Answer: 17.2594

## Explanation To test whether the slope coefficient is different from 0, we use a t-test with the following hypothesis: - **Null Hypothesis (H₀):** β = 0 - **Alternative Hypothesis (H₁):** β ≠ 0 The test statistic is calculated as: $$T = \frac{\hat{\beta} - \beta_{H_0}}{\text{SEE}_{\hat{\beta}}}$$ Where: - $\hat{\beta} = 1.65$ (given slope coefficient) - $\beta_{H_0} = 0$ (null hypothesis value) - $\text{SEE}_{\hat{\beta}}$ is the standard error of the slope coefficient ### Calculating Standard Error of $\hat{\beta}$ The standard error of the slope coefficient is: $$\text{SEE}_{\hat{\beta}} = \sqrt{\frac{s^2}{n \hat{\sigma}^2_X}}$$ Given: - $s^2 = 20.45$ (residual variance) - $\hat{\sigma}^2_X = 18.65$ (variance of X) - n = 120 (10 years × 12 months = 120 observations) $$\text{SEE}_{\hat{\beta}} = \sqrt{\frac{20.45}{120 \times 18.65}} = \sqrt{\frac{20.45}{2238}} = \sqrt{0.00914} = 0.0956$$ ### Calculating Test Statistic $$T = \frac{1.65 - 0}{0.0956} = 17.2594$$ ### Interpretation The test statistic of 17.2594 is highly significant, indicating strong evidence against the null hypothesis that the slope coefficient equals zero. This suggests that the market return has a statistically significant relationship with the sales company's returns.

Author: Tanishq Prabhu