Hi everyone, hoping I can pick your brains.

I've used hierarchical cluster analysis and k-means to develop a 3 cluster solution in SPSS. I want to determine the extent to which contextual factors predict cluster membership (e.g., gender, year at school) and how the clusters are differentially associated with outcomes. What do I need to do to work this out? Is it multinomial logistic regression?

I tried using linear regression to examine one of the covariates, but I don't know how to interpret the coefficient because I'm not sure it's actually looking at what I want it to.

Any help would be so appreciated!