STAT 705 Spring 2017
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Homework 5
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Do the following problems from the textbook:

11.1, 11.2, 11.6(a,c,d,e,f), 11.19

In addition:
**Do this alteration of problem 11.9:**
 For the cosmetics data in problem 10.13:
(a) Fit an ordinary least squares regression of Y 
against X1, X2, and X3.  Calculate the VIFs.  What 
do these tell you?
(b) Load the MASS package in R and fit the ridge regression 
of Y against X1, X2, and X3, using a biasing constant of lambda=0.1.  
Write the fitted ridge regression equation.  How do the coefficient 
estimates compare to those of the fitted OLS equation?
(c) How do the SSE's for the two models compare?

***Do this alteration of problem 11.12:**
(a) Fit the OLS regression of weight against height and 
use the influence measures to detect any possible 
influential observations.
(b) Load the MASS package in R and use R's rlm()
function to fit Huber's robust regression of weight 
against height. Write the fitted robust regression equation.  
How do the coefficient estimates compare to those
of the fitted OLS equation?

13.1, 13.3, 13.4, 13.10, 13.11(a,b), 13.12, 13.13, 13.14

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.


The "Muscle Mass", "Computer Learning", "Cosmetics Sales", "Weight/Height",
"Patient Satisfaction", "Enzyme Kinetics" and "Drug Responsiveness" 
data can be found on the course web page.