# Residual analysis and two-way interaction terms

I'm a bit confused on some of the terminology involved in my assignment, which is shown in the following image: I understand the main idea behind residual analysis is checking if the main assumptions are in line. This usually involves plotting residuals against fitted values and getting a normal probability plot for general diagnostics. The assignment is specifically asking to check if the two-way interaction terms (in relation to the residuals) are necessary for the model.

My main questions are: What exactly is a two-way interaction term? What characteristics of the residuals justify a two-way interaction term?

• Are all your IVs factors? – Glen_b Oct 24 '16 at 4:56
• What exactly do you mean with IVs factors? – user135934 Oct 24 '16 at 5:08
• You have a y-variable (response, dependent variable) and two predictors/ x-variables/*independent variables*. Are those two independent variables "grouping" variables (like say treatment group or sex -- i.e. factors) or are they - by contrast - numeric (like say 'dosage in ml')? – Glen_b Oct 24 '16 at 5:15
• Or more briefly, please describe the variables in your problem more clearly – Glen_b Oct 24 '16 at 5:17
• In my regression Data I only have numeric values for my independent variables. I am inept to describe the technical specifics. But in this assignment I am running a regression for Patient Satisfaction as a response variable with Age, Illness severity and Anxiety level as quantitative levels represented numerically as predictors. – user135934 Oct 24 '16 at 5:17

## 1 Answer

From Wikipedia: An "interaction variable" is a variable constructed from an original set of variables to try to represent either all of the interaction present or some part of it. In exploratory statistical analyses it is common to use products of original variables as the basis of testing whether interaction is present with the possibility of substituting other more realistic interaction variables at a later stage.

Based on this definition, wouldn't the magnitude of your residual be significantly different with and with out the interaction term?