Financial Risk Manager Part 1

The 95% confidence interval for the slope coefficient b is calculated using the formula:

$CI = \hat{b} \pm t_{\frac{\alpha}{2}, n-2} s_{\hat{b}}$

Where:

• $\hat{b} = 0.6$ (point estimate)
• $s_{\hat{b}} = 0.2$ (standard error)
• $\alpha = 5\%$, so $\alpha/2 = 0.025$
• Degrees of freedom = n - 2 = 36 - 2 = 34
• $t_{0.025,34} = \pm 2.03$ (from t-distribution table)

Calculation: $CI = 0.6 \pm 2.03 \times 0.2 = 0.6 \pm 0.406 = [0.194, 1.006]$

Therefore, the 95% confidence interval is $0.194 < b < 1.006$.

Note: The degrees of freedom are n-2 because we're estimating two parameters (intercept and slope) in simple linear regression.