I need some help in correctly interpreting the results of two regressions calculated for the same data.

The data consists out of several individuals rating multiple classes on n categories like this:

UID | Class | cat_a | cat_b | cat_c | cat_target
1   | A     | 0     | 1     | 0     | 1
1   | B     | 0     | 1     | 1     | 0
2   | A     | 1     | 0     | 0     | 1
2   | B     | 0     | 0     | 0     | 0

All rating data is on a scale of 0/1.

My goal was to calculate a shapley-value regression with categories a-c as predictors of dependent variable cat_target.

However I have two ways of doing this:

  1. Run a regression on the individual case data (considering any unique combination of uid and class a case)

  2. Run a regression with the grouped class data (calculating the average category rating for each class), since I have enough classes this is feasible

The results of both regressions differ strongly in the following regards:

  • Adjusted r² is much higher for the grouped regression (~.7 vs .07)
  • Estimated coefficients and lmg-values differ (e.g. suggesting that cat_a has more predictive value on an individual vs. grouped level)

How can I interpret this correctly? My current intuition would be that they are simply reflecting two different questions:

  1. Can I predict the rating of cat_target an individual will give based on their answers for cat_a-c? (reg 1)

  2. Can I predict the total rating of cat_target for any class based on the total ratings of that class for cat_a-c?

However I have a feeling I am overlooking something and maybe there is even more to it?


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