Problem 6-23 (Algorithmic)

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 Exercise 30 or more minutes at least three times per week

1 41.4 2 45.3 3 47.5 4 45.5 5 46.6 6 44.8 7 48 8 50.2 9 48.1 10 49.3 11 49.9 12 52.3 13 51 14 54.8 15 53.4

a. Choose the correct time series plot. (i) (ii) (iii) (iv)

(i)		(ii)
(iii)		(iv)

1. Does a linear trend appear to be present? no trend/ possible negative/ possible positive
2. use simple linear regression to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300) y-intercept, b₀ = fill in the blank --- Slope, b₁ = fill in the blank --- MSE = fill in the blank ---
3. 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. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300) fill in the blank ---- %
4. Use 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. Do not round your interim computations and round your final answers to four decimal places. For subtractive or negative numbers use a minus sign. (Example: -300) fill in the blank --- %

Possible Positive Linear TrendPossible Negative Linear TrendNo Trend