Chartered Financial Analyst Level 2

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Explanation:

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.

Explanation:

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 $H_0: b_1 = b_2 = 0$ , where $b_1$ and $b_2$ 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:

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none of the additional independent variables in the model.

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only one of the additional independent variables in the model.

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both of the additional independent variables in the model.