To compute the correlation (R) of two variables you need to know their variances ( or standard deviations S1, S2) and their covariance S12 so that R is computed as: R=S12/(S1.S2). A nominal variable has the same value for all pixels of the same category and therefore, a zero variance. A continuous variable has different values for each pixel in the same category with a mean value and a non zero variance. Therefore the covariance of two such variables is zero and there is no way to do correlation analysis.

Dear John

Thank you for your answer. Yes, perhaps association is more meaningful than correlation. I think it is possible that various categories of LU be more related to specific values of a continuous variable.

If other members also have other opinions or solutions, I'll appreciate it if they contribute. 

Thank you

In case of association, you may also take an equivallent nominal value and see at a certain probability level in which interval of continuous values fits best. Let us take k as an equivallent nominal value, then compute x so that P(k-x