Question

The owner of Maumee Motors 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 Maumee Motors during the last year:

Car	Age (years)		Selling Price ($ thousands)		Car		Age (years)		Selling Price ($ thousands)
1	5		$3.2		7		5		$6.2
2	5		6.7		8		4		7.5
3	6		5.4		9		2		7.1
4	14		5.6		10		15		8.2
5	10		3.6		11		7		9.9
6	6		8.7		12		13		3.1

      

a. Determine the correlation coefficient. (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)      

          

r =  

     
b. Determine the coefficient of determination. (Round the final answer to 3 decimal places.)

         
c. Interpret these statistical measures. Does it surprise you that an inverse relationship exists? (Round the final answer to the nearest whole number.)

Weak negative (inverse) correlation between age of car and selling price. So,   percent of the variation in the selling price is explained by the variation in the age of the car.

Answer 1

The computation table for the data: X Y 5 3.2 25 5 6.7 25 6 5.4 36 14 5.6 196 10 3.6 100 6 8.7 36 6.2 25 7.5 16 2 7.1 4 15 8.2 225 7 9.9 49 13 3.1 169 Y 10.24 44.89 29.16 31.36 12.96 75.69 38.44 56.25 50.41 67.24 98.01 9.61 X,Y, 16 33.5 32.4 78.4 36 52.2 31 30 14.2 5 4 123 69.3 40.3 X; = 92 Y; = 75.2 x; = 906 CY* = 524.26 X;Y = 556.3 ;-1 1-1 The correlation coefficient is given by nXY- i-1 2-1 12(556.3)-(92)(75.2) (12(906)–(92)*)(12(524.26) – (75.2)) (10872–8464) (6291.12–5655.04) 6675.6-6918.4 = -242.8 (2408)(636.08) -242.8 = 1531681 -242.8 1237.611 = -0.19618 = rx-0.1962 Therefore, the value of the coefficient of correlation between the two quantitative variables car age( X) and selling price(Y) is rs -0.1962 (b) The value of the coefficient of determination is obtained by squaring the correlation coefficient is of the part (a). R2 = (r) =(-0.19618) 0.038488 R 0.038488 Therefore, the value of the coefficient of determination is R 0.038

The interpretation of the correlation coefficient(r): The correlation coefficient(r=-0.1962) indicates a negative linear relationship between the two quantitative variables car age(x) and selling price(y). The interpretation of the coefficient of determination (Rº): The value of the coefficient of determination is R2 = 3.84 percent of the variation in the dependent variable selling price (v) can be explained by the independent variable car age(x).