An article in the scientic journal Technometrics by S. C. Narula and J. F. Wellington [\"Prediction, Linear Regression, and a Minimum Sum of Relative Error\" (1977, Vol. 19(2), pp. 185190)] presents data on the selling price and annual taxes for 24 houses. The data set is in the le 'houses.x1sx'. a. Assuming that a simple linear regression model is apprOpriate, obtain the least squa- res t relating selling price (y) to taxes paid (:3). What is the estimate of (72? b. Find the mean selling price given that the taxes paid are a: = 7.50. c. Calculate the predicted value of y corresponding to m = 5.898. Find the correSpon- ding residual. (1. Calculate the predicted response @1- for each value of an; used to t the model. Then construct a graph of @1- versus the corresponding observed value m and comment on what this plot would look like if the relationship between y and a: 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 Price/1000 25.9 29.5 27.9 25.9 29.9 29.9 30.9 28.9 35.9 31.5 31 30.9 Taxes (local, school, can nty)/ 1000 4.9176 5.0208 4.5429 4.5573 5.0597 3.891 5.898 5.6039 5.8282 5.3003 6.2712 5.9592 Sale Price/1000 30 36.9 41.9 40.5 43.9 37.5 37.9 44.5 37.9 38.9 36.9 45.8 Taxes (local, school, county)/1000 5.05 8.2464 6.6969 7.7841 9.0384 5.9894 7.5422 8.7951 6.0831 8.3607 8.14 9.1416