Question

The owner of Maumee Ford-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.

Car Age (years) Selling Price ($000)
1 9 11.1
2 5 9.5
3 13 4.4
4 17 4.4
5 7 8.0 6
6 12.0 7
7 10.6
8 14 8.1
9 12 8.1
10 17 4.8
11 4 12.5
12 4 10.7
a. Determine the regression equation. Use the rounded slope value to compute the y-intercept. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
a = ___
b = ___
b. Estimate the selling price (in dollars) of a 7-year-old car. (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)
$____
c. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)
For each additional year, the car decreases $ ___ in value.
(Scroll Down for Answer!)

Answer 1

b= - 1.26317

a = 17.237

b. The selling price (in dollars) of a 7-year-old car

y = 8394.81 dollars

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

1263.17 $ decreases per year

Explanation:

Let y be the selling price in thousands and x be the age in years

Car Age Selling Price

(years) ($000) XY X²

X Y

1 9 11.1 99.9 81

2 5 9.5 47.5 25

3 13 4.4 57.2 169

4 17 4.4 74.8 289

5 7 8.06 56.42 49

6 1 2.07 2.07 1

7 1 0.6 0.6 1

8 14 8.1 113.4 196

9 12 8.1 97.2 144

10 17 4.8 81.6 289

11 4 12.5 50 16

12 4 10.7 42.8 16

∑ 97 84.33 723.49 1276

The estimated regression line of Y on X is

Y= a +bX

and the two normal equations are

∑ y= na + b∑X

∑XY= a∑X + b∑X²

Now

X`= ∑X/n = 97/12= 8.083

b= n∑XY - (∑X)(∑Y)/ n∑ X²- (∑X)²

b= 723.49 - (97)(84.33)/ 12(1276) - (97)²

b= -7456.52/ 5903

b= - 1.26317

a= Y`- b X`

a= 7.0275 - (-- 1.26317)8.083

a = 17.237

Y = 17.237 - 1.26317 X

y= - 1.26317 X + 17.237

b. The selling price (in dollars) of a 7-year-old car

y = - 1.26317 (7) + 17.237

y= 8.39481

y = 8394.81 dollars

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

1.26317 *1000= 1263.17 $ decreases per year