The Centers for Disease Control and Prevention Office on Smoking and health is the lead federal agency responsible for comrehens
ive 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 responsibilites 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 Percentages of Adults who smoke
1 22.8
2 22.5
3 21.6
4 20.9
5 20.9
6 20.8
7 19.8
8 20.6
9 20.6
10 19.3
11 18.9
a. Construct a time series plot. What type of pattern exists in the data?
b. use simple linear regression to fidn the parameters for the line that minimizes MSE for this time series.
c. One of OSH's goals is to cut the percntage of use adults who were users of tobacco to 12% or less within nine years of the last year of these data. Does yoru 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.
a) The percentage of adults who smoke are decreasing with time. b) the equation that best described this data is y=-0.3364x+22.809 (R^2=0.859) in which y is the percentage of adults who smoke and x the number of years. c) the percentage of adults who smoke will be 19.8% and it will not meet the expected 12%, it would take 32 years to reach that value.
Step-by-step explanation:
The data can be plotted to which years is the independent variable and percentage of adults who smoke is the dependent variable. The linear trendline that described this data has a negative slope which indicates that the percentage of adults is decreasing with time. In order to determine if the OSH target is being met, the x is replaced by 9 which is the goal period of nine years. The y is 19% which is higher than the 12% goal. In order to know the period it will take to the reach the goal of 12%, the y is replaced by 12 in the curve and the x is the answer in years = 32 years.
