# Question about redundant categorical predictors in regression

I have two categorical predictors (one is binary, one has six categories) that I'd like to include in a regression. However, it seems to me that they must be correlated in some way, by looking that the following contingency table in R:

         1   2   3   5   6   7
0   1  76  28 108   1  19
1   0   0 273   0   1   2


It seems that knowing I'm in category 1 in the binary predictor tells me I'm likely in category 3 in the six-category predictor i.e. one predictor seems to predict the other predictor to some extent. If I wanted to include both of these in a regression since I know they're both important, what would be a good way to proceed? Could I somehow combine them?

• What's wrong with just including them both? Correlated predictors are practically unavoidable and not necessarily the end of the world. – dsaxton Mar 22 '16 at 3:40
• Can't doing this effect the variance of the estimates? – roccomay Mar 22 '16 at 4:09
• It increases the variance, yes. – dsaxton Mar 22 '16 at 14:00
• So isn't the point to try to limit the effect of them, if possible? – roccomay Mar 22 '16 at 16:38