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:Regression StatisticsMultiple R 0.865689R Square 0.749417Adjusted R Square 0.738754Standard Error 4.176602Observations 50ANOVA dfSSMSFRegressiona2451.9737021225.987dResidualb819.8680976c Total493271.8418 CoefficientsStandard Errort StatIntercept58.157082.65824820821.87797Horsepower-0.117530.032643428-3.60028Weight-0.006870.001401173-4.90349(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) The regression equation is Y= 58.15708 -0.11753 Horsepower -0.00687 Weight Unit increase in…

Answered: A research department of an American…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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:

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%.

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