Question

Question 1 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 (y) and annual taxes (x) for 24 houses. The taxes include local, school and county taxes. The data are shown in the following table. Sale Price/1000 Taxes/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 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) Calculate the least squares estimates of the slope and intercept. β^1=Enter your answer; beta1 (Round your answer to 3 decimal places.) β^0=Enter your answer; beta0 (Round your answer to 2 decimal places.) (b) Find the mean selling price given that the taxes paid are x = 5.3. Enter your answer in accordance to the item b) of the question statement (Round your answer to 2 decimal places.) (c) Calculate the fitted value of y corresponding to x = 5.0208 (observation #2). Find the corresponding residual. y^=Enter your answer; the fitted value of y (Round your answer to 2 decimal places.) y−y^=Enter your answer; the corresponding residual (Round your answer to 2 decimal places.) Statistical Tables and Charts Question Attempts: 0 of 2 used SAVE FOR LATER SUBMIT ANSWER

Answer 1

=( Xi) / n = (4.9176 + ... + 9.1416 ) / 24= 6.4049

=( Yi)/n = (25.9 + ... + 45.8) / 24 = 34.6125

Sxx= (Xi-)2 =(Xi2)-n.2 = 1042.114 - 24 * 6.4049 ^2 = 57.5681

Syy= (Yi-)2 =(Yi2)-n.2 = 29581.65 - 24 * 34.6125 ^2  = 829.04625

Sxy= (Xi-)(Yi-) =(XiYi)-n. = 5511.925 - 24*6.4049* 34.6125 = 191.3746

a)

Least square estimate of slope is

= Sxy/Sxx= 191.3746 / 57.5681 = 3.324

Least square estimate of intercept is

= - . =34.6125 - 3.3243 x 6.4049 = 13.32

b)

So, Regression Equation become-

= + *X = 13.32 + 3.324 *X

Mean selling price when taxes paid are 5.3 is 13.32 + 3.324 * 5.3 = 30.94 (in thosands)

c)

For observation 2,  x = 5.0208 , fitted value = + *X = 13.32 + 3.324 *5.0208 = 30.01

Corresponding residual = Y - = 29.5 - 30.01 = - 0.51

If you find my answer useful please put thumbs up. Thank you.