Solution: Exclude the outlier(s) you identified in Question 1(e) and re-run the simple regression. With the exception of the Diagnostics and Influential Residuals
Question: Exclude the outlier(s) you identified in Question 1(e) and re-run the simple regression. With the exception of the Diagnostics and Influential Residuals output, request the same output as in question 1. Save your output as Appendix B. Then answer the following questions:
- (7 pts.) What are the value of slope ( b 1 ) and its standard error ( S b 1 )? Use these two values to conduct the test of H 0 : 1 = 0 at = .05. What is your p value? What is your conclusion about the effects of predictor on the outcome variable?
- (7 pts.) What’s the null hypothesis of F test? Using values from the ANOVA table, compute the F value. What is your p value? Suppose = .05, what is your statistical conclusion for this hypothesis testing?
- (7 pts.) Square the t value for the slope from Question 2(a), and compare it to the F value from Question 2(b). Explain your findings. Does F -test and t -test lead to the same statistical conclusion?
- (7 pts.) Manually compute the 95% confidence interval (C.I.) around the estimated slope (b 1 ). What does this interval tell you about the population value of slope? What does this interval suggest about the relationship between starting salary and age? Compare this information to that given by the t test in Question 2(a), does this C.I. lead to the same statistical conclusion as the t test?
- (7 pts.) Manually compute R 2 using quantities from the ANOVA table. Interpret the meaning of this value.
- (7 pts.) Do you think this predictor is important in predicting the outcome variable? Why do you think it is important (or not important)?
- (7 pts.) Check the scatterplot between studentized residuals and predicted Y. Does the assumption of homogeneity of error variance seem to meet for this regression analysis?
- (7 pts.) Does the fitted model seem to be similar to or different from the model based on the 25 cases? Comment on any differences you see between these two models.
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