Calculate impact of the mean of several groups on respective members of this groups

Hi there,

I am stuck with the following problem:

I have asked students about the perceived international orientation of their university and would like to see if that has an influence on their intercultural competence (DV). Now if I run a linear regression between the two scores, the result is not significant. But as this only measures the impact of each students' individual impression on his/her intercultural competene score, I was wondering if there was a way to use the median score of the international orientation of the different universities as independent variable instead.

So uni A has a total median score of its international orientation of M = 3,6, uni B of M = 3,9, uni C = 4,1 etc. I would like to see if THAT score has an impact on the respective students' intercultural competence score (which in this example is significantly higher for students from uni C than uni A). Is it possible to make a new variable with these values, and if yes, how? Or is there another way?

Thanks ahead for your help!

Anyone an idea on how to do this?

So basically I would like to measure the impact of the international orientation of a university on its students' intercultural competence skills (the independent variable being the mean of all answers from students' enrolled at that university).

It would be great if someone could help me with this one!