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In: Statistics and Probability

Problem 6-21 (Algorithmic) The Centers for Disease Control and Prevention Office on Smoking and Health (OSH)...

Problem 6-21 (Algorithmic)

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 22.7
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. e 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.

    years

Solutions

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Answer:

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 -0.1556

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