# Regression for continuous dependent variable with independent ordinal variable

My situation is as follows: as a teacher, I've given students the option to make 5 sets of homework during the year, which does not count for their grade, but solely to practice and receive feedback; in hopes to prepare them better for their exam.

For every student I now have two lists: how many of the sets of homework they have made (so an integer from 0 to 5) and their exam grade (between 0 and 10). The number of homework made is severely skewed: 66% of the values are 5, 20% are 4, the rest is 0,1,2 or 3. The grades aren't rounded so can (probably?) be treated as continuous and according to Shapiro-Wilk they are distributed normally.

I'd like a good way to measure the impact of the number of homework made on the final grade, and if possible apply regression. I applied linear regression and calculated the Pearson R-coefficient, but is this a good method considering the ordinal variable? Or should I apply a transformation to the homework, or use a different kind of regression altogether?

• For ordinal variables potentially looking at the rank correlation (eg. Spearman's $\rho$) can be more appropriate. Having said that, you seem to have a typical ordinal regression task. Check the functions clm from the package ordinal and polr from MASS. – usεr11852 Jan 30 '16 at 18:39