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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_4r.pdf")
> 
> xy<- matrix(c( 1,    0.53,
+        2,   1.183,
+        3,   1.603,
+        4,   1.994,
+        5,   2.708,
+        6,   3.006,
+        7,   3.867,
+        8,   4.059,
+        9,   4.349,
+       10,   4.699,
+       11,   4.983,
+       12,     5.1,
+       13,   5.288,
+       14,   5.374,
+        1,   0.184,
+        2,   0.664,
+        3,   1.553,
+        4,    1.91,
+        5,   2.585,
+        6,   3.009,
+        7,   3.403,
+        8,   3.892,
+        9,   4.367,
+       10,   4.551,
+       11,   4.656,
+       12,   4.754,
+       13,   4.842,
+       14,   4.969),byrow=T,ncol=2)
> 
> nobs <- nrow(xy)
> y <- xy[,2]
> x1 <- xy[,1]
> x0 <- matrix(rep(1,nobs),ncol=1)
> x2 <- x1*x1
> x3 <- x1*x2
> 
> x <- cbind(x0,x1,x2,x3)
> xf8_2 <- x[1:14,1:4]
> y8_2 <- y[1:14]
> 
> orp0 <- x0[1:14,]
> orp1 <- 2*x1[1:14]-15
> orp2 <- 0.5*x2[1:14]-7.5*x1[1:14]+20
> orp3 <- (5/3)*x3[1:14]-37.5*x2[1:14]+(698.5/3)*x1[1:14]-340
> 
> orpx3 <- cbind(orp0,orp1,orp2,orp3)
> 
> orpx3
      orp0 orp1 orp2 orp3
 [1,]    1  -13   13 -143
 [2,]    1  -11    7  -11
 [3,]    1   -9    2   66
 [4,]    1   -7   -2   98
 [5,]    1   -5   -5   95
 [6,]    1   -3   -7   67
 [7,]    1   -1   -8   24
 [8,]    1    1   -8  -24
 [9,]    1    3   -7  -67
[10,]    1    5   -5  -95
[11,]    1    7   -2  -98
[12,]    1    9    2  -66
[13,]    1   11    7   11
[14,]    1   13   13  143
> 
> 
> betaorp <- solve(t(orpx3) %*% orpx3) %*% t(orpx3) %*% y8_2
> yhat <- orpx3 %*% betaorp
> 
> sseorp <- t(y8_2 - orpx3 %*% betaorp) %*% (y8_2 - orpx3 %*% betaorp)
> s2orp <- sseorp/(nrow(orpx3)-ncol(orpx3))
> 
> varbetaorp <- s2orp[1,1]*solve(t(orpx3) %*% orpx3)
> sebetaorp <- sqrt(diag(varbetaorp))
> 
> print(round(cbind(betaorp,sebetaorp),5))
              sebetaorp
orp0  3.48164   0.03123
orp1  0.19198   0.00387
orp2 -0.04180   0.00433
orp3 -0.00072   0.00037
> 
> tbeta3orp <- betaorp[4,]/sebetaorp[4]
> tcritb3orp <- qt(.975,nrow(orpx3)-ncol(orpx3))
> probtb3orp <- 2*(1-pt(abs(tbeta3orp),nrow(orpx3)-ncol(orpx3)))
> 
> print(cbind(tbeta3orp,tcritb3orp,probtb3orp))
     tbeta3orp tcritb3orp probtb3orp
orp3 -1.910112   2.228139 0.08518918
> 
> dev.off()
null device 
          1 
> 
>