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. Car Age (years) Selling Price ($000) Car Age (years) Selling Price ($000) 1 11 12.1 7 10 10.5 2 8 10.5 8 14 9.0 3 14 5.7 9 13 9.0 4 17 4.9 10 17 4.5 5 9 5.0 11 6 12.5 6 8 13.4 12 6 11.5 Picture Click here for the Excel Data File (a) Determine the regression equation. (Round your answers to 3 decimal places. Negative values should be indicated by a minus sign.) a = b = (b) Estimate the selling price of a 7-year-old car (in $000). (Round your answer to 3 decimal places.) Selling price (c) Interpret the regression equation (in dollars). (Round your answer to nearest dollar amount.) For each additional year, the car decreases $ in value.

Explanation / Answer

Answer:

Regression Lines from the follwing data, also Estimate x when y = 0

In this age if car is independent variable and selling price of car is dependent variable

Solution:
Mean x=xi / n

=11+8+14+17+9+8+10+14+13+17+6+6 / 12

=133 / 12

=11.08



Mean y=yi / n

=12.1+10.5+5.7+4.9+5+13.4+10.5+9+9+4.5+12.5+11.5 / 12

=108.6 / 12

=9.05



x=11.08 is not an integer, use assumed mean A=11

Use assumed mean B=y=9.05

bxy=dxdy / dy2

=-102.75 / 115.89

=-0.89


Regression Line x on y
x-x=bxy(y-y)

x-11.08=-0.89(y-9.05)

x-11.08=-0.89y+8.02

x=-0.89y+8.02+11.08

x=-0.89y+19.11


Now Estimate x for y=0

x=-0.89×0+19.11

x=0+19.11

x=19.11

Car Age Price 1 11 12.1 2 8 10.5 3 14 5.7 4 17 4.9 5 9 5 6 8 13.4 7 10 10.5 8 14 9 9 13 9 10 17 4.5 11 6 12.5 12 6 11.5

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