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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.

       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.

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

       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:

attach( cats )
catsF <- cats[Sex=="F",-1]  # makes a data frame of just females
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,

Compute the linear regression Hwt on Bwt. Give the fitted regression equation and the value of tex2html_wrap_inline149 .
Perform a goodness of fit test. What do you conclude?
Plot a 95% confidence ellipsoid for tex2html_wrap_inline153 . Superimpose on this plot the rectangle determined by the Bonferroni intervals for tex2html_wrap_inline153 with a 95% simultaneous confidence level. What feature of this example causes the rectangular region to be so much larger than the ellipse?
Is tex2html_wrap_inline157 a plausible combination of values for tex2html_wrap_inline159 and tex2html_wrap_inline161 ? Why or why not? Why is the rectangular region not useful for answering this question?

Brett Presnell
Thu Apr 18 15:52:37 EDT 1996