Page 100 - Statistics II for Dummies

84 Part II: Using Different Types of Regression to Make Predictions

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 your estimate on recent gold prices, the price
of other commodities on the market that move with or against gold, and a
host of other possible 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, you want
to find out 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 + b x , where b is the y-intercept and b is the slope.
0 1 1 0 1
(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’s
related to y. Call these x variables x , x , . . . x . In the most basic multiple
1 2 k
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 finding
the best-fitting linear function for the data. This linear function looks like
the following: y = b + b x + b x + . . . + b x , and you can call it the multiple
0 1 1 2 2 k k
(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 + 3x + 24x is a linear equation using three x variables.
1 2 3
If any of the x terms are squared, the function is a quadratic one; if an x term
is taken to the third power, the function is a cubic function, and so on. In this
chapter, I consider only linear functions.

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