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A certain agency has a goal of reducing the death and disease caused by tobacco use and exposure to second-hand smoke. One of the many responsibilities of the agency is to collect data on tobacco use. Suppose the following data show the percentage of adults in the United States who were users of tobacco during an 11-year period: Percentage of Adults Who Smoke Year Percent of Adults Who Smoke 1 2 3 4 7 5 8 6 9 10 20 11 (a) Construct a time series plot. 15 20 10- 0 0 15- 10- 5 04 0 2 2 4 4 22.6 22.3 21.4 20.7 20.7 20.5 19.6 20.3 20.4 19.1 18.7 6 Period 6 Period 8 8 10 12 10 12 What type of pattern exists in the data? O The time series plot exhibits a horizontal pattern. O The time series plot exhibits a cyclical pattern. O The time series plot exhibits a seasonal pattern. O The time series plot exhibits a trend pattern. O Percent of Adults Who Smoke Percent of Adults Who Smoke 15 10- 5 0 0 15- 10- 0 2 2 4 4 6 Period. 6 Period 8 8 10 Does your regression model from part (b) suggest that the agency is on target to meet this goal? OYes O No 10 12 (b) Use simple linear regression to find the parameters for the line that minimizes MSE for this time series. (Round your answers to three decimal places.) b₁ = b = Find the forecast of the percent of adults who smoke for year 20. (Round your answer to one decimal place.) 20- % 12 6 (c) One of the agency's goals is to cut the percentage of adults in the United States who were users of tobacco to 12% or less by year 20. Q If not, use your model from part (b) to estimate the year in which the agency will achieve this goal. (Enter 20 if the goal will be met by year 20.)

A certain agency has a goal of reducing the death and disease caused by tobacco use and exposure to second-hand smoke. One of the many responsibilities of the agency is to collect data on tobacco use. Suppose the following data show the percentage of adults in the United States who were users of tobacco during an 11-year period: Percentage of Adults Who Smoke Year Percent of Adults Who Smoke 1 2 3 4 7 5 8 6 9 10 20 11 (a) Construct a time series plot. 15 20 10- 0 0 15- 10- 5 04 0 2 2 4 4 22.6 22.3 21.4 20.7 20.7 20.5 19.6 20.3 20.4 19.1 18.7 6 Period 6 Period 8 8 10 12 10 12 What type of pattern exists in the data? O The time series plot exhibits a horizontal pattern. O The time series plot exhibits a cyclical pattern. O The time series plot exhibits a seasonal pattern. O The time series plot exhibits a trend pattern. O Percent of Adults Who Smoke Percent of Adults Who Smoke 15 10- 5 0 0 15- 10- 0 2 2 4 4 6 Period. 6 Period 8 8 10 Does your regression model from part (b) suggest that the agency is on target to meet this goal? OYes O No 10 12 (b) Use simple linear regression to find the parameters for the line that minimizes MSE for this time series. (Round your answers to three decimal places.) b₁ = b = Find the forecast of the percent of adults who smoke for year 20. (Round your answer to one decimal place.) 20- % 12 6 (c) One of the agency's goals is to cut the percentage of adults in the United States who were users of tobacco to 12% or less by year 20. Q If not, use your model from part (b) to estimate the year in which the agency will achieve this goal. (Enter 20 if the goal will be met by year 20.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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A certain agency has a goal of reducing the death and disease caused by tobacco use and exposure to second-hand smoke. One of the many responsibilities of the agency is to collect data on tobacco use. Suppose the following data show the percentage of adults in the United States who were users of tobacco during an 11-year period: Percent of Adults Who St Percent of Adults Who Smoke Year Percentage of Adults Who Smoke b₁ = bo = 2 1 20 15 3 8 (a) Construct a time series plot. 25 10 4 9 5 10 6 11 20 7 10 5 O No 25- 15+ 5 0 2 2 4 22.6 22.3 21.4 20.7 20.7 20.5 19.6 20.3 20.4 19.1 18.7 6 Period What type of pattern exists in the data? 6 Period 8 8 10 10 12 12 The time series plot exhibits a horizontal pattern. The time series plot exhibits a cyclical pattern. The time series plot exhibits a seasonal pattern. The time series plot exhibits a trend pattern. no Percent of Adults Who Smoke ǝ Percent of Adults Who Smoke O 25 20 15- 10- 5 25 20 0 15- 10+ 0 0 2 2 4 4 6 Period 6 Period 8 8 10 12 (b) Use simple linear regression to find the parameters for the line that minimizes MSE for this time series. (Round your answers to three decimal places.) 10 12 (c) One of the agency's goals is to cut the percentage of adults in the United States who were users of tobacco to 12% or less by year 20. Find the forecast of the percent of adults who smoke for year 20. (Round your answer to one decimal place.) % 20 Does your regression model from part (b) suggest that the agency is on target to meet this goal? Yes If not, use your model from part (b) to estimate the year in which the agency will achieve this goal. (Enter 20 if the goal will be met by year 20.)
Transcribed Image Text:A certain agency has a goal of reducing the death and disease caused by tobacco use and exposure to second-hand smoke. One of the many responsibilities of the agency is to collect data on tobacco use. Suppose the following data show the percentage of adults in the United States who were users of tobacco during an 11-year period: Percent of Adults Who St Percent of Adults Who Smoke Year Percentage of Adults Who Smoke b₁ = bo = 2 1 20 15 3 8 (a) Construct a time series plot. 25 10 4 9 5 10 6 11 20 7 10 5 O No 25- 15+ 5 0 2 2 4 22.6 22.3 21.4 20.7 20.7 20.5 19.6 20.3 20.4 19.1 18.7 6 Period What type of pattern exists in the data? 6 Period 8 8 10 10 12 12 The time series plot exhibits a horizontal pattern. The time series plot exhibits a cyclical pattern. The time series plot exhibits a seasonal pattern. The time series plot exhibits a trend pattern. no Percent of Adults Who Smoke ǝ Percent of Adults Who Smoke O 25 20 15- 10- 5 25 20 0 15- 10+ 0 0 2 2 4 4 6 Period 6 Period 8 8 10 12 (b) Use simple linear regression to find the parameters for the line that minimizes MSE for this time series. (Round your answers to three decimal places.) 10 12 (c) One of the agency's goals is to cut the percentage of adults in the United States who were users of tobacco to 12% or less by year 20. Find the forecast of the percent of adults who smoke for year 20. (Round your answer to one decimal place.) % 20 Does your regression model from part (b) suggest that the agency is on target to meet this goal? Yes If not, use your model from part (b) to estimate the year in which the agency will achieve this goal. (Enter 20 if the goal will be met by year 20.)
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