tortoise=read.table("tortoise.txt", header=TRUE)

attach(tortoise)

linmod=lm(eggs~Carapace)

summary(linmod)


Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.43532   17.34992  -0.025    0.980
Carapace     0.02759    0.05631   0.490    0.631

Residual standard error: 3.411 on 16 degrees of freedom
Multiple R-Squared: 0.01478,    Adjusted R-squared: -0.0468 
F-statistic:  0.24 on 1 and 16 DF,  p-value: 0.6308 


quadmod=lm(eggs~Carapace+I(Carapace^2))

summary(quadmod)

Coefficients:
                Estimate Std. Error t value Pr(>|t|)   
(Intercept)   -8.999e+02  2.703e+02  -3.329  0.00457 **
Carapace       5.857e+00  1.750e+00   3.347  0.00441 **
I(Carapace^2) -9.425e-03  2.829e-03  -3.332  0.00455 **
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

Residual standard error: 2.671 on 15 degrees of freedom
Multiple R-Squared: 0.4338,     Adjusted R-squared: 0.3583 
F-statistic: 5.747 on 2 and 15 DF,  p-value: 0.01403 


cubemod=lm(eggs~Carapace+I(Carapace^2)+I(Carapace^3))

summary(cubemod)

Coefficients:
                Estimate Std. Error t value Pr(>|t|)
(Intercept)   -5.108e+03  6.870e+03  -0.744    0.469
Carapace       4.672e+01  6.667e+01   0.701    0.495
I(Carapace^2) -1.415e-01  2.154e-01  -0.657    0.522
I(Carapace^3)  1.420e-04  2.317e-04   0.613    0.550

Residual standard error: 2.728 on 14 degrees of freedom
Multiple R-Squared: 0.4486,     Adjusted R-squared: 0.3305 
F-statistic: 3.797 on 3 and 14 DF,  p-value: 0.03496