标题: R2 vs. Adjusted R2 [打印本页] 作者: anshultongia 时间: 2011-7-13 16:24 标题: R2 vs. Adjusted R2
Can somebody please help me understand this conceptually?作者: troymo 时间: 2011-7-13 16:24
It's just saying that R2 will rise the and indicate a better fit as you add more independent variables but often times, the new variables do sh*t all for helping improve the predictability of the dependent variable but because of the way quants works, the R2 value goes up.
To adjust for this, you calculate adjusted R2 which is just deflated based on N-1/N-k-1 to compensate for the increased number of independent variables.
'Unlike R2, the adjusted R2 increases only if the new term improves the model more than would be expected by chance. The adjusted R2 can be negative, and will always be less than or equal to R2.' (From Wikipedia)
R2 shows the total variation in the dependent variable explained by the independent variables..you want this to be high for a good model. Problem is, R2 will always increase when you add more independent variables, even if they aren't contributing to the model.
Therefore R2 adjusted takes this into account and gives you a more realistic total variation explained. It's always equal to or less than R2..and can actually even be negative in special circumstances.
Hope this helped !作者: zephyranalyst 时间: 2011-7-13 16:24
I would summarize it by:
R2 adjusted usually less than R2
R2 adj = 1 - [ (n-1) / (n-k-1) x (1 - R2 ) ]
R2 adj is better because it takes into consideration the number of indep v.
