Assignment 5

Due Friday, March 1.

Turn in problem # 1.

Problem 1:

The data frame ``cats'' in the MASS library from Venables and Ripley is described as follows:

Anatomical data from domestic cats.

SUMMARY:
       The heart and body weights of samples of male  and  female
       cats  used  for  digitalis experiments.  The cats were all
       adult, over 2 kg body weight.

DATA DESCRIPTION:
       This data frame contains the following columns:
Sex:   Sex factor. Levels Female and Male.
Bwt:   Body weight in kg.
Hwt:   Heart weight in g.

SOURCE:
       R. A. Fisher (1947) "The analysis of covariance method for
       the  relation  between  a part and the whole", Biometrics,
       vol. 3, pp 65-68.

The files rawlings-ex4-8.St and rawlings-ex4-14.St have the commands you need for this problem. The following commands might also be useful:

library(MASS)
attach( cats )
catsF <- cats[Sex=="F",-1]  # makes a data frame of just females
detach()
catsF.lm <- lm( Hwt ~ Bwt, data=catsF )
catsF.oneway <- lm( Hwt ~ factor(Bwt), data=catsF )
attach( catsF )
tapply( Hwt, Bwt, mean )

Restricting attention to the FEMALE CATS ONLY,

(a)

Compute the linear regression Hwt on Bwt. Give the fitted regression equation and the value of .

(b)

Perform a goodness of fit test. What do you conclude?

(c)

Plot a 95% confidence ellipsoid for . Superimpose on this plot the rectangle determined by the Bonferroni intervals for with a 95% simultaneous confidence level. What feature of this example causes the rectangular region to be so much larger than the ellipse?

(d)

Is a plausible combination of values for and ? Why or why not? Why is the rectangular region not useful for answering this question?