I am running an experiment. There are two features: Gender and Area.
Gender has two levels (Male/Female) and Area has four (North/South/East/West).
The dependent variable is height. My sample size is really big (about a million people).
My goal is to find out whether/how much of the difference in height between men and women is due to the area they live in.
Because the data groups are of different sizes, and I can't guarantee normality of distribution of homogeneity of variance, I didn't think I could use ANOVA. Instead, I was trying to use linear regression with dummy variables and check whether the interaction terms were significant. I got this idea by reading https://en.wikipedia.org/wiki/Dummy_variable_%28statistics%29#Interactions_among_dummy_variables.
Is this the right approach, and if so, how do I find out whether the individual coefficients are significant if I have a really large data set? I have read about some examples involving popular statistics packages that gave a std. error, t-statistic and p value, but given how much data I am using I wasn't sure they would be able to handle it. I know there are faster ways to get (or at least to accurately estimate i.e. stochastic gradient descent) just the coefficients, but I don't know about the standard error.