Title: Understanding SPSS regression output
Course: UGQuants (SSPS) > Section: Correlation and Regression

Understanding SPSS regression output

It does not take too long to learn how to identify the key parts of the output that we are interested in. The figure below shows the output where the dependent variable is the number of hours per week spent on housework and the independent variable is the number of hours spent in paid work.

When we are evaluating the results of our regressions we are interested in two types of information: the performance of the model as a whole, and the results of individual coefficients.

The first output box of SPSS simply records the model we have constructed, listing the dependent and independent variables:

The second box gives the value for R squared (or R^2).  When we are interested in the performance of the model as a whole, typically we look to the R^2.

This is the coefficient of determination and gives us the proportion of the dependent variable that is explained by the independent variable.  When we are dealing with bivariate regression (in other words when we have only one independent variable) we can use R^2 but when we are comparing models with different numbers of independent variables we typically use the Adjusted R^2 because it controls for the number of IVs in our model. It is therefore good practice to get into the habit of using the Adjusted R^2.

The R^2 (and the adjusted R^2) figure varies between 0 and 1.  The closer to 1 we are, the better the performance of the model as a whole, although across the social sciences there are different levels of acceptance for what makes a ‘good’ model. When we are dealing with aggregate data we tend to expect higher R^2 values than if we are dealing with individual data, largely because individuals are more unpredictable than markets or states (usually).  An R^2 of .32 tells us that 32% of the variation in the dependent variable is explained by the presence of the independent variable(s).

Much as with correlation coefficients, we can distinguish among different levels of strength:

Weak | Below .2
Moderate | .2 to .4
Strong | .4 to .64
Very Strong | .65 and above

If we were to calculate R^2 by hand we would use this formula

r² = 1 minus (the sum of squares of the residuals divided by the total sums of squares)

(these figures are available in SPSS output from the ANOVA table)

The third SPSS output box 'ANOVA', or analysis of variance, reports the sum of squared deviations for the dependent variable (Total), the regression model (regression) and the residuals (residual). If we wanted the values for the variance rather than the sum of squares, we could divide these numbers by (n-1). You can check for yourself that dividing the value for the regression by that for the total will give you the value for r squared.