A paint company collects data on the durability of its paint and that of its competitors. They measured the lifetimes of three samples of each type of paint in several American cities. The results are given in Table SE13.

TABLE SE13 Data for Exercise 13

 

Avg. Temp (?F)

Mean Annual

Lifetime (years)

City

January July

Precipitation (in.)

Sponsor”s Paint Competitor”s Paint

Atlanta, GA

41.9

78.6

48.6

11.5

10.7

12.3

10.8

11.1

10.2

Boston, MA

29.6

73.5

43.8

11.7

10.1

12.5

10.7

11.6

11.0

Kansas City, KS

28.4

80.9

29.3

12.3

13.4

12.8

11.8

12.2

11.3

Minneapolis, MN

11.2

73.1

26.4

10.5

9.9

11.2

10.4

9.6

9.2

Dallas, TX

45.0

86.3

34.2

11.2

10.6

12.0

10.6

10.1

11.4

Denver, CO

29.5

73.3

15.3

15.2

14.2

13.8

13.4

14.4

13.2

Miami, FL

67.1

82.4

57.5

8.7

7.9

9.4

8.1

8.6

7.6

Phoenix, AZ

52.3

92.3

7.1

11.1

11.8

12.4

10.9

10.1

9.9

San Francisco, CA

48.5

62.2

19.7

16.7

17.2

15.9

15.8

15.4

14.9

Seattle, WA

40.6

65.3

38.9

14.2

14.1

13.6

12.6

13.6

14.1

Washington, DC

35.2

78.9

39.0

12.6

11.5

12.0

11.9

10.9

11.4

 

a. Prior testing suggests that the most important factors that influence the lifetimes of paint coatings are the minimum temperature (estimated by the average January temperature), the maximum temperature (estimated by the average July temperature), and the annual precipitation. Using these variables, and products and powers of these variables, construct a good model for predicting the lifetime of the sponsor’s paint and a good model (perhaps different) for predicting the lifetime of the competitor’s paint.

b. Using the models developed in part (a), compute the expected lifetimes for these two paints for someone living in Cheyenne, Wyoming, where the January mean temperature is 26.1?F, the July mean temperature is 68.9?F, and the mean annual precipitation is 13.3 in.