# Multiple regression - when to use interaction terms?

I have the equation $$y = \beta_1 + \beta_2 x_2 + \beta_3 x_3 + \beta_4 x_4 + \beta_5 x_5 + \beta_6 x_6 + \beta_7 x_7 + \beta_8 x_8 + \beta_9 x_9 + \varepsilon$$

The dependent variable is weight of child at birth, and independent variables are Age, BMI, Social Class and different types of Vitamin intake.

Clearly there are 2 categorical variables (bmi and social) which I have used SPSS to create dummy variables for. I therefore now have 7 dummy variables (By leaving one out for each).

Must I now include interactions? Im not sure what this means and how this would be incorporated in the model. Do i multiply each dummy variable by every other dummy variable in the model?

• Add self-study tag for assignments. – Michael Chernick Apr 13 '17 at 23:48
• Are you asking when to include interaction terms in a model (in general), or are you asking whether you must include interaction terms because two of the independent variables are categorical (as in your specific case)? – Groovy_Worm Apr 14 '17 at 6:55
• Yes Im looking for both of those answers! I dont know whether for my data, I need to use interactions for the multiple regression? – Btzzzz Apr 14 '17 at 14:14
• Do you have a scientific hypothesis that the effect of BMI (which is a continuous variable by the way) varies by social class? – mdewey Apr 14 '17 at 16:23
• No i have no hypotheses! And BMI is categorical in this case - 1 for underweight, 2 for normal, 3 for overweight and 4 for obese.. – Btzzzz Apr 14 '17 at 16:51

Use GLM module instead of Regression module. SPSS Regression, just like proc reg of SAS, does not handle categorical variable in a friendly way.

Go to Analyze > General Linear Model > Univariate:

Put your outcome in the dependent variable slot, categorical variables into fixed factor slot, continuous variables into covariate slot. Then click "Model."

First, click "Custom" to specify your model. Hold down Ctrl and click on the variables from the list, and transfer them over as "main effect" (you can change that in the middle drop down menu):

And then, specify them as "interaction" by choosing interaction at the drop down menu and then carry over the variables you wish to interact to the right:

Then, click "Continue" and then go into "Option", ask for parameter estimates or you will not get any regression coefficients reported in the output:

Click "Continue" and then "OK". You should be able to get what you are trying to get.

For the technical part now... you can you compute the interaction by hand as well. For two categorical variables with j and k levels, you'll need (j-1)*(k-1) interaction terms. Which can be hard to compute when there are many levels. GLM can automate this process.