Answer: F-statistic = 17.40; At least one of the 4 independent variables is significantly different from zero.

## Explanation This question involves testing the joint significance of all independent variables in a multiple regression model using an F-test. ### Hypotheses: - **H₀**: B₁ = B₂ = B₃ = B₄ = 0 (All coefficients are zero) - **H₁**: At least one Bⱼ ≠ 0 (At least one coefficient is not zero) ### F-statistic Calculation: The F-statistic formula for testing joint significance is: F = [ESS/k] / [SSR/(n-k-1)] Where: - TSS = total sum of squares = 540 - SSR = residual sum of squares = 250 - ESS = explained sum of squares = TSS - SSR = 540 - 250 = 290 - k = number of independent variables = 4 - n = number of observations = 65 (since n-k-1 = 60, so n = 60 + 4 + 1 = 65) F = [290/4] / [250/60] = 72.5 / 4.167 = 17.4 ### Decision: The calculated F-statistic (17.40) is greater than the critical F-value at 5% significance level with 4 and 60 degrees of freedom. Therefore, we reject the null hypothesis. ### Conclusion: At least one of the 4 independent variables is significantly different from zero. This matches option A: F-statistic = 17.40; At least one of the 4 independent variables is significantly different from zero.

Author: Tanishq Prabhu