An article in Technometrics by S. C. Narula and J. F. Wellington [Prediction, Linear Regression, and a Minimum Sum of Relative Errors (1977, Vol. 19)]

An article in Technometrics by S. C. Narula and J. F. Wellington [€œPrediction, Linear Regression, and a Minimum Sum of Relative Errors€ (1977, Vol. 19)] presents data on the selling price and annual taxes for 24 houses. The data are in the Table E11-2.

(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 σ²?

(b) Find the mean selling price given that the taxes paid are x = 7.50. TABLE 11-2 House Data

(c) Calculate the fitted value of y corresponding to x = 5.8980. Find the corresponding residual.

(d) Calculate the fitted y_i for each value of xi used to fit the model. Then construct a graph of y_i 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?

Sale es Sale es Price/ 1000 (local, school), county)/1000 Price/ 1000 (local, school), county)/1000 25.9 4.9176 30.0 5.0500 29.5 5.0208 36.9 8.2464 27.9 6.6969 4.5429 41.9 25.9 4.5573 40.5 7.7841 5.0597 29.9 43.9 9.0384 29.9 37.5 3.8910 5.9894 7.5422 30.9 5.8980 37.9 28.9 5.6039 44.5 8.7951 35.9 5.8282 37.9 6.0831 31.5 5.3003 38.9 8.3607 36.9 31.0 6.2712 8.1400 30.9 5.9592 45.8 9.1416