Im doing research on the effect of salary inequality on team performance in the Major League Soccer, seasons 2007-2014. So for every season, I have data of all the salaries of all the teams, so I created some gini coefficients to measure the income inequality. For team performance/succes, the share of points of a team per season is used. But now, since I have several seasons, and the number of teams participating in the competition during every season changes, I have to take this into account. Having more teams in the competition, means that obviously, the mean share of points will be lower.
Also, for the salary inequality, I created a variable which captures the relative salary inequality: the gini coefficient of a team divided by the total of the gini coefficients of all teams, per season.
So, to see how these variables are connected, is it best to perform just a linear regression? (Using the scatter plot, I think the relationship is somewhat linear) And, for this number of teams per season problem, can this be simply accounted for by including dummies for the seasons? Because I tried it, and the coefficients of these dummies makes sense, but it seems so simple. Or should I try just a completely different modeling approach/model?