Question

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 sur- veyed 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 reported that they exercise for 30 or more 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 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?

Answer 1

a)

a linear trend appear to be present

b)

Regression Statistics
Multiple R	0.9045
R Square	0.8182
Adjusted R Square	0.8042
Standard Error	1.5415
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	139.03	139.03	58.51	0.0000
Residual	13	30.89	2.38
Total	14	169.92
	Coefficients	Standard Error	t Stat	P-value	lower 95%	upper 95%
Intercept	42.5495	0.838	50.800	0.0000	40.7400	44.36
X	0.7046	0.092	7.649	0.0000	0.5056	0.9037

so, regression line is   Ŷ =   42.550   +   0.705   *x

c)

Predicted Y at X=   16   is          
Ŷ =   42.5495   +   0.7046   *16=   53.824

d)

No, extrapolation of variable X can lead to wrong prediction