Quant - R2, F-stat, adjusted R2 increase, adjusted, decrease, number, either

maratikus

as you increase the number of variables why does R2 increase and the F-stat and R2 adjusted either increase or decrease?

yalo

Because you can keep adding variables even though the relationship is spurious. It all comes down to the relationship of the performance of the S&P to the growth of a tree theory. If you have a fundamental factor model that tries to predict the return of the S&P and you add a coefficient related to the growth of a tree, R^2 will increase.

NO EXCUSES

ningning1984

If I ask you whether your salary is related to your level of education, you will probably say yes, somewhat (a weak R2). Now add years of experience. You would say yes, that help explain salary. Add gender. Yeah, that adds to it too. Add person's height, weight, looks, etc, even seemingly unrelated ones, like color of your car or your knowledge of Greek history....they will probably increase R2, but are they all justified?

I'm not sure about the other statement about F-stat and adjusted R2 decreasing.

19831985

Dreary

Thanks for correcting the formula.

I only have Schweser Notes of 2009.

I see on Pg 187 in the middle of the page..

they make the following statement:
1. when there is more than 1 indep. var - adj_R^2 <= R^2
2. Adding an indep. variable may increase R^2.
If R^2 increased - Ra^2 (given the (1-r^2) in the formula) would decrease.
But if R^2 decreased - Ra^2 might increase.

If R^2 gets low enough -> Ra^2 may be negative or even 0.

So Ra^2 might increase or decrease.

CP

SeanWest

"If R^2 gets low enough -> Ra^2 may be negative or even 0. "

If it is negative it is treated as zero , in the footnotes in bottom of page in CFAI text