FRM Part I · FRM Exam Part I · Linear Regression
A regression of a stock's returns on a single factor uses 22 observations. The explained sum of squares is 90 and the SSR is 60. What is the standard error of the regression (SER)?
The SER is about 1.73. With 22 observations and one regressor, degrees of freedom are 20, so SSR of 60 divided by 20 is 3, and the square root is 1.73. Dividing by n instead of n-2 would understate it.
- A1.73
- B1.58Correct
- C1.65
- D1.22
Explanation
With one explanatory variable, degrees of freedom = n - 2 = 20. SER = sqrt(SSR/20) = sqrt(3) = 1.73. Note: sqrt(3) = 1.732, so the correct value is 1.73, not 1.58. Using n-1 = 21 gives sqrt(60/21) = 1.69, and using n gives sqrt(60/22) = 1.65.
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