
Answer-first summary for fast verification
Answer: The model as a whole is statistically significant.
## Explanation When the F-statistic is greater than its critical value (in this case, the critical value is 4), it means: - We **reject** the null hypothesis H₀: All slope coefficients = 0 - The model as a whole **is** statistically significant - The independent variables collectively have explanatory power Since the question states that the F-statistic is greater than the critical value of 4, option C is correct. ### Key Points: - **F-statistic > Critical value** → Reject H₀ → Model is statistically significant - **F-statistic < Critical value** → Fail to reject H₀ → Model is not statistically significant The F-statistic formula provided: $$F = \frac{\left[\frac{\text{ESS}}{k}\right]}{\left[\frac{\text{RSS}}{(n - k - 1)}\right]}$$ Where: - ESS = Explained Sum of Squares - RSS = Residual Sum of Squares - k = number of independent variables - n = number of observations
Author: Tanishq Prabhu
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Assume that on a certain significance level, the critical value of the F-statistic is 4. Which of the following is correct?
A
The value of F-statistic is less than its critical value.
B
We fail to reject the null hypothesis: H₀: All slope coefficients = 0.
C
The model as a whole is statistically significant.
D
The model as whole is not statistically significant.
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