FRM Part I · FRM Exam Part I · Linear Regression
A regression with 27 observations has one explanatory variable. Total sum of squares is 500 and explained sum of squares is 300. The sum of squared deviations of X from its mean is 200. What is the t-statistic for the slope coefficient testing H0: slope = 0?
The t-statistic is about 6.12. Residual variance is 200 divided by 25, equal to 8, so the slope's standard error is 0.20. The slope is the square root of 300/200, about 1.2247. Dividing gives 6.12, consistent with t squared equal to 37.5 from R-squared.
- At = 5.00
- Bt = 6.12Correct
- Ct = 6.00
- Dt = 3.54
Explanation
Slope-related: SSR = 500 - 300 = 200; s^2 = 200/25 = 8. Var(slope) = 8/200 = 0.04, SE = 0.20. Slope = sqrt(ESS/Sxx) = sqrt(300/200) = 1.2247. t = 1.2247/0.20 = 6.12. Equivalent check: t^2 = R^2(n-2)/(1-R^2) = 0.6 x 25/0.4 = 37.5, t = 6.12. Using n-1 or n degrees of freedom gives other values such as 5.00 or 6.00 wrongly.
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