FRM Part I · FRM Exam Part I · Linear Regression
In a simple regression of Y on X with n = 5 observations, X values are 1, 2, 3, 4, 5 and the OLS slope is 2.0. The residual sum of squares is 12. What is the standard error of the slope estimator, assuming homoskedastic errors?
The standard error is about 0.63. Residual variance is 12 divided by 3 degrees of freedom, giving 4. The X sum of squared deviations is 10, so slope variance is 0.4 and its square root is 0.632.
- A0.35
- B0.45
- C0.63Correct
- D1.26
Explanation
Residual variance s^2 = RSS/(n-2) = 12/3 = 4. Sum of squared deviations of X: mean 3, deviations -2,-1,0,1,2, sum of squares = 10. Var(b) = 4/10 = 0.4, so SE = sqrt(0.4) = 0.632. Dividing RSS by n instead of n-2 gives 2.4/10 = 0.24, SE 0.49, which is wrong.
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