Answer: [1.3998, 1.9002]

## Explanation The confidence interval for the slope coefficient $\hat{\beta}$ is calculated using the formula: $$ [\hat{\beta} - C_t \times \text{SEE}_{\hat{\beta}}, \hat{\beta} + C_t \times \text{SEE}_{\hat{\beta}}] $$ **Step 1: Determine the sample size and degrees of freedom** - 10 years × 12 months = 120 months (n = 120) - Degrees of freedom = n - 2 = 120 - 2 = 118 **Step 2: Find the critical t-value** - For a 99% confidence interval, α = 0.01, so α/2 = 0.005 - With 118 degrees of freedom, the critical t-value (C_t) = 2.617 **Step 3: Calculate the standard error of the slope coefficient** $$ \text{SEE}_{\hat{\beta}} = \sqrt{\frac{s^2}{n\hat{\sigma}^2_X}} = \sqrt{\frac{20.45}{120 \times 18.65}} = \sqrt{\frac{20.45}{2238}} = \sqrt{0.00914} = 0.0956 $$ **Step 4: Construct the confidence interval** $$ [1.65 - 2.617 \times 0.0956, 1.65 + 2.617 \times 0.0956] = [1.65 - 0.2502, 1.65 + 0.2502] = [1.3998, 1.9002] $$ Therefore, the 99% confidence interval for $\hat{\beta}$ is [1.3998, 1.9002], which corresponds to option D.

Author: Tanishq Prabhu