FRM Part I · FRM Exam Part I · Linear Regression
In a simple linear regression of a fund's monthly returns on a benchmark's returns, the total sum of squares (TSS) is 200 and the sum of squared residuals (SSR) is 50. What is the regression R-squared?
R-squared is 0.75. It equals one minus the ratio of the residual sum of squares to the total sum of squares, so 1 - 50/200 = 0.75. Equivalently, the explained sum of squares of 150 divided by the total of 200 gives the same figure.
- A0.25
- B0.33
- C0.75Correct
- D0.80
Explanation
R-squared = 1 - SSR/TSS = 1 - 50/200 = 0.75. The explained sum of squares is 150, and 150/200 gives the same result. The 0.25 option is the unexplained fraction (SSR/TSS), and 0.33 is SSR/ESS (50/150), which is not R-squared.
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