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# Moving Company: Predicting Labor Hours

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The owner of a large moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach had proved useful in the past, but he would like to be able to develop a more accurate method of predicting the labor hours by using the amount of cubic feet moved. In a preliminary effort to provide a more accurate method, he has collected data for 36 moves, in which the travel time was an insignificant portion of the labor hours worked.

Hours Feet Large Elevator
24.00 545 3 Yes
13.50 400 2 Yes
26.25 562 2 No
25.00 540 2 No
9.00 220 1 Yes
20.00 344 3 Yes
22.00 569 2 Yes
11.25 340 1 Yes
50.00 900 6 Yes
12.00 285 1 Yes
38.75 865 4 Yes
40.00 831 4 Yes
19.50 344 3 Yes
18.00 360 2 Yes
28.00 750 3 Yes
27.00 650 2 Yes
21.00 415 2 No
15.00 275 2 Yes
25.00 557 2 Yes
45.00 1028 5 Yes
29.00 793 4 Yes
21.00 523 3 Yes
22.00 564 3 Yes
16.50 312 2 Yes
37.00 757 3 No
32.00 600 3 No
34.00 796 3 Yes
25.00 577 3 Yes
31.00 500 4 Yes
24.00 695 3 Yes
40.00 1054 4 Yes
27.00 486 3 Yes
18.00 442 2 Yes
62.50 1249 5 No
53.75 995 6 Yes
79.50 1397 7 No

a) Set up a scatter diagram.
b) Assuming a linear relationship, find the regression coefficients, b0, b1, and its regression equation.
c) Interpret the meaning of the slope b1 in this problem.
d) Predict the labor hours for moving 500 cubic feet.
e) What factors besides the cubic feet moved might affect labor hours?
f) Determine the coefficient of determination, r2, and interpret its meaning.
g) Find the standard error of the estimate.
h) How useful do you think this regression model is for labor hours?
i) Determine if the assumption of normality is violated by using the normal probability plot for residuals.
j) At the 0.05 level of significance, is there evidence of a linear relationship between the numbers of cubic feet moved and labor hours?
k) Set up a 95% confidence interval estimate of the population slope, β1.
l) Set up a 95% confidence interval estimate of the average labor hours for all moves of 500 cubic feet.
m) Set up a 95% confidence interval of the labor hours of an individual move that has 500 cubic feet.
n) Explain the difference in the results obtained in (l) and (m).