Answer: 4.169, $\beta$ is significantly different from zero

## 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.

Author: Tanishq Prabhu