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?

Thanks in advance.

  • $\begingroup$ 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. $\endgroup$
    – usεr11852
    Commented Jan 30, 2016 at 18:39

1 Answer 1


As a pragmatic approach to handle dual character of an ordinal variable,(categorical and continuous) is a calibration. Otherwise. it will be complex to work with a set independent standards due to levels from an ordinal variable.

So the continuous dependent variable needs to be re-scaled to one chosen level from the ordinal variable. After calibrate it from all levels to one chosen level, there is a re-scaled set as if the dependent dataset is based at one level. The categorical character of the ordinal variable can be disregard. Then a regression is possible with the re-scaled set with "ordinal" variable as continuous variable. Any conclusion from regression can be translated back by "un-scaling".


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.