Computer lab 3: Multiple regression – standard analyses
Multiple linear regression models are used to examine the relationship between a response variable
y and several explanatory variables x1, x2... xp-1. The models are natural extensions of simple linear
regression models and will not be further commented here.
Learning objectives
After reading the recommended text and completing the computer lab the student shall be able to:
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Formulate a multiple linear regression model and interpret the model parameters;
Write the regression model in matrix form;
Make inference about the model parameters (including simultaneous statements);
Compute and interpret confidence interval for the expected response and prediction interval
for a new observation at given levels for the explanatory variables;
Use different diagnostic procedures (often plots) for the evaluation of the regression model.
Recommended reading
Chapter 6 in Kutner et al.
Assignment 1: Standard regression analysis
Consider the data set in exercise 6.18 in the textbook and carry out the exercises 6.18 a-e (skip the
analysis of two-factor interaction in “e”), 6.19 and develop prediction interval and confidence
interval for property 1 in 6.20. Don’t give all plots in 6.18, but choose some important ones and
comment the rest in the text.
Assignment 2: Matrix formulation of the regression model
Give the matrix formulation of the regression model in exercise 6.18. Print out the response vector Y
and the design matrix X.
Assignment 3: Further analysis
Apparently, the explanatory variable x3 is not significant in the regression model above. It then
seems natural to reduce the regression model in 6.18 by excluding x3. Fit the regression model with
x1, x2 and x4 as explanatory variables. Compare the obtained values of the F-test and R2 from this
model with the model obtained from assignment 1 and comment.
To hand in
Answers to assignments 1-3, including output from assignment 3.
The lab report should be handed in no later than 5 days after the scheduled computer lab. Use Lisam
(lisam.liu.se) for handing in the assignments.