Testing two independent variables (categorical and interval) and interactive effects on continuous data?


I'm not sure if there is an actual statistical test for this, but I want to see how Side (Left or Right, categorical) and Depth (Interval, fixed at every 250, but I don't have data for all depths) affect a continuous parameter I have.

I initially tried a multiple linear regression, I am not sure if this was the correct way to go due to the nature of my IV. I have tried a factorial ANOVA, but it doesn't quite give me enough information, i.e. exactly how side and depth interact. As I have so many variables, i.e, my maximum depth 3700, a Tukey HSD and Bonferroni aren't very helpful.

Is there a different test I should be looking at?

EDIT - A very important thing I missed out, my DV is not normally distributed!
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