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21. The Centers for Disease Control and Prevention Office on Smoking and Health (OSH) is the lead federal agency responsible for comprehensive tobacco prevention and control, OSH was established in 1965 to reduce the death and disease caused by tobacco use and exposure to secondhand smoke. One of the many responsibilities of the OSH is to collect
data on tobacco use. The following data show the percentage of U.S. adults who were tics users of tobacco for a recent I1-year period thttp://www.cde.gov/tobaccordata statis /tables/trends/cig_smoking/index.htm). Year Percentage of Adults Who Smoke 22.8 22.5 21.6 20.9 20.9 20.8 19.8 20.6 20.6 19.3 18.9 4. 10 Construct a time series plot. What type of pattern exists in the data? Use simple linear regression to find the parameters for the line that minimizes MSE for this time series. a. b. c. One of OSHs goals is to cut the percentage of U.S. adults who were users of tobacco to 12% or less within nine years of the last year of these data. Does your regression model from part (b) suggest that OSH is on target to meet this goal? If not, use your model from part (b) to estimate the number of years that must pass after these data have been collected before OSH will achieve this goal.
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Answer #1

a) For the givena data the time series plot is as showa below: Time Series Plot of Percentages of Adults who smoke o 22 21- 2

B)

Year (t)

Percentage of Adult who smoke (y)

T = t-tm

Y= y-ym

TY

T2

1

22.8

-5

2

-10

25

2

22.5

-4

1.7

-6.8

16

3

21.6

-3

0.8

-2.4

9

4

20.9

-2

0.1

-0.2

4

5

20.9

-1

0.1

-0.1

1

6

20.8

0

0

0

0

7

19.8

1

-1

-1

1

8

20.6

2

-0.2

-0.4

4

9

20.6

3

-0.2

-0.6

9

10

19.3

4

-1.5

-6

16

11

18.9

5

-1.9

-9.5

25

Total = 66

228.7

-37

110

tm = Mean of t = 66/11 = 6

ym = Mean of y = 228.7/11 = 20.791

b1 = -37/110 = -0.33636

b0 = 20.8 – (-0.33636) (6) = 22.8091

c)

Substitute x=9 in the fitted regression line.

y = 22.8091 - 0.33636 x

= 22.8091 - 0.33636*(9)

= 19.78186

Regression model from part b does not suggest that OSH is on target to meet this goal.

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