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. |
Car | Age (years) | Selling Price ($000) | Car | Age (years) | Selling Price ($000) |
1 | 15 | 12.0 | 7 | 13 | 9.7 |
2 | 10 | 10.1 | 8 | 17 | 9.0 |
3 | 17 | 5.4 | 9 | 16 | 9.0 |
4 | 19 | 4.9 | 10 | 19 | 4.9 |
5 | 12 | 5.6 | 11 | 8 | 11.4 |
6 | 11 | 12.6 | 12 | 8 | 9.9 |
(a) |
Determine the regression equation. (Round your answers to 3 decimal places. Negative values should be indicated by a minus sign.) |
a = |
b = |
(b) |
Estimate the selling price of a 11-year-old car (in $000). (Round your answer to 3 decimal places.) |
Selling price |
(c) |
Interpret the regression equation (in dollars). (Round your answer to nearest dollar amount.) |
For each additional year, the car decreases $ in value. |
(a)
Independent variable: Age
Dependent varibale: selling price
Following table shows the calculations:
X | Y | X^2 | Y^2 | XY | |
15 | 12 | 225 | 144 | 180 | |
10 | 10.1 | 100 | 102.01 | 101 | |
17 | 5.4 | 289 | 29.16 | 91.8 | |
19 | 4.9 | 361 | 24.01 | 93.1 | |
12 | 5.6 | 144 | 31.36 | 67.2 | |
11 | 12.6 | 121 | 158.76 | 138.6 | |
13 | 9.7 | 169 | 94.09 | 126.1 | |
17 | 9 | 289 | 81 | 153 | |
16 | 9 | 256 | 81 | 144 | |
19 | 4.9 | 361 | 24.01 | 93.1 | |
8 | 11.4 | 64 | 129.96 | 91.2 | |
8 | 9.9 | 64 | 98.01 | 79.2 | |
Total | 165 | 104.5 | 2443 | 997.37 | 1358.3 |
Sample size: n =12
Now
Slope of the regression equation is
and intercept of the equation will be
The requried regression equation is
y ' = 14.909-0.451x
(b)
The selling price of a 11-year-old car (in $000) is
y ' = 14.909-0.451*11 = 9.948
So required estimated selling price is $9.948..
(c)
For each additional year, price of dollar decreased by (0.451*1000) = $451
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