Question

Cars lose value the farther they are driven. A random sample of

11

1111 cars for sale was taken. All

11

1111 cars were the same make and model. A line was fit to the data to model the relationship between how far each car had been driven and its selling price.

Which of these linear equations best describes the given model?

Based on this equation, estimate the price of a car that had been driven

56

5656 thousand kilometers.

Answer 1

y = -0.25x + 40 ; $26,000

Explanation:

From the graph attached ;

The regression equation, y could be obtained :

y = mx + c

m = slope = Rise / Run = (y2 - y1) / (x2 - x1)

Slope = (15 - 40) / (100 - 0)

Slope = - 25 / 100

Slope = - 0.25

c = intercept, where the regression line crosses the y-axis, from. The graph, c = 40

The regression equation goes thus :

y = -0.25x + 40 ; y = price of car ; x = number of miles driven

Price of car that has been driven for 56000 miles

y = - 0.25(56) + 40

y = - 14 + 40

y = 26

Hence, price of car is $26,000