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
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 | 9 | 8.1 | 7 | 8 | 7.6 |
2 | 7 | 6.0 | 8 | 11 | 8.0 |
3 | 11 | 3.6 | 9 | 10 | 8.0 |
4 | 12 | 4.0 | 10 | 12 | 6.0 |
5 | 8 | 5.0 | 11 | 6 | 8.6 |
6 | 7 | 10.0 | 12 | 6 | 8.0 |
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a. | If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable? |
is the independent variable and
is the dependent variable. |
b-1. | Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) |
X | Y | ( )2 | ( )2 | ( )( ) | ||
9.0 | 8.1 | 1.192 | 0.007 | 1.420 | 0.099 | |
7.0 | 6.0 | -0.908 | 3.674 | 0.825 | 1.741 | |
11.0 | 3.6 | 2.083 | 4.340 | 10.945 | -6.892 | |
12.0 | 4.0 | 3.083 | 9.507 | 8.458 | -8.967 | |
8.0 | 5.0 | -0.917 | -1.908 | 3.642 | 1.749 | |
7.0 | 10.0 | -1.917 | 3.092 | 9.558 | -5.926 | |
8.0 | 7.6 | -0.917 | 0.692 | 0.840 | -0.634 | |
11.0 | 8.0 | 2.083 | 1.092 | 4.340 | 2.274 | |
10.0 | 8.0 | 1.083 | 1.092 | 1.174 | 1.192 | |
12.0 | 6.0 | 3.083 | -0.908 | 9.507 | 0.825 | |
6.0 | 8.6 | -2.917 | 1.692 | 8.507 | 2.862 | -4.934 |
6.0 | 8.0 | -2.917 | 1.092 | 8.507 | 1.192 | -3.184 |
107.000 | 82.900 | |||||
= | = | sx | = | sy | = |
r | = |
b-2. | Determine the coefficient of determination. (Round your answer to 3 decimal places.) |
c. | Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to nearest whole number.) |
correlation between age of car and selling price. So, % of the variationin the selling price is explained by the variation in the age of the car.
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