Question

Used Cars - Actual Data: Below are the scatterplots, regression equations, and corresponding statistics for mileage, model year, and price for 15 different Honda Civics found on craigslist in May 2012.

Mileage -vs- Price: x = Mileage (in thousands of miles) y = Price (in dollars) correlation coefficient: r = −0.880 regression equation: ŷ = −75.50x + 15,553.6 sample size: n = 15

Model Year -vs- Price: x = Model Year y = Price (in dollars) correlation coefficient: r = 0.891 regression equation: ŷ = 999.91x − 1,995,733.3 sample size: n = 15

Suppose you see a 2004 Honda Civic with 140 thousand miles on it. Estimate a reasonable price for this car via the following methods.

(a) Estimate the price using the mileage. Round your answer to the nearest dollar.
$

(b) Estimate the price using the year. Round your answer to the nearest dollar.
$

(c) Estimate the price using the multiple linear regression equation given by

ŷ = 716.9x₁ − 42.9x₂ − 1,424,349

where x₁ is the model year and x₂ is the mileage (in thousands). Round your answer to the nearest dollar.
$

(d) Which of the following statements are valid?

The estimate based only on mileage (part a) is too low because it doesn't consider the model year.

The estimate based only on the year (part b) is too high because it doesn't consider the mileage.     

The estimate from part (c) considers both variables (year and mileage) to produce a better estimate.

All of these are valid statements.

Answer 1

a)

x = Mileage (in thousands of miles) = 140 thousand miles
y = Price (in dollars)

Predicted Price = −75.50*(140) + 15,553.6 = $ 4983.6

b)

x = Model Year = 2004
y = Price (in dollars)

Predicted price = 999.91 *(2004) − 1,995,733.3 = $ 8086.34

c)

x1 is the model year = 2004

x2 is the mileage (in thousands) = 140 thousand miles

Predicted price = 716.9*(2004) − 42.9*(140) − 1,424,349 = $ 6312.6

d)

The estimate based only on mileage (part a) is too low because it doesn't consider the model year. as price and model year are positively correlated the statement is true

The estimate based only on the year (part b) is too high because it doesn't consider the mileage.    as milage and price are negatively correlated the statement is true

The estimate from part (c) considers both variables (year and mileage) to produce a better estimate. as both milage and model year have high correlation with price.

hence, All of these are valid statements.