Financial Risk Manager Part 1

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Explanation:

Explanation

C is correct. The t-test would not be sufficient to test the joint null hypothesis. In order to test the joint null hypothesis, examine the F-statistic, which in this case is statistically significant at the 95% confidence level. Thus, the joint null hypothesis can be rejected.

Key Points:

Individual t-tests vs. Joint F-test: The t-tests examine whether individual coefficients are significantly different from zero, while the F-test examines whether the entire set of coefficients (excluding the intercept) is jointly significant.
P-values:
- β₁ p-value = 0.07 > 0.05 → Not individually significant at 95% confidence
- β₂ p-value = 0.06 > 0.05 → Not individually significant at 95% confidence
- F-statistic p-value = 0.045 < 0.05 → Jointly significant at 95% confidence
Interpretation: Even though neither coefficient is individually significant at the 95% level, the overall regression model is jointly significant, meaning the predictors together explain a significant portion of the variation in corporate revenue.

A, B, and D are incorrect per the explanation for C above.

Explanation:

Explanation

Key Points:

Individual t-tests vs. Joint F-test: The t-tests examine whether individual coefficients are significantly different from zero, while the F-test examines whether the entire set of coefficients (excluding the intercept) is jointly significant.
P-values:
- β₁ p-value = 0.07 > 0.05 → Not individually significant at 95% confidence
- β₂ p-value = 0.06 > 0.05 → Not individually significant at 95% confidence
- F-statistic p-value = 0.045 < 0.05 → Jointly significant at 95% confidence
Interpretation: Even though neither coefficient is individually significant at the 95% level, the overall regression model is jointly significant, meaning the predictors together explain a significant portion of the variation in corporate revenue.

A, B, and D are incorrect per the explanation for C above.

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For a sample of 400 firms, the relationship between corporate revenue (Y_i) and the average years of experience per employee (X_i) is modeled as follows: $Y_i = \beta_1 + \beta_2 * X_i + \varepsilon_i \quad i = 1, 2, ..., 400$

An analyst wants to test the joint null hypothesis that $\beta_1 = 0$ and $\beta_2 = 0$ at the 95% confidence level. The p-value for the t-statistic for $\beta_1$ is 0.07, and the p-value for the t-statistic for $\beta_2$ is 0.06. The p-value for the F-statistic for the regression is 0.045. Which of the following statements is correct?

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The analyst can reject the joint null hypothesis because each $\beta$ is different from 0 at the 95% confidence level.

14.3%

The analyst cannot reject the joint null hypothesis because neither $\beta$ is different from 0 at the 95% confidence level.

4.8%

The analyst can reject the joint null hypothesis because the F-statistic is significant at the 95% confidence level.

76.2%

The analyst cannot reject the joint null hypothesis because the F-statistic is not significant at the 95% confidence level.

4.8%