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 22.9
2 21.7
3 21
4 20.3
5 20.3
6 19.9
7 19.4
8 20.7
9 20.7
10 19
11 18.8
What type of pattern exists in the data?
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 =
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

The given data shows a downward trend in the percentage of U.S. adults who smoke tobacco over an 11-year period. Using simple linear regression analysis, the parameters for the line that minimizes MSE can be found. The regression model suggests whether OSH is on target to meet its goal of reducing the percentage of adult smokers to 12% or less within nine years.

Step-by-step explanation:

The given data shows the percentage of U.S. adults who smoke tobacco over an 11-year period. We are asked to determine the type of pattern in the data, find the parameters for the line that minimizes mean squared error (MSE), and assess if the goal of reducing the percentage of adult smokers to 12% or less within nine years is on target.

To determine the type of pattern in the data, we can examine the trend of the percentage of adult smokers over time. Looking at the numbers, we can see that the percentage decreases initially, experiences a slight increase, and then decreases again. This suggests a downward trend followed by some fluctuation.

To find the parameters for the line that minimizes MSE, we can use simple linear regression analysis. This involves finding the slope (b1) and y-intercept (b0) of the regression line that represents the best fit for the data. Using the given data points, we can calculate the values of b1, b0, and MSE.

Using the regression model from part (b), we can estimate the number of years it will take for OSH to achieve the goal of reducing the percentage of adult smokers to 12% or less. This can be done by plugging in the desired percentage into the regression equation and solving for the number of years. The rounded answer will give us the estimated number of years.

Answer 2

1.) A negative linear pattern

2.) Y = - 0.298X1 + 22.241

3.) slope = - 0.298 ; intercept = 22.241

Kindly check explanation

Step-by-step explanation:

Fitting the time series data using technology, the regression equation obtained is :

Y = - 0.298X+ 22.241

Where ; y = percentage of adults who smoke

x = year

Comparing with the linear equation model :

y = b1x + b0

y = - 0.298x + 22.41

-0.298 = slope

22.41 = intercept

The mean squared error, MSE = 0.512

To achieve, percentage users of 12% or less :

y = 12

Y = - 0.298X+ 22.241

12 = - 0.298X + 22.241

12 - 22.241 = - 0.298X1

-10.241 = - 0.298X

X = 10.241 / 0.298

X = 34.365

X = 35 years

From the model OSHA is not on target to meet it's goal as it will take 35 - 11 = 24 years from the last year of the data to achieve a smoker percentage less Than 12%