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Answer: none of the additional independent variables in the model.
## Explanation When conducting a joint hypothesis test with: - Null hypothesis: $H_0: b_1 = b_2 = 0$ (both coefficients are zero) - F-statistic < critical F-value - F-statistic > 0 This means we **fail to reject the null hypothesis**. The evidence is insufficient to conclude that at least one of the coefficients is different from zero. **Decision Rule:** - If F-statistic > critical F-value → Reject H₀ → Include at least one variable - If F-statistic < critical F-value → Fail to reject H₀ → Do not include either variable Since we fail to reject the null hypothesis, we conclude that neither variable significantly improves the model fit, so **none of the additional independent variables should be included** in the model. **Note:** This is a joint test, so we cannot determine which specific variable might be significant individually - we only test whether at least one of them is significant.
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An analyst conducts a joint hypothesis test to determine whether adding two independent variables can improve the fit of a multiple regression model. The null hypothesis is , where and are the partial regression coefficients of the two additional independent variables. If the F-statistic is less than the critical F-value but greater than zero, the analyst should include:
A
none of the additional independent variables in the model.
B
only one of the additional independent variables in the model.
C
both of the additional independent variables in the model.