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.