H:\public_html\sta6208\rpd>C:\R-2.9.0\bin\Rterm --vanilla
R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
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> pdf("rpd2_13.pdf")
>
>
> X1 <- matrix(
+ c(11.1,25.2,33.0,1576,12.6,26.0,48.2,1767,
+ 9.3,27.3,27.3,1580,9.8,26.7,34.3,1578,
+ 5.8,25.7,27.3,1222,12.1,28.3,20.4,1926),byrow=T,ncol=4)
>
> Xmn <- colMeans(X1)
>
> Xmeans <- rbind(t(Xmn),t(Xmn),t(Xmn),t(Xmn),t(Xmn),t(Xmn))
>
> Xss <- c()
>
> for (i in 1:ncol(X1)) {
+ Xss[i] <- (nrow(X1)-1)*var(X1[,i])
+ }
>
> Xsse <- rbind(t(Xss),t(Xss),t(Xss),t(Xss),t(Xss),t(Xss))
> X <- (X1-Xmeans)/sqrt(Xsse)
>
> svdX <- svd(X)
>
> U <- svdX$u
> Z <- svdX$v
> lambdasr <- svdX$d
>
> Xchk <- U %*% diag(lambdasr) %*% t(Z)
>
> L <- diag(lambdasr *lambdasr)
>
> A1 <- lambdasr[1]*U[,1]%*%t(Z[,1])
> gfA1X <- L[1,1]/sum(L)
> A2 <- lambdasr[2]*U[,2]%*%t(Z[,2])
> A1A2 <- A1+A2
> gfA1A2X <- (L[1,1]+L[2,2])/sum(L)
> A3 <- lambdasr[3]*U[,3]%*%t(Z[,3])
> A1A2A3 <- A1+A2+A3
> gfA1A2A3X <- (L[1,1]+L[2,2]+L[3,3])/sum(L)
> A4 <- lambdasr[4]*U[,4]%*%t(Z[,4])
> A1A2A3A4 <- A1+A2+A3+A4
> gfA1A2A3A4X <- (L[1,1]+L[2,2]+L[3,3]+L[4,4])/sum(L)
>
> X
[,1] [,2] [,3] [,4]
[1,] 0.1781461 -0.5232448 0.05911669 -0.06099562
[2,] 0.4498945 -0.2092979 0.77797563 0.30118564
[3,] -0.1479519 0.3008657 -0.21045541 -0.05341067
[4,] -0.0573691 0.0654056 0.12059805 -0.05720315
[5,] -0.7820314 -0.3270280 -0.21045541 -0.73226351
[6,] 0.3593117 0.6932993 -0.53677954 0.60268732
> U
[,1] [,2] [,3] [,4]
[1,] 0.113995446 0.30890504 -0.81067801 -0.2600878
[2,] -0.251977329 0.70751171 0.33970108 0.3192609
[3,] -0.007580354 -0.30320296 0.27743163 -0.5683636
[4,] 0.028067447 0.02776646 0.32662617 -0.3571239
[5,] 0.735417443 -0.23488778 0.06555068 0.4811250
[6,] -0.617922653 -0.50609246 -0.19863154 0.3851894
> lambdasr
[1] 1.49689599 1.24489228 0.45408594 0.05789254
> Z
[,1] [,2] [,3] [,4]
[1,] -0.595024891 0.3361311 -0.3832041 -0.62138220
[2,] -0.451775888 -0.5407533 0.6579572 -0.26566268
[3,] -0.004941779 0.7686939 0.6390506 0.02645002
[4,] -0.664695046 0.0609215 -0.1089090 0.73661924
> Xchk
[,1] [,2] [,3] [,4]
[1,] 0.1781461 -0.5232448 0.05911669 -0.06099562
[2,] 0.4498945 -0.2092979 0.77797563 0.30118564
[3,] -0.1479519 0.3008657 -0.21045541 -0.05341067
[4,] -0.0573691 0.0654056 0.12059805 -0.05720315
[5,] -0.7820314 -0.3270280 -0.21045541 -0.73226351
[6,] 0.3593117 0.6932993 -0.53677954 0.60268732
> L
[,1] [,2] [,3] [,4]
[1,] 2.240698 0.000000 0.0000000 0.000000000
[2,] 0.000000 1.549757 0.0000000 0.000000000
[3,] 0.000000 0.000000 0.2061940 0.000000000
[4,] 0.000000 0.000000 0.0000000 0.003351547
> A1
[,1] [,2] [,3] [,4]
[1,] -0.101534646 -0.077090733 -8.432618e-04 -0.113423115
[2,] 0.224433782 0.170402571 1.863959e-03 0.250712240
[3,] 0.006751748 0.005126301 5.607437e-05 0.007542295
[4,] -0.024999405 -0.018980935 -2.076241e-04 -0.027926531
[5,] -0.655029239 -0.497334516 -5.440124e-03 -0.731725171
[6,] 0.550377760 0.417877311 4.570977e-03 0.614820281
> gfA1X
[1] 0.5601744
> A2
[,1] [,2] [,3] [,4]
[1,] 0.12926040 -0.20794858 0.29560392 0.023427574
[2,] 0.29605617 -0.47628247 0.67704702 0.053658184
[3,] -0.12687438 0.20411006 -0.29014737 -0.022995125
[4,] 0.01161879 -0.01869181 0.02657086 0.002105828
[5,] -0.09828809 0.15812167 -0.22477377 -0.017814054
[6,] -0.21177289 0.34069114 -0.48430067 -0.038382407
> A1A2
[,1] [,2] [,3] [,4]
[1,] 0.02772575 -0.28503931 0.29476066 -0.08999554
[2,] 0.52048996 -0.30587990 0.67891098 0.30437042
[3,] -0.12012263 0.20923636 -0.29009130 -0.01545283
[4,] -0.01338061 -0.03767275 0.02636324 -0.02582070
[5,] -0.75331733 -0.33921284 -0.23021389 -0.74953922
[6,] 0.33860487 0.75856845 -0.47972969 0.57643787
> gfA1A2X
[1] 0.9476136
> A3
[,1] [,2] [,3] [,4]
[1,] 0.14106415 -0.24220557 -0.23524571 0.040091301
[2,] -0.05911057 0.10149220 0.09857578 -0.016799590
[3,] -0.04827522 0.08288801 0.08050619 -0.013720114
[4,] -0.05683544 0.09758582 0.09478166 -0.016152983
[5,] -0.01140632 0.01958452 0.01902175 -0.003241746
[6,] 0.03456340 -0.05934497 -0.05763967 0.009823132
> A1A2A3
[,1] [,2] [,3] [,4]
[1,] 0.16878990 -0.52724488 0.05951495 -0.04990424
[2,] 0.46137938 -0.20438771 0.77748676 0.28757083
[3,] -0.16839785 0.29212437 -0.20958510 -0.02917294
[4,] -0.07021605 0.05991307 0.12114490 -0.04197369
[5,] -0.76472365 -0.31962833 -0.21119214 -0.75278097
[6,] 0.37316827 0.69922348 -0.53736937 0.58626101
> gfA1A2A3X
[1] 0.9991621
> A4
[,1] [,2] [,3] [,4]
[1,] 0.009356242 0.004000122 -0.0003982618 -0.01109138
[2,] -0.011484898 -0.004910197 0.0004888711 0.01361480
[3,] 0.020445969 0.008741369 -0.0008703119 -0.02423773
[4,] 0.012846959 0.005492525 -0.0005468491 -0.01522946
[5,] -0.017307701 -0.007399649 0.0007367270 0.02051746
[6,] -0.013856571 -0.005924170 0.0005898247 0.01642631
> A1A2A3A4
[,1] [,2] [,3] [,4]
[1,] 0.1781461 -0.5232448 0.05911669 -0.06099562
[2,] 0.4498945 -0.2092979 0.77797563 0.30118564
[3,] -0.1479519 0.3008657 -0.21045541 -0.05341067
[4,] -0.0573691 0.0654056 0.12059805 -0.05720315
[5,] -0.7820314 -0.3270280 -0.21045541 -0.73226351
[6,] 0.3593117 0.6932993 -0.53677954 0.60268732
> gfA1A2A3A4X
[1] 1
>
>
> dev.off()
null device
1
>