(a) Calculate the least squares estimates of the slope and intercept. Â₁ (Round your answer to 3 decimal places.) Bo = (b) Find the mean selling price given that the taxes paid are x = 5.3. (Round your answer to 2 decimal places.) (Round your answer to 2 decimal places.) (c) Calculate the fitted value of y corresponding to x = 5.0597 (observation # 5). Find the corresponding residual. ŷ = i (Round your answer to 2 decimal places.) y-ŷ = i (Round your answer to 2 decimal places.)
(a) Calculate the least squares estimates of the slope and intercept. Â₁ (Round your answer to 3 decimal places.) Bo = (b) Find the mean selling price given that the taxes paid are x = 5.3. (Round your answer to 2 decimal places.) (Round your answer to 2 decimal places.) (c) Calculate the fitted value of y corresponding to x = 5.0597 (observation # 5). Find the corresponding residual. ŷ = i (Round your answer to 2 decimal places.) y-ŷ = i (Round your answer to 2 decimal places.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Transcribed Image Text:Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise.
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.
i
Sale Price/1000 Taxes/1000
y - y =
25.9
29.5
i
27.9
25.9
29.9
29.9
30.9
28.9
35.9
31.5
31.0
30.9
30.0
36.9
41.9
40.5
43.9
37.5
37.9
44.5
37.9
38.9
(a) Calculate the least squares estimates of the slope and intercept.
B₁
36.9
45.8
Bo= i
(b) Find the mean selling price given that the taxes paid are x = 5.3.
(Round your answer to 2 decimal places.)
4.9176
5.0208
4.5429
4.5573
5.0597
3.8910
5.8980
5.6039
5.8282
5.3003
6.2712
5.9592
5.0500
8.2464
6.6969
7.7841
9.0384
5.9894
7.5422
8.7951
6.0831
8.3607
8.1400
9.1416
(Round your answer to 3 decimal places.)
(c) Calculate the fitted value of y corresponding to x = 5.0597 (observation # 5). Find the corresponding residual.
(Round your answer to 2 decimal places.)
(Round your answer to 2 decimal places.)
(Round your answer to 2 decimal places.)
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