Part 2: More reasoning about scatterplots, correlation, and regression

At Terry's Toyotas, many used Toyota cars are for sale.Is there a relationship between the price of a used Toyota car (in dollars) and the number of miles that Toyota car has been driven by previous owners?The scatterplot below shows the results of an analysis of a sample of used Toyota cars from Terry's car lot.For each car, the price was recorded, along with the number of miles driven by previous car owners. The correlation between price and miles is r = -0.89.The regression equation to predict price based on miles is:Predicted price = 21215 - 0.101(miles).

Use the information above to answer Questions 7 through 9.

1. What percentage of the variability in price can be explained by the regression equation?

2. Would it be correct to say the units for r in this example are "dollars per mile"?Please explain why or why not.

3. Suppose that instead of measuring price in dollars, we decide it would be better to measure price in cents.If we change the units of measurement in this way, how would you expect the correlation (or r) to change?

4.Terry's best friend, Heather, is the owner of Heather's Hondas.Like Terry, Heather sells used cars, and she too would like to try to predict the price of a used car based on the number of miles the car was driven by previous owners.When Heather creates a scatterplot, she notices a linear relationship between these two variables, and she obtains the following regression equation.

Predicted price = 18855.05 - 0.101(miles)

Heather also finds that r-squared is equal to 46.9%.This means the correlation (or r) between price and miles for Heather's sample of cars must be equal to what value?