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Homework answers / question archive / Grand Canyon UniversityBUS BUS-660 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

Grand Canyon UniversityBUS BUS-660 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

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Grand Canyon UniversityBUS BUS-660

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.

Year ---- Percentage of Adults Who Exercise 30 or more minutes at least three times per week

1 41.8

2 44.5

3 47.6

4 44.7

5 46.6

6 48

7 48.2

8 51.3

9 49.6

10 49.2

11 49.7

12 53

13 51

14 54.8

15 52.9

 

b) 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 = __________

Slope, b1 = __________

MSE = _________

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. 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)

________%

d) 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)

________%

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Solution:

(b) ->

y-intercept, b0 = 43.0657

Slope, b1 = 0.7243

MSE = 2.1378

 

So,

Trend equation is:

Percentage of adults who will report that they exercise for 30 or more minutes at least three times per week = 43.0657 + 0.7243*Year

 

(c) ->

For the next year,

Year = 15 + 1 = 16

So,

percentage of adults who will report that they exercise for 30 or more minutes at least three times per week

= 43.0657 + 0.7243*16

= 54.6545

 

Hence 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 is 54.6545%

 

(d) ->

For three years from now,

Year = 15 + 3 = 18

So,

percentage of adults who will report that they exercise for 30 or more minutes at least three times per week

= 43.0657 + 0.7243*18

= 56.1031

Hence 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 is 56.1031%

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