Without a reproducible example, called a reprex, my answer is necessarily general.

Your table `Y`

has two variables, which I'll call `title`

and `industry`

. Formally, you want to know E(title | industry), the expectation of title given industry. You can of course *count* each combination and then do an `ANOVA`

or other form of contingency table to see how far that gets you. A simple `t.test`

might show so little association as to make `Y`

unhelpful.

But let's assume that there is some substantial nexus between the two. Can you model it? Since the outcome variable Y is multinomial categorical and the industry covariates X_i ... X_n are, also, you can't do OLS. (Well, you can, sort of, but only econometricians go there.) Which means logistic regression, for which you'll need to create a lot of dummy binary variables to represent whether a given title observation is classified as in an industry.

That would give you a usable model to apply to table `X`

, but the way described your unknown is not *industry* but *job function*. Before much progress is likely, the best advice I can offer is to go back to defining the problem more closely.