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Default Multiple regression on conjoint anaysis data

Hello! I've run a conjoint experiement with 110 samples, and am having
trouble figuring out how to analyze the data.

I have 15 "sets" of the product variation, each with 5 attributes, or
variables. Each respondant rated each of the 15 sets on a scale of 0 -10. I
can easily run a regression for one respopndant to get their regression line,
but how do I run a regression for all 110 respondants to get a regression for
ALL of them?

The only solution i can come up with right now is to run each one
individually, then average the coefficiants of each variable in the equaiton.
Please tell me there is an easier way!!
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