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11.7. Machine speed. The number of defective items produced by a machine (Y) is known to be linearly related to the speed setting of the machine (X). The data below were collected from recent quality control records. i: 1 2 3 4 56 7 8 9 10 11 12 Xi: 200 400 300 400 200 300 300 400 200 400 200 300 Yi: 40 28 75 37 53 22 52 30 58 96 46 69

11.7. Machine speed. The number of defective items produced by a machine (Y) is known to be linearly related to the speed setting of the machine (X). The data below were collected from recent quality control records. i: 1 2 3 4 56 7 8 9 10 11 12 Xi: 200 400 300 400 200 300 300 400 200 400 200 300 Yi: 40 28 75 37 53 22 52 30 58 96 46 69

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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11.7. Machine speed. The number of defective items produced by a machine (Y) is known to be linearly related to the speed setting of the machine (X). The data below were collected from recent quality control records. i: 1 2 3 4 5 6 7 8 9 10 11 12 Xi: 200 400 300 400 200 300 300 400 200 400 200 300 Yi: 40 28 96 75 46 37 52 53 30 22 69 58 a. Fit a linear regression function by ordinary least squares, obtain the residuals, and plot the residuals against X. What does the residual plot suggest? b. Conduct the Breusch-Pagan test for constancy of the error variance, assuming loge oi2 = yo + y1 Xi; use a = .10. State the alternatives, decision rule, and conclusion. c. Plot the squared residuals against X. What does the plot suggest about the relation between the variance of the error term and X?
Transcribed Image Text:11.7. Machine speed. The number of defective items produced by a machine (Y) is known to be linearly related to the speed setting of the machine (X). The data below were collected from recent quality control records. i: 1 2 3 4 5 6 7 8 9 10 11 12 Xi: 200 400 300 400 200 300 300 400 200 400 200 300 Yi: 40 28 96 75 46 37 52 53 30 22 69 58 a. Fit a linear regression function by ordinary least squares, obtain the residuals, and plot the residuals against X. What does the residual plot suggest? b. Conduct the Breusch-Pagan test for constancy of the error variance, assuming loge oi2 = yo + y1 Xi; use a = .10. State the alternatives, decision rule, and conclusion. c. Plot the squared residuals against X. What does the plot suggest about the relation between the variance of the error term and X?
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