Question

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. 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.

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 suggest that OSH is on target to meet this goal?

3. 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 in years.

Answer 1

Let y=Percentage of Adults Who Smoke

x=year

The regression line that we want ot estimate is

Using the data, we get the following

Calculate the sum of squares

The estimate of slope is

The estimate of intercept is

The sum of square error SSE is

The mean square error is

ans:

y-intercept, b0 = 21.785

Slope, b1 = -0.263

MSE = 0.517

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 suggest that OSH is on target to meet this goal?

The estimated regression equation is

The predicted percentage of U.S. adults who were users of tobacco in nine years of the last year of these data, which is x=11+9=20 is

That is, percentage of U.S. adults who were users of tobacco in nine years of the last year of these data is predicted to be 16.53%.

ans: the percentage of U.S. adults who were users of tobacco is not 12% or less within nine years of the last year of these data. Hence, regression model suggest that OSH is not on target to meet this goal.

3. 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 in years.

We want to find x which will given us a predicted y=12

For year=37.25, the predicted value of y is 12%. That means 37.25-11=26.25 years need to pass for the percentage to be less than 12%

ans: the number of years that must pass after these data have been collected before OSH will achieve this goal is 26 years (rounding to the nearest whole number)

Note: If we round 37.25 to the nearest integer, it would be 37. This produces a predicted y=12.06%, which is greater than 12. Hence if we need the percentage to be 12% or less, then we need to round up 37.25 to 38. Hence number of years that must pass would then be 27 years