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

Year	Percentage of Adults Who Smoke
1	22.7
2	21.9
3	21.2
4	20.8
5	20.8
6	20.2
7	19.3
8	20.6
9	20.6
10	19.8
11	18.9

1. 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 =
   
2. 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. Yes or No
   
   years=

Answer 1

(a)y-intercept, b0=22.4146

slope, b1=-0.2827

MSE=0.3471

(b) here slope=-0.2827, which change in dependent variable when unit change is done in independent variable.

so each year there will decrease in smoking by 0.2827%

so in 9 years there would decrease =9*0.2827=2.5443%, so  regression model from part (b) does not suggest that OSH is on target to meet this goal

required number of years=12/0.2827=42.4877 ( required number of 42 years, nearest whole number)

Regression Statistics
Multiple R	0.858998
R Square	0.737878
Adjusted R Square	0.708753
Standard Error	0.589118
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	8.792818	8.792818	25.33511	0.000706
Residual	9	3.123545	0.347061
Total	10	11.91636
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	22.31455	0.380965	58.57372	6.21E-13	21.45274	23.17635
X Variable 1	-0.28273	0.05617	-5.0334	0.000706	-0.40979	-0.15566