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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_1r.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
> 
> plot(x1,y,xlab="Days",ylab="Density of Algae")
> 
> 
> x <- cbind(x0,x1,x2,x3)
> xf8_2 <- x[1:14,1:4]
> y8_2 <- y[1:14]
> 
> betaf8_2 <- solve(t(xf8_2) %*% xf8_2) %*% t(xf8_2) %*% y8_2
> 
> ssef8_2 <- t(y8_2 - xf8_2%*%betaf8_2) %*% (y8_2 - xf8_2%*%betaf8_2)
> s2f8_2 <- ssef8_2/(nrow(xf8_2)-ncol(xf8_2))
> 
> varbetaf8_2 <- s2f8_2[1,1]*solve(t(xf8_2) %*% xf8_2)
> sebetaf8_2 <- sqrt(diag(varbetaf8_2))
> 
> print(round(cbind(betaf8_2,sebetaf8_2),5))
            sebetaf8_2
    0.00948    0.16761
x1  0.53074    0.09343
x2  0.00595    0.01422
x3 -0.00119    0.00062
> 
> tbeta3 <- betaf8_2[4]/sebetaf8_2[4]
> tcritb3 <- qt(.975,nrow(xf8_2)-ncol(xf8_2))
> probtb3 <- 2*(1-pt(abs(tbeta3),nrow(xf8_2)-ncol(xf8_2)))
> 
> print(cbind(tbeta3,tcritb3,probtb3))
      tbeta3  tcritb3    probtb3
x3 -1.910112 2.228139 0.08518918
> 
> xr8_2 <- x[1:14,1:2]
> 
> betar8_2 <- solve(t(xr8_2) %*% xr8_2) %*% t(xr8_2) %*% y8_2
> 
> sser8_2 <- t(y8_2 - xr8_2%*%betar8_2) %*% (y8_2 - xr8_2%*%betar8_2)
> 
> ssef8_2
          [,1]
[1,] 0.1365819
> sser8_2
         [,1]
[1,] 1.458121
> 
> fbeta23 <- ((sser8_2-ssef8_2)/(ncol(xf8_2)-ncol(xr8_2)))/(ssef8_2/(nrow(xf8_2)-ncol(xf8_2)))
> fcritb23 <- qf(.95,ncol(xf8_2)-ncol(xr8_2),nrow(xf8_2)-ncol(xf8_2))
> fprobb23 <- 1-pf(fbeta23,ncol(xf8_2)-ncol(xr8_2),nrow(xf8_2)-ncol(xf8_2))
> 
> print(cbind(fbeta23,fcritb23,fprobb23))
              fcritb23            
[1,] 48.37897 4.102821 7.21106e-06
> 
> 
> dev.off()
null device 
          1 
>