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?

Thu Apr 18 15:52:37 EDT 1996