FRM Part I · FRM Exam Part I · Linear Regression
A multiple regression with 3 explanatory variables is estimated on 25 observations and has an R-squared of 0.60. What is the adjusted R-squared, to three decimals?
Adjusted R-squared is about 0.543. It is one minus the unexplained share of 0.40 scaled by (n-1)/(n-k-1), which is 24/21. That gives 1 - 0.457 = 0.543, lower than the unadjusted 0.60 because it penalises the three regressors.
- A0.543Correct
- B0.564
- C0.600
- D0.650
Explanation
Adjusted R-squared = 1 - (1 - R^2)(n - 1)/(n - k - 1) = 1 - 0.40 x 24/21 = 1 - 0.457 = 0.543. The 0.564 option uses n - k = 22 in the denominator, and 0.650 inverts the degrees-of-freedom ratio (21/24).
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