Question

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 users of tobacco for a recent 11-year period (http://www.cdc.gov/tobacco/data_statistics/tables/trends/cig_smoking/index.htm).

Year Percentage of Adults Who Smoke

1. 22.9

2 22.1

3 21.6

4 20.9

5 20.9

6. 20.4

7 19.5

8 20.4

9 20.4

10 19.6

11 18.9

Use simple linear regression analysis 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 three decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)

y-intercept, b0 =

Slope, b1 =

MSE =

One of OSH's 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?

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. Round your answer to the nearest whole number.

Answer 1

	Year (t)	Percentage of Adults who smoke (Yt)	t*Yt	t2
	1	22.9	22.9	1
	2	22.1	44.2	4
	3	21.6	64.8	9
	4	20.9	83.6	16
	5	20.9	104.5	25
	6	20.4	122.4	36
	7	19.5	136.5	49
	8	20.4	163.2	64
	9	20.4	183.6	81
	10	19.6	196	100
	11	18.9	207.9	121
Total	66	227.6	1329.6	506
Average	6	20.69

Y_t = b₀ + b₁t

b₁ =

b₁ = -0.327

= 20.69 - (-0.327)*6 = 22.655

Y_t = 22.655 -0.327t

Year (t)	Percentage of Adults who smoke (Y)	Forecast	Forecast error	Squared Forecast error
1	22.9	22.328	0.572	0.327184
2	22.1	22.001	0.099	0.009801
3	21.6	21.674	-0.074	0.005476
4	20.9	21.347	-0.447	0.199809
5	20.9	21.02	-0.12	0.0144
6	20.4	20.693	-0.293	0.085849
7	19.5	20.366	-0.866	0.749956
8	20.4	20.039	0.361	0.130321
9	20.4	19.712	0.688	0.473344
10	19.6	19.385	0.215	0.046225
11	18.9	19.058	-0.158	0.024964
			Total	2.067329

MSE = = 2.067/11 = 0.188

After 9 years from the last year means t = 20

for t = 20

Y_t = 22.655 - 0.327*20 = 16.11%

Regression model from part (b) does not suggest that OSH is on target to meet this goal of 12%.

For Y = 12%

t = ?

12 = 22.622 - 0.327t => t = 35.6 years which means it will take 24.6 years from the previous year to meet this target.