any chance we actually have to know this formula or just know that it’s used to fix the issue of overestimating the impact on adding additional variables. adjusted r^2 < r^2

adjusted r2 is not always < r2. Just read that up. adjusted r2 is a multiple regression equation reflects the impact of adding on additional independent variables - and need not always be < r2. and if you thought about it, that formula is not so huge. 1 - (1-r^2)*(n-1)/(n-k-1)

adj r^2 less than or equal to r^2 the formula is pretty straight forward adj r^2 = 1 - [(1-r^2)(n-1/n-k-1)]

It looks true that adj R^2 <= R^2. It also says: while adding a new indep. variable to the model will increase R^2, it may either increase or decrease the adj. R^2. In addition, the adj. R^2 may be less than 0 if R^2 is low enough. Weird for me again, imaginary correlation?

q bank says that adj R^2 is always less than R^2 when there is more than one independent variables. i guess this makes sense given that as k increases in the formula, adj R^2 decreases. this formula doesn’t seem that bad anymore. just yet another piece of obscure information to store for test day and forget immediately after.