The term *multiple* attached to linear regression means that
there are two or more *X*-variables used to predict *Y*.
Recall the Saturn price data again, but this time with the Model year included.

The mileage, model year, and price (highest bid) for 12 Saturn cars on eBay in July 2002: Car Miles Year Price 1 73676 1996 2000 2 77006 1998 2750 3 10565 2000 15500 4 146088 1995 960 5 15000 2001 4400 6 65940 2000 8800 7 9300 2000 7100 8 93739 1996 2550 9 153260 1994 1025 10 17764 2002 5900 11 57000 1998 4600 12 15000 2000 4400

This time, consider the prediction problem:

Problem: How much would I expect to get for a model 1996 Saturn car that has been driven 60000 miles?

Unlike the previous section, we now know the model year
of the car, not just the mileage. Since we want to predict PRICE given
YEAR and MILES, we want to fit a regression
model that looks like this:

where

How do we interpret the coefficients in ( 11.1)? For Saturn cars
*within the same model year*, every additional mile driven corresponds to
a price drop of about 3 cents (or a drop of about $327 for every 10000
additional miles). Similarly, *mileage being equal*, a more recent model year
will tend to have a higher price, on the average about $404 per year difference.

CAUTION: If theXvariables are highly correlated, the coefficients may have a meaningless interpretation. This is called the multicollinearity problem (see optional section below).

We can now use the fitted model ( 11.1) to estimate the selling price
of a model year 1996 Saturn car with 60000 miles. Plugging in the desired values
for MILES and YEAR, we get

A car with the same mileage 60000 miles from

This can be verified by using the fitted model ( 11.1) on the new numbers