The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between t

Question

The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Age (years) Selling Price ($000) Age (years) Selling Price ($000) Car 2 4 6 Car 6.0 3.6 4.0 5.0 10.0 7.6 8.0 8.0 6.0 8.6 8.0 10 12 12 12 Click here for the Excel Data File a. Determine the regression equation. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) b. Estimate the selling price of a 10-year-old car (in $000). (Round your answer to 3 decimal places.) C. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.) For each additional year, the car decreases $ in value

Explanation / Answer

Solution:

Here, we have to find the regression equation for the prediction of a selling price ($000) of a car based on the age of car in years.

Regression output by using excel is given as below:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.543646332

R Square

0.295551334

Adjusted R Square

0.225106468

Standard Error

1.732105125

Observations

12

ANOVA

df

SS

MS

F

Significance F

Regression

1

12.58728503

12.58729

4.195499

0.067701617

Residual

10

30.00188164

3.000188

Total

11

42.58916667

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

11.17723824

2.143271172

5.215037

0.000393

6.401732492

15.95274399

Age

-0.47875569

0.233734146

-2.04829

0.067702

-0.99954782

0.042036439

Part a

Answer:

a = 11.177

b = -0.479

Y-intercept of the regression equation is 11.177 while slope of the regression equation is given as -0.479.

Regression equation is given as below:

Selling Price ($000) = 11.177 – 0.479*Age

Part b

Here, we have to find selling price of a 10 year old car.

Age = 10 years

Selling Price ($000) = 11.177 – 0.479*Age

Selling Price ($000) = 11.177 - 0.479*10

Selling Price ($000) = 6.387

Part c

For each additional year, the car decreases $0.479*1000 = $479 in value.

(Slope of a regression equation is given as b = - 0.479, which indicate decrement in selling price as unit number of year increase. Also, negative slope indicate a negative relationship between the age of car and selling price.)

For each additional year, the car decreases $479 in value.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.543646332

R Square

0.295551334

Adjusted R Square

0.225106468

Standard Error

1.732105125

Observations

12

ANOVA

df

SS

MS

F

Significance F

Regression

1

12.58728503

12.58729

4.195499

0.067701617

Residual

10

30.00188164

3.000188

Total

11

42.58916667

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

11.17723824

2.143271172

5.215037

0.000393

6.401732492

15.95274399

Age

-0.47875569

0.233734146

-2.04829

0.067702

-0.99954782

0.042036439

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.