Financial Risk Manager Part 1
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Elizabeth Graham, FRM, runs a regression of monthly stock returns on five independent variables over 66 months. The explained sum of squares is 270, and the sum of squared residuals is 250. Graham then performs a statistical test at the 10% significance level with the null hypothesis that all five of the independent variables are equal to zero. Quote the F-statistic and the conclusion.
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NNikitesh
A
F-statistic = 12.96; At least one of the 5 independent variables is significantly different from zero
B
F-statistic = 1.946; At least one of the 5 independent variables is significantly different from zero
C
F-statistic = 72.5; All the 5 independent variables are significantly different from zero
D
F-statistic = 17.40; None of the independent variables is significantly different from zero
Explanation:
The F-statistic is calculated using the formula: F = [ESS/k] / [SSR/(n-k-1)] where:
- ESS (Explained Sum of Squares) = 270
- SSR (Sum of Squared Residuals) = 250
- k (number of independent variables) = 5
- n (number of observations) = 66
F = [270/5] / [250/(66-5-1)] = [54] / [250/60] = 54 / 4.1667 = 12.96
The critical F-value at 10% significance level with 5 and 60 degrees of freedom is approximately 1.946. Since 12.96 > 1.946, we reject the null hypothesis that all five independent variables are equal to zero. Therefore, we conclude that at least one of the five independent variables is significantly different from zero.
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