CFA Level I · CFA Level I Exam · Applications of Simple Linear Regression in Finance
An analyst regresses a fund's returns on a benchmark's returns using 32 observations. The sum of squared errors is 150. The standard error of estimate is closest to:
The standard error of estimate is about 2.24. It equals the square root of the sum of squared errors divided by n minus 2 degrees of freedom, so sqrt(150/30) = sqrt(5) = 2.236. Using the wrong degrees of freedom gives a different value.
- A2.24Correct
- B2.31
- C2.37
Explanation
For simple regression, SEE = sqrt(SSE/(n-2)) = sqrt(150/30) = sqrt(5) = 2.236, about 2.24. Using n-1 = 31 gives sqrt(4.84) = 2.20, and using n = 32 gives sqrt(4.69) = 2.17; sqrt(150/28), from deducting 4, gives 2.31, an error in degrees of freedom. The correct divisor is n-2.
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