Question

Please use DataAnalysis

A study was conducted to build a regression model to predict miles per gallon (MPG) of vehicles. To develop the model, you obtained MPG of 43 random vehicles. In addition, you collected the following information - Length: vehicle length (inches) - Width: vehicle width (inches) - Weight: vehicle weight (pounds) - Made in Japan: whether the car is manufactured in Japan or not a. Fit a multiple regression model using all four independent variables. For "made in Japan" variable create an indicator/dummy variable with "not made in Japan" as the reference/baseline group. Provide the equation of the fit line. Interpret the regression model parameters in the context of the problem. b. What proportion of variability in the dependent variable is explained by the independent variables? c. Test whether the regression model is statistically significant d. Is the variable "width" a significant predictor of MPG? e. Is the variable "weight" a significant predictor of MPG? f. For a car that is 200 inches long, 79 inches wide, weighs 4220 pounds and is not made in Japan, what would be the predicted MPG? g. Does the variable "width" have a non-linear effect on the dependent variable? (fit a multiple regression model with all independent variables)

Answer 1

using excel we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.838297
R Square	0.702743
Adjusted R Square	0.671452
Standard Error	2.505461
Observations	43
ANOVA
	df	SS	MS	F	Significance F
Regression	4	563.9264	140.9816	22.45883	1.4E-09
Residual	38	238.5387	6.277334
Total	42	802.4651
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	43.99318	8.476698	5.189896	7.33E-06	26.833	61.15336
Length	-0.00387	0.044495	-0.08699	0.931133	-0.09395	0.086205
width	-0.10644	0.139471	-0.76316	0.450077	-0.38878	0.175905
weight	-0.00413	0.000833	-4.95462	1.53E-05	-0.00581	-0.00244
made in japan	-1.32279	0.814564	-1.62393	0.112659	-2.97179	0.326207

estimated mpg= 43.99-0.004 length -0.106 width -0.004 weight -1.323 Made in japan

Interpret the regression model parameters

for one unit increase in length, there is a corresponding 0.004 decrease in mpg.

for one unit increase in width, there is a corresponding 0.106 decrease in mpg.

for one unit increase in weight, there is a corresponding 0.004 decrease in mpg.

if vehicles are made in Japan, there is a corresponding 1.323 decrease in mpg.

Ans b ) 70.27 % variability in the dependent variable is explained by the independent variable

Ans c ) since the p-value of f statistic is less than 0.05, so the regression model is statistically significant.

Ans d ) width is not statistically significant because p-value 0.4500 is greater than 0.05

Ans e ) weight is statistically significant because p-value 0.0000 is less than 0.05.

Ans f ) for length =200 inches

width = 79 , weight = 4220 and not made in japan

estimated mpg= 43.99-0.004*200 -0.106*79 -0.004 *4220 -1.323*0 =17.936

g ) yes, the width have a non linear effect on the dependent variabale