Question - Performance bonuses, continued. Refer to the previous exercise.
(a) Now run the simple linear regression for the variables sqrt(rating) and percent of salary from incentive payments.
(b) Obtain the residuals and assess whether the assumptions for the linear regression analysis are reasonable. Include all plots and numerical summaries used in doing this assessment.
(c) Construct a 95% confidence interval for the square root increase in rating given a 1% increase in the percent of salary from incentive payments.
(d) Consider the values 0%, 20%, 40%, 60%, and 80% of salary from incentives. Compute the predicted rating for this model and the one in the previous exercise. For the model in this problem, you will need to square the predicted value to get back to the original units.
(e) Plot the predicted values versus the percent and connect those values from the same model. For which regions of percent do the predicted values from the two models vary the most?
(f) Based on the comparison of regression models (both predicted values and residuals), which model do you prefer? Explain.