The medical community unanimously agrees on the health benefitsof regular exercise, but are adults listening? during each of thepast 15 years, a polling organization has sur- veyed americansabout their exercise habits. in the most recent of these polls,slightly over half of all american adults reported that theyexercise for 30 or more minutes at least three times per week. Thefollowing data show the percentages of adults who reported thatthey exercise for 30 or more minutes at least three times per weekduring each of the 15 years of this study.
YEAR | Percentage of adults who reported that they exercise for 30 ormore minutes 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 | 48.9 |
12 | 52.1 |
13 | 50.6 |
14 | 54.6 |
15 | 52.4 |
a. Construct a time series plot. does a linear trend appear tobe present?
b. use simple linear regression to find the parameters for theline that minimizes mSe for this time series.
c. use the trend equation from part (b) to forecast thepercentage of adults next year (year 16 of the study) who willreport that they exercise for 30 or more minutes at least threetimes per week.
d. Would you feel comfortable using the trend equation from part(b) to forecast the percentage of adults three years from now (year18 of the study) who will report that they exercise for 30 or moreminutes at least three times per week?
