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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("rpd8_5.r")
> 
> xy <- matrix(c(
+  1,      -1,        -1,        -1,         53, 
+  1,      -1,        -1,         1,         54, 
+  1,      -1,         1,        -1,         40, 
+  1,      -1,         1,         1,         37, 
+  1,       1,        -1,        -1,         84, 
+  1,       1,        -1,         1,         76, 
+  1,       1,         1,        -1,         40, 
+  1,       1,         1,         1,         50, 
+  1,       0,         0,         0,         50, 
+  1,   1.215,         0,         0,         61,
+  1,  -1.215,         0,         0,         54,
+  1,       0,     1.215,         0,         39,
+  1,       0,    -1.215,         0,         67,
+  1,       0,         0,     1.215,         44,
+  1,       0,         0,    -1.215,         61,
+  2,      -1,        -1,        -1,         50,
+  2,      -1,        -1,         1,         42,
+  2,      -1,         1,        -1,         31,
+  2,      -1,         1,         1,         28,
+  2,       1,        -1,        -1,         57,
+  2,       1,        -1,         1,         78,
+  2,       1,         1,        -1,         49,
+  2,       1,         1,         1,         54,
+  2,       0,         0,         0,         50,
+  2,   1.215,         0,         0,         76,
+  2,  -1.215,         0,         0,         45,
+  2,       0,     1.215,         0,         33,
+  2,       0,    -1.215,         0,         54,
+  2,       0,         0,     1.215,         45,
+  2,       0,         0,    -1.215,         38,
+  3, -1.2500,   -1.8867,   -0.6350,         46,
+  3,  0.8600,   -2.2200,   -0.4250,         66,
+  3,  1.0000,   -2.2400,   -0.3100,         68,
+  3,  2.1165,   -2.4167,   -0.1450,         75,
+  3,  2.5825,   -2.4900,   -0.0800,         75,
+  3,  3.2475,   -2.6667,    0.0800,         68,
+  3,  1.1760,   -1.3333,         0,         78,
+  3,  1.4700,   -1.6667,         0,         93,
+  3,  1.7640,   -2.0000,         0,         96,
+  3,  2.0580,   -2.3333,         0,         66), byrow=T, ncol=5)
>  
> y <- xy[,5]
> x01 <- c(rep(1,15),rep(0,25))
> x02 <- c(rep(0,15),rep(1,15),rep(0,10))
> x03 <- c(rep(0,30),rep(1,10))
> x1 <- xy[,2]
> x2 <- xy[,3]
> x3 <- xy[,4]
> x11 <- x1*x1
> x22 <- x2*x2
> x33 <- x3*x3
> x12 <- x1*x2
> x13 <- x1*x3
> x23 <- x2*x3
>  
> xf <- cbind(x01,x02,x03,x1,x2,x3,x11,x22,x33,x12,x13,x23)
>  
> betaf <- solve(t(xf) %*% xf) %*% t(xf) %*% y
> yhatf <- xf %*% betaf
> ssef <- t(y-yhatf) %*% (y-yhatf)
> dfef <- nrow(xf)-ncol(xf)
> s2f <- ssef[1,1]/dfef
> varbetaf <- s2f[1]*solve(t(xf) %*% xf)
> sebetaf <- sqrt(diag(varbetaf))
> tbetaf <- betaf/sebetaf
> 
> print(cbind(betaf,sebetaf,tbetaf))
                sebetaf            
x01 61.8439867 3.440772 17.97386986
x02 56.5106534 3.440772 16.42383008
x03 70.4079421 8.227833  8.55728856
x1   9.1271660 1.771973  5.15084855
x2  -9.8516000 1.854669 -5.31178429
x3   0.2632813 1.861929  0.14140246
x11 -1.2601941 1.464480 -0.86050616
x22 -6.4976734 2.014588 -3.22531071
x33 -2.9849162 2.952339 -1.01103449
x12 -0.9339081 1.510510 -0.61827327
x13  2.2419511 2.150452  1.04254858
x23 -0.1392224 2.137808 -0.06512388
> print(cbind(s2f,dfef))
          s2f dfef
[1,] 76.53377   28
> 
> 
> 
> xr <- cbind(x01,x02,x03,x1,x2,x22)
>  
> betar <- solve(t(xr) %*% xr) %*% t(xr) %*% y
> yhatr <- xr %*% betar
> sser <- t(y-yhatr) %*% (y-yhatr)
> dfer <- nrow(xr)-ncol(xr)
> s2r <- sser[1,1]/dfer
> varbetar <- s2r[1]*solve(t(xr) %*% xr)
> sebetar <- sqrt(diag(varbetar))
> tbetar <- betar/sebetar
>  
> print(cbind(betar,sebetar,tbetar))
               sebetar          
x01 59.034845 2.429201 24.302170
x02 53.701512 2.429201 22.106660
x03 70.560136 7.603604  9.279828
x1   9.212551 1.474434  6.248197
x2  -9.820102 1.759983 -5.579658
x22 -6.895506 1.558674 -4.423957
> print(cbind(s2r,dfer))
          s2r dfer
[1,] 69.08662   34
> 
> 
> ffullred <- ((sser-ssef)/(dfer-dfef))/(ssef/dfef)
> ffrcrit <- qf(.95,dfer-dfef,dfef)
> probffr <- 1-pf(ffullred,dfer-dfef,dfef)
> 
> print(cbind(ffullred,ffrcrit,probffr))
                ffrcrit          
[1,] 0.4486023 2.445259 0.8397384
> 
> 
> dev.off()
null device 
          1 
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