Financial Risk Manager Part 1

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Explanation:

To test a joint null hypothesis that all slope coefficients (in this case, $\beta_1$ and $\beta_2$ , if we treat both as coefficients in a specific model context, or usually all non-intercept coefficients) are equal to zero simultaneously, the $F$ -test is used.

The given p-value for the $F$ -statistic is 0.09. Since the significance level ( $\alpha$ ) is 10% (0.10) and $0.09 < 0.10 $, the$ F$-statistic is statistically significant at the 10% level. Therefore, we can reject the joint null hypothesis.

Note that individual $t$ -tests have p-values of 0.12 and 0.11, which are greater than 0.10, so neither $\beta_1$ nor $\beta_2$ are individually significant at the 10% level. However, they are jointly significant.

Explanation:

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Q.74 A sample of 200 firms reveals the following relationship between the annual stock return ( $Y_i$ ) and the average years of experience per employee, $X_i$ :
$Y_i = \beta_1 + \beta_2 X_i + \epsilon_i \quad i = 1, 2, \dots, 200$
An analyst wishes to test the joint null hypothesis that $\beta_1 = 0$ and $\beta_2 = 0$ at the 10% level of significance. The p-value for the t-statistics of $\beta_1$ and $\beta_2$ are 0.12 and 0.11, respectively. The p-value for the F-statistic for the regression is 0.09. This implies that the analyst:

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Last updated: June 22, 2026 at 14:11

Can reject the null hypothesis since β₁ and β₂ are different from zero at the 10% level of significance.

Can reject the null hypothesis because the F-statistic is significant at the 10% level.

Cannot reject the null hypothesis because we have insufficient evidence to prove both β₁ and β₂ are different from zero at the 10% level of significance.

Cannot reject the null hypothesis because the F-statistic is not significant at the 10% level.