The owner of Maumee Ford-Mercury-Volvo

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

Picture Click here for the Excel Data File

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?

b-1.
Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

X Y Picture Picture (Picture )2 (Picture )2 (Picture )(Picture )
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

Picture =
8.9167
Picture =
6.9083
sx =
2.2344
sy =
1.9677

r =
-0.5436

b-2. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

-0.554

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 variation in the selling price is explained by the variation in the age of the car.

 

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