FRM Part I · FRM Exam Part I · Regression Diagnostics
A regression of a stock's return on three factors uses 64 monthly observations. The total sum of squares is 400 and the residual sum of squares is 160. What is the adjusted R-squared?
Unadjusted R-squared is 0.60. Adjusting for 64 observations and 3 regressors gives 1 - (160/60)/(400/63) = 0.58. The adjustment penalizes additional regressors by using degrees of freedom, so the adjusted value is slightly below the unadjusted R-squared.
- A0.600
- B0.580Correct
- C0.617
- D0.571
Explanation
R-squared = 1 - 160/400 = 0.60. With n = 64 and k = 3, the degrees of freedom for residuals are 60. Adjusted R-squared = 1 - (160/60)/(400/63) = 1 - 2.6667/6.3492 = 1 - 0.42 = 0.58. The 0.600 option is the unadjusted value.
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