Question

*****Show step-by-step in Excel******

An automobile rental company wants to predict the yearly maintenance expense (Y) for an automobile using the number of miles driven during the year ( X1 ) and the age of the car ( X2 , in years) at the beginning of the year. The company has gathered the data on 10 automobiles and the regression information from Excel is presented below. Use this information to answer the following questions.

Summary measures Multiple R 0.9689 R-Square 0.9387 Adj R-Squared 0.9212 StErr of Estimate 72.218

	Regression Coefficient
	Coefficient	std err	t-value	p-value
constant	33.796	48.181	0.7014	0.5057
Miles Driven	0.0549	0.0191	2.8666	0.0241
Age of Car	21.467	20.573	1.0434	0.3314

a. Use the information above to write out the estimated linear regression model.

b. Interpret each of the estimated coefficients of the regression model in part (a).

c. Identify and interpret the coefficient of determination ( R2 ) and the adjusted R2 .

d. Does the given set of explanatory variables do a good job of explaining changes in the maintenance costs? Explain why or why not.

Answer 1

SolutionA:

the estimated linear regression model is

yearly maintenance expense =33.796+0.0549*Miles Driven+21.467*Age of car

SolutionB:

b. Interpret each of the estimated coefficients of the regression model in part (a).

For Miles Driven the coeffi cient is 0.0549

slope=y/x

0.0549=Expense/miles

it means Holding all others variables constant , for each additional mile driven the predicted yearly maintenance expense increases by 0.0549

For Age of car the coefficient is 21.467

it means that Holding all others variables constant , for each additional increase in age of car,the predicted the yearly maintenance expense increases by 21.467 .

c. Identify and interpret the coefficient of determination ( R2 ) and the adjusted R2 .

R sq=0.9387

93.87% variation in yearly maintenance expense is explained by model .

Good model.

Ad j R sq=0.9212

SolutionD:

For the variable Miles Driven

t=2,8666

p=0.0241

p<0.05

Miles Driven is significant variable in Predicting  yearly maintenance expense

For the variable,

Age of Car

t=1.0434

p=0.3314

p>0.05

Age of car is not a significant varaible in Predicting  yearly maintenance expense.