.1043207236 -0.5790987555
[2,] -1.18559098 0.175928343 -0.0126021068 -0.0073178230 0.0070431263
[3,] 0.05398014 -0.012602107 0.0057754415 -0.0006941549 -0.0006343297
[4,] -0.10432072 -0.007317823 -0.0006941549 0.0040318326 -0.0026454607
[5,] -0.57909876 0.007043126 -0.0006343297 -0.0026454607 0.0056154644
>
> print(cbind(BETALO,BETAHI))
[,1] [,2]
[1,] 60.88544741 107.65258596
[2,] -3.93198148 -2.20764665
[3,] -0.14821864 0.16420672
[4,] -0.24722509 0.01381364
[5,] -0.06885221 0.23921575
>
> # Bonferroni's Method
>
>
> BETALOBON <- BETAHAT - qt(1-(.05/(5*2)),DFRESID) * DHAT
> BETAHIBON <- BETAHAT + qt(1-(.05/(5*2)),DFRESID) * DHAT
>
> print(cbind(BETALOBON,BETAHIBON))
[,1] [,2]
[1,] 52.6585408 115.87949259
[2,] -4.2353129 -1.90431524
[3,] -0.2031781 0.21916613
[4,] -0.2931450 0.05973352
[5,] -0.1230451 0.29340864
>
>
> # Scheffe's Method
>
>
> BETALOSCH <- BETAHAT - sqrt(ncol(X)*qf(0.95,ncol(X),DFRESID)) * DHAT
> BETAHISCH <- BETAHAT + sqrt(ncol(X)*qf(0.95,ncol(X),DFRESID)) * DHAT
>
> print(cbind(BETALOSCH,BETAHISCH))
[,1] [,2]
[1,] 43.3568295 125.1812039
[2,] -4.5782730 -1.5613551
[3,] -0.2653176 0.2813057
[4,] -0.3450640 0.1116526
[5,] -0.1843180 0.3546816
>
> dev.off()
null device
1
>