Financial Risk Manager Part 1
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An analyst runs a regression of monthly value-stock returns on 8 independent variables. Given the following information: Explained Sum of Squares=1435 Residual sum of Squares=1335 Number of observations=28 R² and the F-statistic, respectively, are closest to:
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NNikitesh
A
53%, 4
B
51%, 3.8
C
52%, 2.6
D
50%, 4
Explanation:
Step-by-step calculation:
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Calculate Total Sum of Squares (TSS): TSS = Explained Sum of Squares (ESS) + Residual Sum of Squares (RSS) TSS = 1435 + 1335 = 2770
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Calculate R²: R² = ESS / TSS = 1435 / 2770 = 0.518 ≈ 52%
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Calculate F-statistic:
- Degrees of freedom for explained variation (numerator) = number of independent variables = 8
- Degrees of freedom for residual variation (denominator) = n - k - 1 = 28 - 8 - 1 = 19
F = (ESS / k) / (RSS / (n - k - 1)) F = (1435 / 8) / (1335 / 19) F = 179.375 / 70.263 F = 2.553 ≈ 2.6
Interpretation:
- R² of 52% indicates that 52% of the variation in value-stock returns is explained by the 8 independent variables.
- F-statistic of 2.6 tests the joint significance of all independent variables. This value would need to be compared to critical F-values to determine statistical significance.
Therefore, the closest values are 52% and 2.6, which corresponds to option C.
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