Financial Risk Manager Part 1

Explanation

To test whether the regression coefficient β is significantly different from zero, we use a t-test:

Given:

• S_xx = 12.0
• S_xy = 8.0
• n = 18
• Standard error of β = 0.16

Step 1: Calculate the slope coefficient β $\beta = \frac{S_{xy}}{S_{xx}} = \frac{8.0}{12.0} = 0.6667$

Step 2: Calculate the test statistic $t = \frac{\beta - 0}{SE(\beta)} = \frac{0.6667}{0.16} = 4.169$

Step 3: Determine critical value For a two-tailed test at 1% significance level with n-2 = 16 degrees of freedom:

• t_critical ≈ 2.921

Step 4: Make conclusion Since |t| = 4.169 > 2.921, we reject the null hypothesis H₀: β = 0.

Conclusion: β is significantly different from zero at the 1% significance level.

The correct answer is D: 4.169, β is significantly different from zero._