A research department of an American automobile company wants to develop a model to predict gasoline mileage (measured in MPG) of the company’s vehicles by using their horsepower and weights (measured in pounds). To do this, it took a random sample of 50 vehicles to perform a regression analysis as follows: SUMMARY OUTPUT Regression Statistics Multiple R 0.865689 R Square 0.749417 Adjusted R Square 0.738754 Standard Error 4.176602 Observations 50 ANOVA df SS MS F Regression a 2451.973702 1225.987 d Residual b 819.8680976 c Total 49 3271.8418 Coefficients Standard Error t Stat Intercept 58.15708 2.658248208 21.87797 Horsepower -0.11753 0.032643428 -3.60028 Weight -0.00687 0.001401173 -4.90349 (a) State the multiple regression equation. Interpret the meanings of the coefficients for horsepower and weight. (b) Test the validity of this multiple regression equation at the significance level of 1%. Show your reasoning. (c) The research department claims that the weight of the vehicle is negatively linearly related to its gasoline mileage. Test its claim at the significance level of 1%.

A research department of an American automobile company wants to develop a model to predict gasoline mileage (measured in MPG) of the company’s vehicles by using their horsepower and weights (measured in pounds). To do this, it took a random sample of 50 vehicles to perform a regression analysis as follows: SUMMARY OUTPUT Regression Statistics Multiple R 0.865689 R Square 0.749417 Adjusted R Square 0.738754 Standard Error 4.176602 Observations 50 ANOVA df SS MS F Regression a 2451.973702 1225.987 d Residual b 819.8680976 c Total 49 3271.8418 Coefficients Standard Error t Stat Intercept 58.15708 2.658248208 21.87797 Horsepower -0.11753 0.032643428 -3.60028 Weight -0.00687 0.001401173 -4.90349 (a) State the multiple regression equation. Interpret the meanings of the coefficients for horsepower and weight. (b) Test the validity of this multiple regression equation at the significance level of 1%. Show your reasoning. (c) The research department claims that the weight of the vehicle is negatively linearly related to its gasoline mileage. Test its claim at the significance level of 1%.

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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