Question

1. Engineer wants to develop a model to describe the gas mileage of a sport utility vehicle. He collects the data presented in following table.

2008 Model	Engine Size (liters)	Cylinders	Final Drive Ratio	Miles per Gallon
Mercedes Benz	5	8	4.38	13
Jeep Wrangler	3.8	6	3.21	16
Mitsubishi Endeavor	3.8	6	4.01	18
Toyota Land Cruiser	5.7	8	3.91	15
Kia Sorento	3.3	6	3.33	18
Jeep Commander Sport	4.7	8	3.73	15
Dodge Durango	4.7	8	3.55	15
Lincoln Navigator	5.4	8	3.73	15
Chevrolet Tahoe	4.8	8	3.23	16
Ford Escape	3	6	2.93	20
Ford Expedition	5.4	8	3.31	14
Buick Enclave	3.6	6	3.16	19
Cadillac Escalade	6.2	8	3.42	14
Hummer	3.7	5	4.56	15
Saab 9-7X	4.2	6	3.73	16

1. Identify the dependent variable and independent variables.

2. Build a multiple linear regression model to predict miles per gallon.

3. Can this model used to make predictions? Explain.

Answer 1

1. Identify the dependent variable and independent variables.

The dependent variable for this regression model is given as miles per gallon, while the independent variables for this regression model are given as engine size in liters, number of cylinders, and final drive ratio.

2. Build a multiple linear regression model to predict miles per gallon.

A required multiple regression model by using excel to predict the miles per gallon is given as below:

Regression Statistics
Multiple R	0.882349692
R Square	0.778540978
Adjusted R Square	0.718143063
Standard Error	1.051642968
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	3	42.76785108	14.25595036	12.89019627	0.000637609
Residual	11	12.16548225	1.105952932
Total	14	54.93333333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	29.58398137	3.141907801	9.415929188	1.34438E-06	22.66868893	36.49927381
Engine Size (liters)	-1.275237681	0.615848639	-2.070699846	0.062697156	-2.630711395	0.080236032
Cylinders	-0.226707152	0.506257962	-0.447809555	0.66298163	-1.340973413	0.887559108
Final Drive Ratio	-1.755526363	0.666953946	-2.6321553	0.023317377	-3.223482098	-0.287570627

Required regression model or equation is given as below:

Miles per gallon = 29.58398137 - 1.275237681* Engine Size - 0.226707152* Cylinders - 1.755526363* Final Drive Ratio

3. Can this model used to make predictions? Explain.

Yes, this model can used to make predictions because the p-value for this regression model is given as 0.0006376 which is very smaller than 1% level of significance. Also, multiple correlation coefficient is given as 0.8823 which suggest the strong linear relationship between the dependent variable and combination of independent variables.