STAT 705 Spring 2010
--------------------

Homework 7
----------

26.2, 26.4, 26.5(c,d,e,f), and the extra 
problems given below:

Extra Problem 1:  In the "Muscle Mass" data set, the 
first column (Y) is a measure of muscle mass for a sample 
of women and the second column (X) is age in years.  It is 
conjectured that the regression of muscle mass on age follows 
a two-piece linear relation, with the slope changing at 
age 60 years without discontinuity.

(a) State the regression model that applies if the conjecture 
is correct.  What are the respective mean response functions 
when age is 60 or less and when age is over 60?

(b) Fit the regression model specified in part (a) and state 
the estimated regression function.

(c) Plot the data with the estimated piecewise regression 
function overlain on top of it.

(d) Test whether the piecewise linear regression function is 
needed; use alpha=0.05.  State the alternatives, decision rule,
and conclusion.  What is the P-value of the test?

(e) Specify the regression model for the case when the slope 
changes at age 40 and again at age 60, with no discontinuities.

Extra Problem 2:  
Consider an sample (of size n) of i.i.d. Binomial(1, pi) observations.  
We showed in class that the sample proportion of "successes" is the least-squares 
estimator of pi.  Show that it is also the maximum likelihood estimator of pi.
(Hint:  It is easier to maximize the logarithm of the likelihood function.)

NOTE: For 26.4(b), show the residuals plotted for each machine
level, and state your conclusions.

The "Muscle Mass" and "Bottling Plant Production" data sets 
are given on the course web page.

Please write your answers neatly and clearly!