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.

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?

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

a. Age is Independent variable and selling price is dependent variable.

b.

Step 1: Find XY , X2 and Y2 as it was done in the table below.

Step 2: Find the sum of every column to get:

X=107 , Y=82.9 , XY=712.9 , X2=1009 , Y2=615.29

Step 3: Use the following formula to work out the correlation coefficient.

r  = nXYXY/sqrt[nX2(X)2][nY2(Y)2]= 12712.910782.9/sqrt[1210091072][12615.2982.92]0.5436

c. Here r=-0.5436 so its moderately correlated

X Y XY XX YY   9 8.1 72.9 81 65.61 7 6 42 49 36 11 3.6 39.6 121 12.96 12 4.0 48 144 16 8 5.0 40 64 25 7 10.0 70 49 100 8 7.6 60.8 64 57.76 11 8.0 88 121 64 10 8.0 80 100 64 12 6.0 72 144 36 6 8.6 51.6 36 73.96 6 8.0 48 36 64

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