Homework 3
STAT 8320
Due March 21, 2007
Problem 1: The following four measurements were made upon three species of iris (Fisher
1936):
y1= sepal length, in mm.
y2= sepal width, in mm.
y3= petal length, in mm.
y4= petal width, in mm.
The data are attached in the file labelled problem 1. Additionally, they are an example data
set in SAS. These data will be used to perform a discriminant analysis.
a. First, perform a linear discriminant analysis on the complete data, assuming that the
variance-covariance matrices are equal. Talk about the assumptions that you use. Addition-
ally, discuss the resubstitution error estimates; specifically what is the estimate of the error
rate, and what are the possible problems with using this procedure.
b. Next, select 10 observations from each of the three species at random. Use these 30
observations to form a test set. Use the remaining observations to form a linear discriminant
rule. Consider the measures of error from both resubstitution and based upon the test data
set. Discuss their relative merits, and any differences in your conclusions.
c. Finally, perform the analysis without assuming that the covariance matrices are equal.
Look at the error rates from resubstitution and cross-validation. Discuss the differences
between these methods. Additionally, what can you say about the assumption of equal
variance-covariance matrix?
Problem 2: Suppose that we have data which we believe has arisen from the nonlinear
model
Yi=θ1xθ2
1iexp(θ3x2i) + ²i
1
