Interpreting main effect and interaction I am doing a simple marketing project that has the following types of variables:


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*X1 - continuous (e.g. income)

*X2 - categorical (e.g. gender)

*Y - continuous (e.g. number of a product type purchased such as tubs of ice-cream) 


I am interested in the relationship between income (X1) and product purchase (Y) but also the effect of gender (X2) on this relationship. (i.e. interaction or moderation effect).
I have centered X1 and have used the general linear model in SPSS. The result on Y is as follows:


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*X1 - significant

*X2 - not significant

*X1*X2 - not significant


How do I interpret this result in terms of main effect and interaction?
 A: Your results suggest that there is no interaction--you simply have a main effect of X1.  You could say something like, "The number of tubs of ice-cream people buy is related to their income.  For instance, if person A's income is one unit higher than person B's income, person A typically buys $\beta_1$ more tubs of ice-cream than person B.  Our data suggest that this relationship between income and ice-cream buying is similar for both men and women."
(Incidentally, if your response variable is a count, you should use Poisson regression rather than the general linear model, but I don't know if that's just your example.)
A: In general, you should not base your model selection solely on statistical significance. Substantive meaning is more important.
In this particular case, you can graph the predicted values for males and females, with the x-axis being income and the y-axis the number of items bought, and a line for each gender.
@gung makes a good point that, if the y-variable is a count, you should use an appropriate model, such as Poisson regression, or, more likely, negative binomial regression, since over-dispersion is very common in count regression.  
