Homework
Homework exercises will be assigned throughout the summer session. These exercises will be discussed in class, but
will not be submitted for grading.
The due dates given below refer to the date of the class discussion.
due June 9
1) (Introduction to R)
Use R to execute all of the commands in
the command file that I started discussing in class on June 7.
due June 14
2) (Bayes classifier) Suppose that for class 0 X has a uniform (0, 1) distribution, and for
class 1 X has a beta distribution having pdf
f(x) = 2x I(0, 1)(x).
Assuming that cases to be classified are just as likely to
come from class 1 as they are class 0, obtain the Bayes classifier and give its error rate.
Also give the Bayes classifier and its error rate if cases to be classified are twice as likely to come from class 1
as they are class 0.
due June 23
3) (Sampling distribution of nearest neighbor)
Do Ex. 2.3 in HTF (which is to derive equation (2.24)).
4) (CART Walkabout) Go through the
Interactive Walkabout for CART. (It takes 30
minutes or so to go through it
carefully.) Make a note of any questions that you may have about it, and I will try to answer
some of your questions in class. (Note: It seems to me that the Walkabout may pertain to a slightly
older version of CART. I don't think it's necessary to specify so much information about the target
variable for classification and other categorical veriables --- I think that the latest
version of CART figures out that information on
it's own.) (I wonder if the variable importance values given by CART by would be useful for selecting
predictor variables to be used in k-nearest-neighbors classification --- one wouldn't want to let weak predictors
contribute the same as strong ones in determining the distances, and so some way of omitting weak predictors would be
good.)
5) (Tactics for multiple regression when there are a relatively large number (compared to the sample size) of
explanatory variables) Go through the R example I have pertaining to the lasso, ridge regression, and
principal components
rregression, and also go
through the R example I have pertaining to the example introduced on p. 17 of HTF.
Make a note of any questions that you may have about them, and I will try to answer
some of your questions in class.
due June 28
6) (Linear regression spline)
Go through the R example I posted on the lecture supplements web page, but without looking at it, use R to fit a
linear regression spline for the data used in the example (using knots at 30, 60, and 90), and use the software output
to produce a piecewise expression for E(Y|x), with each piece being of the form ax + b.
7) (Cubic splines for regression modeling) Go through the R example I have pertaining to the use of natural cubic
splines in a multiple regression
setting.
(Here is some information about the data used in
the example.)
due June 30
8) (MARS Walkabout) Go through the
Interactive Walkabout for MARS.