Multiple regression

Multiple regression includes a family of techniques that can be used to explore the relationship between one continuous dependent variable and a number of independent variables or predictors. Multiple regression can be used to address questions such as:

• how well a set of variables is able to predict a particular outcome.
• which variable in a set of variables is the best predictor of an outcome.
• whether a particular predictor variable is still able to predict an outcome when the effects of another variable are controlled for.

This is the most commonly used multiple regression analysis. All the independent variables are entered into the equation simultaneously. Each independent variable is evaluated in terms of its predictive power. This approach would also tell you how much unique variance in the dependent variable is explained by each of the independent variables.

1. Click on Analyze\Regression\Linear.
2. Move your continuous dependent variable into the Dependent box.
3. Move your independent variables into the Independent box.
4. For Method make sure Enter is selected.
5. Click on the Statistics button and select: Estimates, Confidence Intervals, Model fit, Descriptives, Part and Partial correlations and Collinearity diagnostics.
6. In the Residuals section, select Casewise diagnostics and Outliers outside 3 standard deviations. Click continue.
7. Under Options, select Exclude cases pairwise. Click continue.
8. Click on the Plots button, click on *ZRESID and move it into the Y box. Click on *ZPRED and move it into the X box.
9. In the section headed Standardized Residual Plots, tick the Normal probability plot option. Click continue.
10. Click on the Save button. In the section labeled Distances, select Mahalanobis box and Cook’s.
11. Click on Continue and then OK.

Note: before interpreting results of multiple regression, it's important to check that a number of assumptions are met. For more information, consult the Further resources section of this guide.

Evaluating the multiple regression model

The value given under the heading R square tells you how much of the variance in the dependent variable is explained by the model (independent variables or predictors). In this example, the independent variables included in the model explain 31.0% of the variance in the dependent variable.

Reprint Courtesy of International Business Machines Corporation, © International Business Machines Corporation. SPSS Inc. was acquired by IBM in October, 2009.

Significance of the model

The statistical significance is given by the Sig value in the ANOVA table.

Reprint Courtesy of International Business Machines Corporation, © International Business Machines Corporation. SPSS Inc. was acquired by IBM in October, 2009.

Evaluating each of the independent variables

The Beta values indicate which variable makes the strongest unique contribution to explaining the dependent variable, when the variance explained by all other variables in the model is controlled for. For each variable, check the Sig value to assess whether the variable is making a statistically significant unique contribution to the model.

Reprint Courtesy of International Business Machines Corporation, © International Business Machines Corporation. SPSS Inc. was acquired by IBM in October, 2009.