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 :	Xi:	Yi:
1	200	28
2	400	75
3	300	37
4	400	53
5	200	22
6	300	58
7	300	40
8	400	96
9	200	46
10	400	52
11	200	30
12	300	69

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

i2 = 0 + 1 Xi; use = .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?