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Part II: Making Predictions by Using Regression
regression model (Chapter 4). Some of the concepts are a little more com-
plex, as you may guess because the model is more complex. But the concepts
and the results should make intuitive sense, which is always good news.
Discovering the uses of multiple regression
One situation in which multiple regression is useful is when the y variable is
hard to track down; that is, its value can’t be measured straight up, and you
need more than one other piece of information to help get a handle on what
its value will be. For example, you may want to estimate the price of gold
today. It would be hard to imagine being able to do that with only one other
variable. You may base it on recent gold prices, the price of other commodi-
ties on the market that move with or against gold, and a host of other possi-
ble economic conditions associated with the price of gold.
Another case for using multiple regression is when you want to figure out
what factors play a role in determining the value of y. For example, what
information is important to real estate agents in setting a price for a house
going on the market?
Looking at the general form of
the multiple regression model
The general idea of simple linear regression is to fit the best straight line
through that data that you possibly can and use that line to make estimates
for y based on certain x-values. The equation of the best-fitting line in simple
linear regression is y = b 0 + b 1x 1, where b 0 is the y-intercept and b 1 is the slope.
(The equation also has the form y = a +bx; see Chapter 4.)
In the multiple regression setting, you have more than one x variable that is
related to y. Call these x variables x 1 , x 2 , . . . x k . In the most basic multiple
regression model, you use some or all of these x variables to estimate y
where each x variable is taken to the first power. This process is called find-
ing the best-fitting linear function for the data. This linear function looks like
the following: y = b 0 + b 1 x 1 + b 2 x 2 + . . . + b k x k , and you can call it the multiple
(linear) regression model. You use this model to make estimates about y
based on given values of the x variables.
A linear function is an equation whose x terms are taken to the first power
only. For example y = 2x 1 + 3x 2 + 24x 3 is a linear equation using three x vari-
ables. If any of the x terms are squared, the function would be a quadratic
one; if an x term is taken to the third power, the function would be a cubic
function, and so on. In this chapter, I consider only linear functions.

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