Financial Risk Manager Part 1

Explanation

The correct answer is B because the estimated regression equation matches the calculated parameters from the given data.

Step-by-Step Calculation:

1. Calculate Covariance between Y and X₁: $\text{Cov}(Y, X_1) = \frac{1}{n - 1} \sum_{i=1}^{n} (X_1 - \bar{X}_1)(Y - \bar{Y})$ From the table, the total sum is 2.759533 $\text{Cov}(Y, X_1) = \frac{1}{6 - 1} \times 2.759533 = 0.5519$

2. Calculate Variance of X₁: $\text{Var}(X_1) = \frac{1}{n - 1} \sum_{i=1}^{n} (X_1 - \bar{X}_1)^2 = 0.9797$

3. Calculate Slope Coefficient (β₁): $\hat{\beta}_1 = \frac{\text{Cov}(Y, X_1)}{\text{Var}(X_1)} = \frac{0.5519}{0.9797} = 0.5633$

4. Calculate Intercept (α): $\hat{\alpha} = \bar{Y} - \hat{\beta}_1 \bar{X}_1$ $\hat{\alpha} = -0.82833 - (0.5633 \times 0.446667) = -1.0799$

Therefore, the estimated regression equation is: $\hat{Y} = -1.0799 + 0.5633X_1$

This matches option B exactly._