Question

The owner of Maumee Ford-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)
    1            11            12.2     
    2            8            11.0     
    3            16            4.9     
    4            18            4.1     
    5            9            6.7     
    6            8            13.6     
    7            10            11.1     
    8            16            9.0     
    9            14            9.0     
    10            18            4.2     
    11            6            12.1     
    12            6            10.4     

Click here for the Excel Data File

Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Estimate the selling price of an 7-year-old car (in $000). (Round your answer to 3 decimal places.)

Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount.)

Answer 1

X	y	(x-xbar)^2	(y-ybar)(x-xbar)
11 8 16 18 9 8 10 16 14 18 6 6 M: 11.6667	12.2 11.0 4.9 4.1 6.7 13.6 11.1 9.0 9.0 4.2 12.1 10.4 M: 9.025	0.4444 13.4444 18.7778 40.1111 7.1111 13.4444 2.7778 18.7778 5.4444 40.1111 32.1111 32.1111 SS: 224.6667	-2.1167 -7.2417 -17.875 -31.1917 6.2 -16.775 -3.4583 -0.1083 -0.0583 -30.5583 -17.425 -7.7917 SP: -128.4

Let x=age

Y = selling price

Sum of X = 140
Sum of Y = 108.3
Mean X = 11.6667
Mean Y = 9.025
Sum of squares (SS_X) = 224.6667
Sum of products (SP) = -128.4

Regression Equation = ŷ = bX + a

b = SP/SS_X = -128.4/224.67 = -0.572

a = M_Y - bM_X = 9.03 - (-0.57*11.67) = 15.693

ŷ = -0.572X + 15.693

B) when x= 7

Y^ = -0.527×7+15.693 . = 11.692

C) slope = -0.572

Every increase in age per year the selling price will ne decrease by 0.572.

Intercept = 15.693

The estimated average value of selljng price is equal to 15.693.