Statistical Methods for Psychology

for the two models. Instead we are going to use Akaike’s Information Criterion (AIC),

which is based on a likelihood ratio statistic that we will not explore. To compute Akaike’s

AIC statistic using SPSS you need to resort to tampering with the syntax, but that is fairly

simple. You simply set up the regression as you normally would, being sure to ask for at

least one statistic (e.g., descriptive statistics). Then instead of submitting the analysis di-

rectly, choose the Paste option and edit the resulting syntax by adding “selection” to the

statistics subcommand. If you do this for the two models, the model using PctSAT will give

you the following summary.

546 Chapter 15 Multiple Regression

Model Summary

Selection Criteria

Model R R Square Adjusted Std. Error Akaike Amemiya Mallows, Schwarz

R Square of the Estimate Information Prediction Prediction Bayesian

Criterion Criterion Criterion Criterion

1 .905a .819 .812 32.459 350.906 .204 3.000 356.642

aPredictors: (Constant), PctSAT, Expend

Model Summary

Selection Criteria

Model R R Square Adjusted Std. Error Akaike Amemiya Mallows, Schwarz

R Square of the Estimate Information Prediction Prediction Bayesian

Criterion Criterion Criterion Criterion

1 .941a .886 .881 25.781 327.869 .128 3.000 333.605

aPredictors: (Constant), LogPctSAT, Expend

The model using LogPctSAT will next give you the following summary.

With Akaike’s AIC, smaller is better. Notice that you have a noticeably smaller AIC when

LogPctSAT is the predictor. Unfortunately there is no statistical test to tell us whether

327.869 is significantly smaller than 350.906. You will just have to take my word for it that

using the log of the percentage of students taking the SAT is preferable.

15.11 Constructing a Regression Equation

A major problem for anyone who has ever attempted to write a regression equation to pre-

dict some criterion or to understand a set of relationships among variables concerns choos-

ing the variables to be included in the model. We often suffer from having too many

potential variables rather than too few. Although it would be possible to toss in all of the

variables to see what would happen, this solution is neither practical nor wise. We have al-

ready seen that tolerance and the variance inflation factor can be useful in helping us to

identify variables that are highly correlated with each other and thus redundant when it

comes to predicting Y. But we also have other ways of optimizing our equation.

Selection Methods

There are many ways to construct some sort of “optimal” regression equation from a large

set of variables. This section will briefly describe several of these approaches. But first we

Akaike’s
Information
Criterion (AIC)