Answer: An article in Technometrics by S. C. Narula and J.

Chapter 11, Problem 11-4

(choose chapter or problem)

An article in Technometrics by S. C. Narula and J. F. Wellington [Prediction, Linear Regression, and a Minimum Sum of Relative Errors (Vol. 19, 1977)] presents data on the selling price and annual taxes for 24 houses. The data are shown in the following table. Taxes Sale (Local, School), Price/1000 County)/1000 25.9 4.9176 29.5 5.0208 27.9 4.5429 25.9 4.5573 29.9 5.0597 29.9 3.8910 30.9 5.8980 28.9 5.6039 35.9 5.8282 31.5 5.3003 31.0 6.2712 30.9 5.9592 Taxes Sale (Local, School), Price/1000 County)/1000 30.0 5.0500 36.9 8.2464 41.9 6.6969 40.5 7.7841 43.9 9.0384 37.5 5.9894 37.9 7.5422 44.5 8.7951 37.9 6.0831 38.9 8.3607 36.9 8.1400 45.8 9.1416 (a) Assuming that a simple linear regression model is appropriate, obtain the least squares fit relating selling price to taxes paid. What is the estimate of 2 ? (b) Find the mean selling price given that the taxes paid are x 7.50. (c) Calculate the fitted value of y corresponding to x 5.8980. Find the corresponding residual. (d) Calculate the fitted for each value of xi used to fit the model. Then construct a graph of versus the corresponding observed value yi and comment on what this plot would look like if the relationship between y and x was a deterministic (no random error) straight line. Does the plot actually obtained indicate that taxes paid is an effective regressor variable in predicting selling price?