An online retailer needs to manage the amount of time needed to select the ordered items and assemble them for shipping. In order to assess the amount of time his assemblers devote to this task, the retailer takes a random sample of 100 orders and records the number of items in each order and the time needed to assemble the shipment.

a. Plot the data on a scatter plot. Is the assumption of linearity satisfied?

b. Fit a least-squares regression line and interpret the coefficients.

c. Consider a transformation of the data to better fit the assumption of linearity. What transformation do you choose and why?

d. Fit a least-squares regression line to the transformed data.

e. Which model provides a better fit to the data? Justify your answer.

f. Predict the amount of time needed to assemble a package containing 13 items using both models

'NoItems' 'Time'

1 4.8

1 14.7

1 13.7

1 9.5

1 2.4

1 11.8

2 10.5

2 12

2 14.3

2 16.4

2 17.9

3 14.5

3 16.7

3 20.1

3 16.8

3 20.8

3 26.8

3 12.9

3 13

3 15.4

4 10.8

4 20.3

4 22.3

4 20

4 21.9

4 20.7

4 20.9

4 19.9

4 17.1

5 19.1

5 17.2

5 18.1

5 17.9

5 12.9

6 19.6

6 27.9

6 22.2

6 23.2

6 17.5

6 15.3

6 21.8

7 17.9

7 20.1

7 18.9

7 29.3

7 21.5

8 26.5

8 28.2

8 25.1

8 26.1

8 28.2

8 22.3

9 21.8

9 25.5

9 24.4

9 18.1

9 26.7

10 24.6

10 30.1

10 21.5

10 25.2

10 28.2

10 22.6

11 31.3

11 27.2

11 28.8

11 29.7

12 34.3

12 27.9

12 29.7

12 28.7

14 34.6

14 38

15 28

16 37

17 32.5

18 39.5

18 39

18 37

19 35.5

20 38.3

21 44

22 39.6

23 42.3

24 34.6

25 44.9

25 47.4

25 49.2

26 45.8

27 44

27 46.1

30 42.9

30 48.3

31 46

37 48.2

39 54.7

40 49.9

41 55.4

45 57.1

46 52.4