CFA Practice Question

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CFA Practice Question

Which of the following are true?

I. If k = 1, adjusted R2 is greater than or equal to R2.
II. When an additional variable is added to a model, adjusted R2 can decrease.
III. k + 1 is the number of regression parameters.
IV. If k > 1, adjusted R2 ≤ R2.
Correct Answer: II and IV

I. Adjusted-R2 is always ≤ R2.
II. Although SSE will decrease when an extra explanatory variable is included, so will the term (n - K - 1). Thus the tem SSE/(n - K) can increase or decrease.
III. k is the number of regression parameters.
IV. R2 is always ≥ adjusted R2.

User Contributed Comments 7

User Comment
johans you would expect if it is N-k-1 instead of N-k that adjusted R^2 < R^2 if k = 1 ...
solnce Both an intercept and slope coeffiecients are regression parameters.
katybo or also "regression coefficients"
bmeisner I have to agree with johans, given the equation, adjusted R^2 ought to be <= R^2 even if k=1. This is because the fraction (n-1)/(n-k-1) is just (n-1)/(n-2) which gives a number less than 1.
annwwar (n-1)/(n-2) > 1 for n>2
weiw Why III is wrong. K is the number of independent variables and K+1 should be the regression parameters, am I right?
ericczhang Yeah I count the constant as a regression parameter so k+1 should be the number of parameters. I think this is just a case giving them the answer that they think it's right.
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