Individual vs. Team Aggregated Data

[JeremyPiven]

I have a set individuals (let's say ID_No 1 through 50) and a set of metrics that pertain to these individuals: things like age, SAT reading score, SAT math score, a motivation index metric, etc.

These individuals are also aggregated into teams (let's say ID_No 1 though 10 is team 1, ID_No 11 through 20 is team 2, etc.). Now for these teams, I have a set of performance metrics on a collective test that each team completed together; so for instance, team 1 scored a 89/100, team 2 scored a 75/100, etc.

I'm simply running a multivariate regression of the individual characteristic metrics against the team performance metric.

But my question is whether it's more appropriate to:

1. Find the average of each characteristic metric (e.g., SAT scores, age) for all individuals on a team and assign that average to each team. In this case, n=5 (the number of teams). So the regression would look like:​

MODEL team_score = team_avg_age team_avg_math team_avg_read ...​

OR

2. Assign the team performance metrics to each individual. In this case, n=50 (the number of individuals), and the same team score would be shared by all of the individuals on that team. So the regression would look like:​

MODEL team_score = age math read ...​

I have played around with some dummy data that I created, and I know there is a difference in the results, but I'm not sure which result is more valid. I'll also be completing simple bivariate regressions and probably PCA on this same data.

Thanks!