FRM Part I · FRM Exam Part I · Linear Regression
A simple regression of Y on X has sample standard deviation of residuals (standard error of regression) of 4.0 with n = 52 observations, giving the variance of the slope estimator as s²/Σ(Xi − X̄)². If Σ(Xi − X̄)² = 400, what is the standard error of the slope estimate (use the residual variance s² = 16 directly)?
The slope variance equals residual variance divided by the sum of squared deviations of X: 16 divided by 400 is 0.04. The standard error is the square root of that, which is 0.20. Reporting 0.04 would confuse variance with standard error.
- A0.04
- B0.20Correct
- C0.80
- D0.16
Explanation
Var(b) = s²/Σ(Xi−X̄)² = 16/400 = 0.04. Standard error = √0.04 = 0.20. Option 0 reports the variance instead of its square root; option 2 uses 4/√25-type confusion using s/√... incorrectly.
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