FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
A regression of Y on X1 and X2 with 30 observations gives a total sum of squares of 500 and a residual sum of squares of 140. What is the adjusted R-squared?
Adjusted R-squared is about 0.70, so the closest option is 0.690. It equals 1 - [140/(30-2-1)]/[500/(30-1)], which is below the unadjusted 0.72 because of the penalty for the two regressors.
- A0.720
- B0.690Correct
- C0.711
- D0.652
Explanation
R-squared = 1 - 140/500 = 0.72. Adjusted R-squared = 1 - (140/27)/(500/29) = 1 - 5.185/17.241 = 1 - 0.3007 = 0.699, which is closest to 0.690? Recompute precisely: 5.1852/17.2414 = 0.30074, so adjusted R-squared = 0.6993. The nearest listed value is 0.690 only approximately, so the key is 0.690 given rounding in the options; 0.720 is the unadjusted value and ignores the degrees-of-freedom penalty.
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