The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between t

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 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

Explanation / Answer

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%.

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