STAT 704 Fall 2026
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Homework 6
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Do the following problems from the textbook:
(See notes below for the parts with asterisks)

10.1, 10.3, 10.8, 10.9(a*,c,e*), 10.12(a*,b,c*,d*), 10.26.
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 lm.ridge with 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?
(d) Verify that the optimal lambda (based on GCV) over a range from 0 to 10 is around 5.2.
How do the estimated coefficients change if we use lm.ridge with lambda=5.2?
(e) Load the glmnet package in R and fit a LASSO regression of Y against X1, X2, and X3, 
choosing the lambda by cross-validation.  How does the fitted LASSO regression equation 
compare to the ridge regression result in (b)?

***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?

NOTE: For 10.9(a) & 10.12(a), you should also find the 
internally studentized residuals and compare 
their absolute values to 2.5 as well as doing the
Bonferroni outlier test with the externally studentized residuals.  

For 10.9(e) and 10.12(d), don't worry about the DFBETAS.

NOTE:  For 10.12(c), we did not do an example like this in class, 
but this can be done most easily using R. After you fit the regression model
with the 'lm' function, you can extract the model matrix X with the model.matrix() function.
Then you can manually create a vector xnew (don't forget the 1 for the intercept term),
and you can do the matrix calculations in Equation (10.29) in R, noting that t() finds the
transpose of a matrix or vector, and solve() finds the inverse of a matrix.

NOTE:  On page 359 and page 433, the book's notation sigma^2{.} is
equivalent to: var{.}

The "Computer Learning", "Cosmetics Sales", "Weight/Height",
and "Commercial Properties" 
data can be found on the course web page.

Please write your answers neatly and clearly!