Priyanka_Chandak23
New Member
1)For a sample of 400 firms, the relationship between corporate revenue (Yi) and the average years of experience per employee (Xi) is modeled as follows:
Yi = β1 + β2 Xi + εi, i = 1, 2,...,400
You wish to test the joint null hypothesis that β1 = 0 and β2 = 0 at the 95% confidence level. The p-value for the t-statistic for β1 is 0.07, and the p-value for the t-statistic for β2 is 0.06. The p-value for the F-statistic for the regression is 0.045. Which of the following statements is correct?
a. You can reject the null hypothesis because each β is different from 0 at the 95% confidence level.
b. You cannot reject the null hypothesis because neither β is different from 0 at the 95% confidence level.
c. You can reject the null hypothesis because the F-statistic is significant at the 95% confidence level.
d. You cannot reject the null hypothesis because the F-statistic is not significant at the 95% confidence level.
Correct answer: c
Explanation: The T-test would not be sufficient to test the joint 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 null can be rejected.
Could someone please explain this, how do we solve such questions without a table if it appears this way in the exam?
GARP 2013
2) You built a linear regression model to analyze annual salaries for a developed country. You incorporated two independent variables, age and experience, into your model. Upon reading the regression results, you noticed that the coefficient of “experience” is negative which appears to be counter-intuitive. In addition you have discovered that the coefficients have low t-statistics but the regression model has a high R2. What is the most likely cause of these results?
a. Incorrect standard errors
b. Heteroskedasticity
c. Serial correlation
d. Multicollinearity
Answer: d.
Explanation:
Age and experience are highly correlated and would lead to multicollinearity. In fact, low t-statistics but a high R2 do suggest this problem also. Answers a, b and c are not likely causes and are therefore incorrect.
What do we mean by low t statistics here with reference to multicollinearity?
Thanks a lot.
Priyanka.
Yi = β1 + β2 Xi + εi, i = 1, 2,...,400
You wish to test the joint null hypothesis that β1 = 0 and β2 = 0 at the 95% confidence level. The p-value for the t-statistic for β1 is 0.07, and the p-value for the t-statistic for β2 is 0.06. The p-value for the F-statistic for the regression is 0.045. Which of the following statements is correct?
a. You can reject the null hypothesis because each β is different from 0 at the 95% confidence level.
b. You cannot reject the null hypothesis because neither β is different from 0 at the 95% confidence level.
c. You can reject the null hypothesis because the F-statistic is significant at the 95% confidence level.
d. You cannot reject the null hypothesis because the F-statistic is not significant at the 95% confidence level.
Correct answer: c
Explanation: The T-test would not be sufficient to test the joint 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 null can be rejected.
Could someone please explain this, how do we solve such questions without a table if it appears this way in the exam?
GARP 2013
2) You built a linear regression model to analyze annual salaries for a developed country. You incorporated two independent variables, age and experience, into your model. Upon reading the regression results, you noticed that the coefficient of “experience” is negative which appears to be counter-intuitive. In addition you have discovered that the coefficients have low t-statistics but the regression model has a high R2. What is the most likely cause of these results?
a. Incorrect standard errors
b. Heteroskedasticity
c. Serial correlation
d. Multicollinearity
Answer: d.
Explanation:
Age and experience are highly correlated and would lead to multicollinearity. In fact, low t-statistics but a high R2 do suggest this problem also. Answers a, b and c are not likely causes and are therefore incorrect.
What do we mean by low t statistics here with reference to multicollinearity?
Thanks a lot.
Priyanka.
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