Homework SourseThe owner of Maumee FordMercuryVolvo wants to study the rela
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.
8.0
Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to nearest whole number.)
| 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 |
Solution
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.
Let X = age (years)
and Y = selling price ($000)
Xbar = sum of x-values / total number of x-values = 107 / 12 = 8.917
Ybar = sum of y-values / total number of y-values = 82.9 / 12 = 6.908
sx = standard deviation of x.
sx = sqrt [ 1/n (x-Xbar)2 ]
sx = sqrt [ 1/12 * 54.917 ] = 2.139
sy is standard deviation of y.
sy = sqrt [ 1/n (y-Ybar)2 ]
sy = sqrt [ 1/12 * 42.589 ] = 1.884
The correlation coefficient formula is,
r = [ (x - Xbar)*(y - Ybar) / n ] / sqrt [ (1/n (x-Xbar)2 ) * (1/n * (y - Ybar)2 ) ]
= (-26.292 / 12) / sqrt [ 1/12 * 54.917 + 1/12 * 42.589 ]
r = -2.191 / 4.030
r = -0.544
There is negative relationship between the age of a car and its selling price.
Determine the coefficient of determination.
coefficient of determination is denoted by R2.
R2 = square of the correlation coefficient
R2 = -0.5442 = 0.2959
So, % of the variation in the selling price is explained by the variation in the age of the car is 0.2959 * 100 = 29.59%.
