The medical community unanimously agrees on the health benefits of regular exercise, but are adults listening? During each of the past 15 years, a polling organization has surveyed Americans about their exercise habits. In the most recent of these polls, slightly over half of all American adults reported that they exercise for 30 or more minutes at least three times per week. The following data show the percentages of adults who reported that they exercise for 30 or more minutes at least three times per week during each of the 15 years of this study.

Percentage of Adults Who Reported That

They Exercise for 30 or More Minutes

Year at Least Three Times per Week

1 .................................................... 41.0

2 .................................................... 44.9

3 .................................................... 47.1

4 .................................................... 45.7

5 .................................................... 46.6

6 .................................................... 44.5

7 .................................................... 47.6

8 .................................................... 49.8

9 .................................................... 48.1

10 ................................................... 48.9

11 ................................................... 49.9

12 ................................................... 52.1

13 ................................................... 50.6

14 ................................................... 54.6

15 ................................................... 52.4

a. Construct a time series plot. Does a linear trend appear to be present?

b. Use simple linear regression to find the parameters for the line that minimizes MSE for this time series.

c. Use the trend equation from part (b) to forecast the percentage of adults next year (Year 16 of the study) who will report that they exercise for 30 or more minutes at least three times per week.

d. Would you feel comfortable using the trend equation from part (b) to forecast the percentage of adults three years from now (Year 18 of the study) who will report that they exercise for 30 or more minutes at least three times per week?