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How to Interpret Regression Results

Now that you are familiar with how to create dummy-coded variables, we will discuss how to interpret your regression results. Below is the SPSS output using the marital status groups to predict the frequency of religious attendance using multiple regression. Below the regression output, there is also the SPSS output that shows the mean for religious attendance for each of the marital status groups.

SPSS output using the marital status groups to predict the frequency of religious attendance using multiple regression.

Coefficientsa

SPSS output that shows the mean for religious attendance for each of the marital status groups.

Descriptives HOW OFTEN R ATTENDS RELIGIOUS SERVICES

Let’s focus on the unstandardized regression coefficients in the output. Each coefficient will indicate how that particular group compares to the reference category (e.g., married) on the dependent variable. The coefficient reflects the comparison between the mean value of the dependent variable for the reference category and the mean value for the group represented by that particular coefficient. For example, first, take a look at the unstandardized regression coefficient for “divorced” (-1.239). This value reflects how the divorced group compares to the married group on religious attendance and indicates that the mean religious attendance for the divorced group is 1.239 units lower than that for the married group. 

A few more things about the output:

• If you subtract the mean for divorced (3.09) from the mean for married (4.33), you can see that you get the absolute value of the coefficient for the divorced variable: 4.33 – 3.09 = 1.24.  (If you round 1.239, you get 1.24.)  

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  If you subtract the mean for divorced (3.09) from the mean for married (4.33), you can see that you get the absolute value of the coefficient for the divorced variable: 4.33 – 3.09 = 1.24.  (If you round 1.239, you get 1.24.)  

• If the value had been positive (1.239 instead of -1.239), it would indicate that the divorced group had a higher mean than the married group on the dependent variable.  

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  If the value had been positive (1.239 instead of -1.239), it would indicate that the divorced group had a higher mean than the married group on the dependent variable.  

• Similar to when you are interpreting the coefficients for continuous predictor variables in a regression model, the difference between the reference category and the indicated group is only considered to be statistically significant if the p-value is less than alpha.  In our results above, if we assume an alpha of .05 (or even .01), each predictor would be statistically significant, indicating that each group (divorced, never married) differs from the reference category of married on the dependent variable.

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  Similar to when you are interpreting the coefficients for continuous predictor variables in a regression model, the difference between the reference category and the indicated group is only considered to be statistically significant if the p-value is less than alpha.  In our results above, if we assume an alpha of .05 (or even .01), each predictor would be statistically significant, indicating that each group (divorced, never married) differs from the reference category of married on the dependent variable.

• Also similar to when you are interpreting the coefficients for continuous predictor variables in a regression model, you can use the absolute value of the standardized regression coefficients to gauge the effect size for each variable; values closer to 0 indicate weaker effects, and values closer to 1 indicate stronger effects.

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  Also similar to when you are interpreting the coefficients for continuous predictor variables in a regression model, you can use the absolute value of the standardized regression coefficients to gauge the effect size for each variable; values closer to 0 indicate weaker effects, and values closer to 1 indicate stronger effects.

Hint: Remember that the unstandardized regression coefficients reflect a comparison to the reference category about the mean value of the outcome variable.

Take a look now at the unstandardized regression coefficient for never married (-1.19). What would be an appropriate interpretation of this value?

The never married group mean for religious attendance is 1.19 units lower than the mean for the divorced group.

The never married group mean for religious attendance is 1.19 units higher than the mean for the divorced group.

The never married mean is 1.19 units lower than the married group mean for the dependent variable.

The never married mean is 1.19 units lower than the married group mean for the independent variable