Do some predictions. The individual whose salary we have been studying wants to do some financial planning. Specifically, she would like to predict her salary 5 years into the future, that is, for Year 25. She is willing to assume that her employment situation will be stable for the next 5 years and that it will be similar to the last 20 years.
(a) Predict her salary for Year 25 using the least-squares regression equation constructed to predict salary from year.
(b) Predict her salary for Year 25 using the least-squares regression equation constructed to predict log salary from year. Note that you will need to take the predicted log salary and convert this value back to the predicted salary. Many calculators have a function that will perform this operation.
(c) Which prediction do you prefer? Explain your answer.
(d) Someone looking at the numerical summaries and not the plots for these analyses says that because both models have very high values of r2, they should perform equally well in doing this prediction. Write a response to this comment.
(e) Write a short summary about the value of graphical summaries and the problems of extrapolation using what you have learned in studying the salary data.