Introduction to Multiple Regression
Dale E. Berger

Claremont Graduate University http://wise.cgu.edu

Overview

Multiple regression is a flexible method of data analysis that may be appropriate whenever a quantitative variable (the dependent or criterion variable) is to be examined in relationship to any other factors (expressed as independent or predictor variables). Relationships may be nonlinear, independent variables may be quantitative or qualitative, and one can examine the effects of a single variable or multiple variables with or without the effects of other variables taken into account (Cohen, Cohen, West, & Aiken, 2003).

Multiple Regression Models and Significance Tests

Many practical questions involve the relationship between a dependent or criterion variable of interest (call it Y) and a set of k independent variables or potential predictor variables (call them X1, X2, X3,..., Xk), where the scores on all variables are measured for N cases. For example, you might be interested in predicting performance on a job (Y) using information on years of experience (X1), performance in a training program (X2), and performance on an aptitude test (X3). A multiple regression equation for predicting Y can be expressed a follows:

(1) [pic]

To apply the equation, each Xj score for an individual case is multiplied by the corresponding Bj value, the products are added together, and the constant A is added to the sum. The result is Y(, the predicted Y value for the case.

For a given set of data, the values for A and the Bjs are determined mathematically to minimize the sum of squared deviations between predicted Y( and the actual Y scores. Calculations are quite complex, and best performed with the help of a computer, although simple cases with only one or two predictors can be solved by