Financial Risk Manager Part 1

Explanation

F-Statistic Calculation

The F-statistic is calculated using the formula:

$F = \frac{[\frac{\text{ESS}}{k}]}{[\frac{\text{SSR}}{(n-k-1)}]}$

Where:

• ESS (Explained Sum of Squares) = 270
• SSR (Sum of Squared Residuals) = 250
• k (number of independent variables) = 5
• n (number of observations) = 66

Substituting the values:

$F = \frac{[\frac{270}{5}]}{[\frac{250}{(66-5-1)}]} = \frac{[54]}{[\frac{250}{60}]} = \frac{54}{4.1667} = 12.96$

Hypothesis Testing

The hypotheses are:

• H₀: B₁ = B₂ = B₃ = B₄ = B₅ = 0 (all coefficients are zero)
• H₁: At least one Bⱼ ≠ 0 (at least one coefficient is non-zero)

Critical Value Comparison

The critical F-value at 10% significance level with:

• Numerator degrees of freedom = k = 5
• Denominator degrees of freedom = n - k - 1 = 66 - 5 - 1 = 60

Critical F-value ≈ 1.946

Since 12.96 > 1.946, we reject the null hypothesis.

Conclusion

We conclude that at least one of the five independent variables is significantly different from zero.

Therefore, option A is correct with F-statistic = 12.96 and the correct conclusion.