Question

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.

Year	Percentage of Adults Who Smoke
1	22.8
2	21
3	20.5
4	20.5
5	20.5
6	19
7	19.4
8	20.2
9	20.2
10	19.3
11	18.9

1. Choose the correct time series plot.
   

   (i)		(ii)
   (iii)		(iv)

   
   
   
   What type of pattern exists in the data?
   
   
   
2. 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 =
   
3. 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

Answer 1

(a)

The time-series plot shows that there is a negative trend in the data.

(b)

y-intercept, b0 = 21.786

Slope, b1 = -0.2627

SSE = 4.6563

MSE = SSE / (n - 1) = 4.6563 / (11 - 1) = 0.466

Note: if the above MSE figure does not match, try 0.517 and 0.423 (there can be various methods to find MSE each is little different from the other, I don't know what's your instructor's choice)

(c)

Y = 12

Y = b0 + b1 x = 12

or, 21.786 - 0.2627*x = 12

or, x = (21.786 - 12) / 0.2627 = 37.3

So, another 38 - 11 = 27 years will be required to attain the target and the regression model does not suggest that the target will be achieved within 9 more years.