CFA Level IQuantitative MethodsMedium
A simple linear regression of a stock's returns on a market index using 42 monthly observations produces a sum of squared residuals (SSE) of 240. What is the standard error of estimate (SEE) for this regression?
- A2.400
- B5.809
- C6.000
- D2.449
Show answer & explanationAnswer & explanation
Correct answer: D. 2.449
SEE = √[SSE/(n−k−1)], where n = 42 and k = 1 independent variable, so degrees of freedom = 42−1−1 = 40. SEE = √(240/40) = √6 ≈ 2.449.
Why the other options are wrong
- A. Simple rounding coincidence; does not follow from correct formula.
- B. Uses n−1=41 as the divisor instead of n−k−1, an incorrect degrees of freedom.
- C. Uses n−k=41 or a different miscalculation, giving too large a value.
Standard Error of Estimate (SEE)
A measure of the dispersion of actual observed values around the regression line, reflecting the average size of the regression's residuals.
- SEE = √[SSE/(n − k − 1)]
- k = number of independent variables in the regression
- Smaller SEE indicates a better model fit relative to the data's scale
Memory trick: Divide leftover error by leftover freedom, then root it out