SEE vs. R2

CFA Level II
#1

Could you say that there is a inverse relationship between SEE and R2?

Or are there situtations where the SEE and R2 are not related to eachother. If so, could you provide an example?

I feel like if SEE increases, variation of residuals increases as well meaning the line would not be as good of a fit for the y variable and thus have a lower R2, but I am not sure if there are examples that would make this into a non definitive relationship/instance where this relationship is not true at all. Thanks in advance.

#2

The answer is a round YES. Just look at the approximation formula for SEE calculation at the book:

SEE = Square Root( SSE / n-2)

Thus, SEE is directly related to SSE.

R2 is inversely related to SEE because, looking at the R2 calculation formula, R2 is just:

R2 = ( SST - SSE ) / SST

Hope this helps!

#3

Also: Adjusted R-squared is the same as:

1 - ([SEE^2]/Var(Y))

…Since SEE^2 is the (estimated) variance of the errors of prediction and Var(Y) is the total variation in the DV…just use a small amount of algebra to rearrange the clunky formula in the book to get the one above…

For reference…

SSE/(n-k-1) = Var(Error)

SST/(n-1) = Var (Y)

SEE = Var(Error)^0.5