STAT 704 Fall 2026
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Homework 7
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PART 1:
Do the following problems from the textbook:

13.2, 13.3, 13.4, 13.10, 13.11(a,b), 13.12, 13.13, 13.14

NOTE:  For 13.12, you may make your conclusion about the requested 
hypothesis test by looking at the appropriate CI.

14.2, 14.4, 14.7, 14.15, 14.33(a), 14.13, 14.19(b), 14.40, 14.46

PART 2:

Problem 1:

Extra Problem:  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.

Problem 2:

The "Masters Golfers" data set on the course web page contains data 
for 60 golfers from the 2007 Masters Tournament in Augusta, GA.  The first variable
is the golfer's name, the second variable is his number of birdies for the tournament,
the third variable his driving distance (how far he typically hit the ball) and the last
variable is his driving accuracy (how accurately he typically hit the ball).
(Note that a lot of birdies is good in golf!)

(a) Fit a Poisson regression model relating number of birdies to driving accuracy.
Is driving accuracy a significant predictor in this model, at the 0.05 level?

(b) Fit a Poisson regression model relating number of birdies to driving distance.
State the estimated regression function.  Is driving distance a significant 
predictor in this model, at the 0.05 level?

(c)  Interpret the estimate b_1 from part (b) in the context of this problem.

(d) In the model with driving distance as the predictor, note that the last 
observation (#60) has the largest absolute deviance residual.  

What is the value of his deviance residual?  What does this tell you about this 
golfer concerning his number of birdies and driving distance?

Bonus:  What is particularly notable about golfer #60 in the context of this data set?

NOTE:  For 14.7(b), just do a scatter plot of the data and the fitted logistic 
response function.  Don't do the "lowess smooth".

NOTE:  For the Poisson regression problem, if you analyze these data in SAS 
you should technically put $17. after the NAME variable in the INPUT statement so SAS
will correctly read in it as a character variable.  It won't mess up your 
analysis for this problem if you don't do this, though.

The "Annual Dues", "Car Purchase", "Masters Golfers", "Muscle Mass"
data can be found on 
the course web page.

Please write your answers neatly and clearly!