C:\sta6167>C:\Progra~1\R\R-2.3.1\bin\Rterm --vanilla 

R : Copyright 2006, The R Foundation for Statistical Computing
Version 2.3.1 (2006-06-01)
ISBN 3-900051-07-0

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> pdf("nit.pdf")
> 
> nit0 <- read.fwf("C:\\data\\fertyld.dat", width=c(8,8,8),
+ col.names=c("nit", "nit20", "yield"))
> 
> x2=nit0$nit20^2
> 
> nit1 <- data.frame(y=nit0$yield, x=nit0$nit20, x2=x2)
> 
> attach(nit1)

	The following object(s) are masked _by_ .GlobalEnv :

	 x2 

> 
> nit1
     y x x2
1 24.5 0  0
2 41.5 1  1
3 52.1 2  4
4 61.4 3  9
5 73.5 4 16
6 86.0 6 36
7 92.8 8 64
8 94.0 9 81
> 
> 
> 
> nit.mod2 <- lm(y ~ x + x2)
> 
> summary(nit.mod2)

Call:
lm(formula = y ~ x + x2)

Residuals:
       1        2        3        4        5        6        7        8 
-0.89532  1.84744 -0.14856 -1.78330  1.04322 -0.01998 -0.13815  0.09464 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 25.39532    1.05065   24.17 2.26e-06 ***
x           15.08788    0.58744   25.68 1.67e-06 ***
x2          -0.83063    0.06191  -13.42 4.12e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.306 on 5 degrees of freedom
Multiple R-Squared: 0.9981,	Adjusted R-squared: 0.9973 
F-statistic:  1314 on 2 and 5 DF,  p-value: 1.571e-07 

> 
> nit.mod3 <- nls(y ~ M - a*(R^x), start=c(M=100, a=75, R=0.5))
> 
> summary(nit.mod3)

Formula: y ~ M - a * (R^x)

Parameters:
   Estimate Std. Error t value Pr(>|t|)    
M 107.65084    3.78478   28.44 1.01e-06 ***
a  83.18346    3.41301   24.37 2.17e-06 ***
R   0.80888    0.01751   46.20 8.98e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.689 on 5 degrees of freedom

> 
> nit.mod4 <- nls(y ~ M*(1-C*exp(k*x)), start=c(M=100, C=.75, k=-1))
> 
> summary(nit.mod4)

Formula: y ~ M * (1 - C * exp(k * x))

Parameters:
   Estimate Std. Error t value Pr(>|t|)    
M 107.65084    3.78478  28.443 1.01e-06 ***
C   0.77272    0.01267  60.987 2.24e-08 ***
k  -0.21210    0.02165  -9.798 0.000188 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.689 on 5 degrees of freedom

> 
> nit2 <- subset(nit1,x>0)
> 
> nit.mod1 <- nls(y ~ a*(x^b), start=c(a=1, b=1), data=nit2)
> 
> summary(nit.mod1)

Formula: y ~ a * (x^b)

Parameters:
  Estimate Std. Error t value Pr(>|t|)    
a 41.31743    1.63878   25.21 1.83e-06 ***
b  0.38768    0.02243   17.28 1.19e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.597 on 5 degrees of freedom

> 
> dev.off()
null device 
          1 
>