If I have a model, lets say y = a + b1male + b2large + b3medium + b4malelarge + b5malemedium where male is dummy coded 1 for male and 0 for female and large and female are dummies (also 0,1 coded) for company size with small as reference categorie, how can I test whether the effect of male varies significantly with company size?
I presume that the t-test for the coeffs tells me the significance of the effect of male on the respective dummy-category compared to the referece category. So e.g. the effect of male varies significantly between large and small companies (=p-value for b4). But since the t-test is always compared to the reference group, how can I test "in general" whether the effect of male varies with company size?
My intuitive approach would be, to run a hierarchical regression with the interactions included in the second block. So if the change in R² is significant, this would mean that the interaction of at least one categorie of the dummy is significant. Is this correct?
And how can I figure out, which categories show sig. differences. Thats particularly hard if I have a large number of categories of one dummy. Do I have to run regressions and change manually the reference category?