Financial Risk Manager Part 1
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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?
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TTanishq
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.
Explanation:
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:
Where:
- ESS = Explained Sum of Squares
- RSS = Residual Sum of Squares
- k = number of independent variables
- n = number of observations
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