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.

   

Determine the regression equation. Use the rounded slope value to compute the y-intercept. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

Estimate the selling price (in dollars) of a 7-year-old car. (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)

Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)

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.

Explanation / Answer

a.

calculation procedure for regression
mean of X = X / n = 12.5
mean of Y = Y / n = 9.65
(Xi - Mean)^2 = 117
(Yi - Mean)^2 = 124.41
(Xi-Mean)*(Yi-Mean) = -87.7
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
= -87.7 / 117
= -0.74957
bo = Y / n - b1 * X / n
bo = 9.65 - -0.74957*12.5 = 19.01966
value of regression equation is, Y = bo + b1 X
Y'=19.01966-0.74957* X
Y'=19.02-0.75* X
a = 19.02, b = -0.75
b.
the selling price (in dollars) of a 7-year-old car
=> Y'=19.02-0.75* 7 = 13.77
c.
for each additional year, the car decreases $0.75 in value

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 13 13.1 0.25 11.9025 1.725 10 11.8 6.25 4.6225 -5.375 15 5.7 6.25 15.6025 -9.875 17 4.9 20.25 22.5625 -21.375 11 6.8 2.25 8.1225 4.275 10 14 6.25 18.9225 -10.875 11 11.4 2.25 3.0625 -2.625 15 9.8 6.25 0.0225 0.375 15 9.8 6.25 0.0225 0.375 17 4.5 20.25 26.5225 -23.175 8 13 20.25 11.2225 -15.075 8 11 20.25 1.8225 -6.075

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