Question

A researcher wants to determine if the number of years of education that a person's father has ("paeduc") is related to the number of years of education that the person has ("educ"). He uses simple linear regression to examine this question. The output from Excel is shown below. Regression Statistics Multiple R 0.527393938 R Square 0.278144366 Adjusted R Square 0.264776669 Standard Error 2.436826202 Observations 56 ANOVA df F Significance F 2.96139E-05 20.8072 Regression Residual Total SS MS 123.555701 123.5557 320.6585847 5.938122 444.2142857 54 55 Intercept paeduc Coefficients Standard Error t Stat P-value 10.58831407 0.95398967 11.09898 1.5E-15 0.349168311 0.076546966 4.561491 2.96E-05 Lower 95% Upper 95% 8.675679939 12.5009482 0.195700884 0.502635739 Referring to the output above, if we were testing a hypothesis about whether the years of education fathers have and the years of education that their children have were related, what would our conclusion be at the 0.05 level of significance? Read carefully! Fail to reject the null hypothesis. We can conclude that the years of education that fathers have has a significant linear relationship with the years of education their children have. O Reject the null hypothesis and conclude that B1 + 61. Therefore, we can conclude that the years of education that fathers have has a significant linear relationship with the years of education their children have. Ο Ο Reject the null hypothesis. We can conclude that the years of education that fathers have does not have a significant linear relationship with the number years of education their children have. Fail to reject the null hypothesis. We cannot conclude that the years of education that fathers have has a significant linear relationship with the years of education their children have. оо Reject the null hypothesis. We can conclude that the years of education that fathers have has a significant linear relationship to the years of education their children have.

Answer 1

Solution: The hypotheses are: H.:B1 = 0 Ha:B1 +0 Referring the p-value column in the output shown, we observe that the p-value for t-stat = 2.96E – 05 = 0.0000296 Level of significance = a = 0.05 Since p-value < a, we reject the null hypothesis H. Conclusion: Reject the null hypothesis. We can conclude that the years of education that fathers have has a significant linear relationship to the years of education their children have.