Question

kari went on-line and looked for used Honda Civics for sale. she found 15 cars listed within 50 miles of her home. For each car, she recorded the asking price, year, and mileage. Below are the summary statistics.

	mean	standar dev.
year	1999.3	4.11
mileage	6392	34466
price	10417	4145

correlation between
year and mileage:	-0.702
year and price:	0.939
mileage and price:	-0.812

a) determine the equation of the least squares line for predicting price from mileage

b) write a sentence or two interpreting the slope coefficient of this equation

C) use this equation to predict the price of a used Honda Civic with 80,000 miles

d) what fraction of the variability in prices is explained by the least squares line with year?

Answer 1

a)

here slope b1=r*sy/sx=(-0.812)*(4145/34466)=-0.0977

intercept bo=(Ybar-b1*Xbar)=(10417-(-0.0977)*6392)=11041.5

therefore  equation of the least squares line for predicting price from mileage is :

Yhat=11041.5+(-0.0977)*x

b)

here slope (-0.0977) represent that for each one unit increase in mileage price decreases by 0.0977 unit.

c)

predicted price =11041.5+(-0.0977)*80000=3225.5

d)

fraction of the variability in prices is explained by the least squares line with year =r² =(-0.812)² =0.6953