11.2.2 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(2), pp. 185-190)] presents data on the selling price and annual taxes for 24 houses. The data are in the table that follows. 1. 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? 2. Find the mean selling price given that the taxes paid are x = 7.50. 3. Calculate the fitted value of y corresponding to x = 5.8980. Find the corresponding residual. 4. Calculate the fitted yiyi for each value of xi used to fit the model. Then construct a graph of yiyi 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?

11.4.4 Consider the data from Exercise 11.2.2 on y = sales price and x = taxes paid. 1. Test H0: 1 = 0 using the t-test; use = 0.05. 2. Test H0: 1 = 0 using the analysis of variance with = 0.05. Discuss the relationship of this test to the test from part (a). 3. Estimate the standard errors of the slope and intercept. 4. Test the hypothesis that 0 = 0.

11.7.4 Refer to the data in Exercise 11.2.2 on house-selling price y and taxes paid x. 1. Find the residuals for the least squares model. 2. Prepare a normal probability plot of the residuals and interpret this display. 3. Plot the residuals versus yyand versus x. Does the assumption of constant variance seem to be satisfied? 4. What proportion of total variability is explained by the regression model?

11.2.2 chart

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