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 | 12 | 10.7 | ||||||||
2 | 8 | 8.8 | ||||||||
3 | 13 | 3.0 | ||||||||
4 | 15 | 2.7 | ||||||||
5 | 10 | 6.0 | ||||||||
6 | 9 | 12.1 | ||||||||
7 | 10 | 9.0 | ||||||||
8 | 13 | 7.8 | ||||||||
9 | 12 | 7.8 | ||||||||
10 | 15 | 4.7 | ||||||||
11 | 6 | 10.8 | ||||||||
12 | 6 | 8.9 | ||||||||
a. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
a=
b=
b. Estimate the selling price of an 8-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.)
Ans:
Car | Age (years) | Selling Price ($000) |
1 | 12 | 10.7 |
2 | 8 | 8.8 |
3 | 13 | 3 |
4 | 15 | 2.7 |
5 | 10 | 6 |
6 | 9 | 12.1 |
7 | 10 | 9 |
8 | 13 | 7.8 |
9 | 12 | 7.8 |
10 | 15 | 4.7 |
11 | 6 | 10.8 |
12 | 6 | 8.9 |
mean | 10.750 | 7.692 |
std. dev | 3.108 | 3.035 |
r | -0.687 | |
slope,b | -0.671 | |
y-intercept,a | 14.908 |
a)Regression equation:
y'=-0.671 x+14.908
a=14.908
b=-0.671
b)
when age=8 years
Predicted selling price,y'=-0.671*8+14.908=9.538
c)
when age=0,then selling price=14.908 thousand dollars=14908 dollars
For each additional year of age,the car selling price decrease by 671 dollars
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