I included an interaction term Gender with my model with several variables that I assumed would differ by gender and saw an increase in the R squared value. No effect on adjusted R squared though.
Well, there are a number of reasons this can occur. A simple explanation would be that R-squared is a function of your between-group sum of squares relative to your total sum of squares, or put another way, the ratio of the variance explained relative to the total variance in the model. When you add another variable, even if it does not significantly account additional variance, it will likely account for at least some (even if just a fracture). Thus, adding another variable into the model likely increases the between sum of squares, which in turn increases your R-squared value. To see what I am talking about, run the model without the interaction and look at the between-group sum of squares in the output - then run the model with the interaction included and check again the between-group sum of squares. That is the most basic (and perhaps plausible explanation), although there could be a few other reasons this is occurring. But I'd bet this is it.
Cheers.
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