FRM Part I · FRM Exam Part I · Linear Regression
An analyst regresses a bond spread change on a single explanatory variable. The sample correlation between the dependent and explanatory variable is 0.60, and the total sum of squares is 500. What is the sum of squared residuals?
The sum of squared residuals is 320. In a one-variable regression R-squared equals the squared correlation, 0.36, so the explained sum of squares is 180 out of 500. The unexplained remainder, SSR, is 500 minus 180, which is 320.
- A180
- B300
- C320Correct
- D360
Explanation
In a simple regression R-squared is the squared correlation: 0.60^2 = 0.36. ESS = 0.36 x 500 = 180, so SSR = 500 - 180 = 320. The 180 option is ESS, not SSR, and 300 comes from wrongly using the correlation (0.60) instead of R-squared.
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