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Answer: F-statistic = 12.96; At least one of the 5 independent variables is significantly different from zero
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.
Author: Nikitesh Somanthe
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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.
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
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