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We would like to use the weight of a car to predict its fuel economy. Weights (in 1000s of pounds) and fuel efficiency (in miles per gallon) are shown in the table below for a sample of ten car models: Weight Fuel Efficiency 25 3.1 3.7 2.2 3.4 2.0 3.9 3.0 2.5 3.6 2.7 21 31 22 35 16 24 27 17 29 It can be shown that i = 3.01, s, = 0.65, ỹ = 24.70, s, = 6.02, (r; – 1)? = 3.8025 and ( – ý)? = 24.92. i=1 The equation of the least-squares regression line is calculated to be ŷ = 51.47 – 8.89r. (a) Write out the simple linear regression model and define all terms. (b) The residual plot is shown below: 3- 2-

We would like to use the weight of a car to predict its fuel economy. Weights (in 1000s of pounds) and fuel efficiency (in miles per gallon) are shown in the table below for a sample of ten car models: Weight Fuel Efficiency 25 3.1 3.7 2.2 3.4 2.0 3.9 3.0 2.5 3.6 2.7 21 31 22 35 16 24 27 17 29 It can be shown that i = 3.01, s, = 0.65, ỹ = 24.70, s, = 6.02, (r; – 1)? = 3.8025 and ( – ý)? = 24.92. i=1 The equation of the least-squares regression line is calculated to be ŷ = 51.47 – 8.89r. (a) Write out the simple linear regression model and define all terms. (b) The residual plot is shown below: 3- 2-

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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We would like to use the weight of a car to predict its fuel economy. Weights (in 1000s of pounds) and fuel efficiency (in miles per gallon) are shown in the table below for a sample of ten car models: Weight Fuel Efficiency 25 3.1 3.7 2.2 3.4 2.0 3.9 3.0 2.5 3.6 2.7 21 31 22 35 16 24 27 17 29 It can be shown that i = 3.01, s, = 0.65, ỹ = 24.70, s, = 6.02, (r; – 1)? = 3.8025 and ( – ý)? = 24.92. i=1 The equation of the least-squares regression line is calculated to be ŷ = 51.47 – 8.89r. (a) Write out the simple linear regression model and define all terms. (b) The residual plot is shown below: 2- -3- 25 3.5 Weight What does the residual plot tell you about the validity of the regression model in (a)? (c) Construct a 95% confidence interval for the parameter ßị in the simple linear re- gression model. (d) Provide an interpretation of the confidence interval in (c). (e) Conduct a test of Ho: B1 = 0 vs. Ha: B1 + 0 at the 5% level of significance to determine whether there exists a linear relationship between the weight of a car and its fuel efficiency. Use the P-value method. (f) Provide an interpretation of the P-value of the test in (e). (g) Calculate a 95% confidence interval for the true mean fuel efficiency of a car that weighs 3200 pounds. jenpisa
Transcribed Image Text:We would like to use the weight of a car to predict its fuel economy. Weights (in 1000s of pounds) and fuel efficiency (in miles per gallon) are shown in the table below for a sample of ten car models: Weight Fuel Efficiency 25 3.1 3.7 2.2 3.4 2.0 3.9 3.0 2.5 3.6 2.7 21 31 22 35 16 24 27 17 29 It can be shown that i = 3.01, s, = 0.65, ỹ = 24.70, s, = 6.02, (r; – 1)? = 3.8025 and ( – ý)? = 24.92. i=1 The equation of the least-squares regression line is calculated to be ŷ = 51.47 – 8.89r. (a) Write out the simple linear regression model and define all terms. (b) The residual plot is shown below: 2- -3- 25 3.5 Weight What does the residual plot tell you about the validity of the regression model in (a)? (c) Construct a 95% confidence interval for the parameter ßị in the simple linear re- gression model. (d) Provide an interpretation of the confidence interval in (c). (e) Conduct a test of Ho: B1 = 0 vs. Ha: B1 + 0 at the 5% level of significance to determine whether there exists a linear relationship between the weight of a car and its fuel efficiency. Use the P-value method. (f) Provide an interpretation of the P-value of the test in (e). (g) Calculate a 95% confidence interval for the true mean fuel efficiency of a car that weighs 3200 pounds. jenpisa
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