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.
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Answer 1

Answer:

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

Step-by-step 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