Assumed knowledge
Data files
Multiple regression in action
 What's your life expectancy? Work it out
using this Life
Expectancy Calculator
 According to this multiple regression equation, what could you
do to improve your life expectancy?
 Estimate the unstandardised regression coefficients for each of
the variables you could change in order to increase your life
expectancy.
 A psychologist studying perceived "quality of life" in a large
number of cities (N = 150) came up with the following equation using
mean temperature (Temp), median income in $1000 (Income), per capita
expenditure on social services (SocSer), and population density (Popul)
as predictors:
Y (predicted) = 5.37  0.01Temp + 0.05Income + 0.003SocSer  0.01Popul
 Interpret the regression equation in terms of the coefficients 
in other words, what is the effect of each of the IVs on the Y
 Assume a city has a mean temperature of 55 degrees, a median
income of $12,000, spends $500 per capita on social services, and
has a population density of 200 people per block. What is the
predicted Quality of Life score?
 What would we predict in a different city that is identical in
every way except that is spends $100 per capita on social services?
(see Howell, p.550551 for answers)
General advice
The general recommended strategy for tackling Multiple Linear
Regression analyses is:
 Check assumptions (see below)
 Conduct a multiple linear regression (standard, hierarchical, stepwise,
forward, or backward)
 Interpret the technical and psychological meaning of the results,
based on:
 R, R^{2}, Adjusted R^{2}, the
statistical significance of R
 Changes in R and the significance of the changes if steps
(i.e., more than 1 model are used)
 Standardised and unstandardised regression coefficients for each
model
 Zeroorder and partial correlations for each IV in each model
 If useful, interpret Yintercept and write a regression equation
for predicting Y
Checking Assumptions
 Check histograms of all variables in an analysis
(are the variables normally distributed?)
 Check scatterplots of the relation between each X variable and the Y
variable
(are the relationships linear? is there homoscedasticity?)
 Check correlation table for linear relations between Xs and Y
(are the XY relationships linear? check for multicollinearity between Xs?)
 Check influential outlying cases using Mahalanobis
distance & Cook’s D.
 In the Linear Regression box, click on
Save and select Mahalanobis and Cooks. SPSS will
create new variables in your data file called mah_1 and coo_1 once you
run the analysis.
 In your output check the Residuals Statistics
table for the maximum Mahalanobis distance and Cook’s distance.
 The
maximum Mahalanobis distance should not be greater than the critical
chisquared value with degrees of freedom equal to number of
predictors & alpha =.001.
 Cook’s D should not be greater than 1. If
you detect any outliers on either measure, consider removing the case
from you analysis.
 In your output check the collinearity statistics in
the Coefficients table. The Variance Inflation Factor (VIF)
should be <3 and tolerance should be >.3.
Francis exercises

5.1 (Worked example)

Exercises
Multiple regression in excel
