Explanation:
The explanation provided in the file content states that the correct answer is option C: "The analyst can reject the joint null hypothesis because the F-statistic is significant at the 95% confidence level." This is because the F-statistic, which is used to test the joint significance of all the coefficients in a regression model, has a p-value of 0.045, which is less than the 95% confidence level threshold of 0.05. This indicates that there is a statistically significant relationship between the variables in the model, and thus the joint null hypothesis that β1 = 0 and β2 = 0 can be rejected. The individual t-tests for β1 and β2, with p-values of 0.07 and 0.06 respectively, are not sufficient to test the joint null hypothesis, as they only test the significance of each coefficient individually.
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In a dataset comprising 400 companies, the relationship between the total income of a company (Yi) and the average years of experience per employee (Xi) is represented by the following linear regression equation: Yi = β1 + β2*Xi + Ei, where i ranges from 1 to 400.
A researcher aims to test the joint null hypothesis that both β1 and β2 are equal to zero, using a 95% confidence level. The p-value associated with the t-statistic for β1 is 0.07, the p-value for the t-statistic for β2 is 0.06, and the p-value for the F-statistic for the overall model is 0.045.
A
The analyst can reject the joint null hypothesis because each β is different from O at the 95% confidence level.
B
The analyst cannot reject the joint null hypothesis because neither β is different from O at the 95% confidence level.
C
The analyst can reject the joint null hypothesis because the F-statistic is significant at the 95% confidence level.
D
The analyst cannot reject the joint null hypothesis because the F-statistic is not significant at the 95% confidence level.