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

## Explanation ### Given Data: - Total Sum of Squares (TSS) = 540 - Sum of Squared Residuals (SSR) = 250 - Number of independent variables (k) = 4 - Number of observations (n) = 65 - Significance level = 5% ### Step 1: Calculate Explained Sum of Squares (ESS) ESS = TSS - SSR = 540 - 250 = 290 ### Step 2: Calculate F-statistic F-statistic = [ESS/k] / [SSR/(n-k-1)] Where: - ESS/k = 290/4 = 72.5 - SSR/(n-k-1) = 250/(65-4-1) = 250/60 = 4.1667 F = 72.5 / 4.1667 = 17.4 ### Step 3: Determine Critical F-value Degrees of freedom: - Numerator: k = 4 - Denominator: n-k-1 = 65-4-1 = 60 At 5% significance level, the critical F-value with (4, 60) degrees of freedom is approximately 2.525. ### Step 4: Decision Rule Since calculated F-statistic (17.4) > critical F-value (2.525), we reject the null hypothesis. ### Step 5: Conclusion Reject H₀: B₁ = B₂ = B₃ = B₄ = 0 Accept H₁: At least one Bⱼ ≠ 0 Therefore, the correct answer is **A** with F-statistic = 17.40 and conclusion that at least one of the 4 independent variables is significantly different from zero. ### Why other options are incorrect: - **B**: Uses the critical F-value (2.525) as the calculated F-statistic - **C**: Uses ESS/k (72.5) as the F-statistic instead of the complete calculation - **D**: Has the correct F-statistic but wrong conclusion (fails to reject null when we should reject it)

Author: Nikitesh Somanthe