## Chapter 11. Regression

The linear least squares fit in the previous chapter is an example of
**regression**, which is the more general
problem of fitting any kind of model to any kind of data. This use of the
term “regression” is a historical accident; it is only indirectly related to
the original meaning of the word.

The goal of regression analysis is to describe the relationship between
one set of variables, called the **dependent
variables**, and another set of variables, called independent or
**explanatory variables**.

In the previous chapter we used mother’s age as an explanatory
variable to predict birth weight as a dependent variable. When there is only
one dependent and one explanatory variable, that’s **simple regression**. In this chapter, we move on to
**multiple regression**, with more than one
explanatory variable. If there is more than one dependent variable, that’s
multivariate regression.

If the relationship between the dependent and explanatory variable is
linear, that’s **linear regression**. For
example, if the dependent variable is y and the explanatory variables are x_{1} and x_{2}, we would write the
following linear regression model:

where β_{0} is
the intercept, β_{1} is
the parameter associated with x_{1}, β_{2} is the parameter associated
with x_{2}, and
ε is the residual due to random variation
or other unknown factors.

Given a sequence of values for y and
sequences for x_{1} and
x_{2}, we can find the parameters, ...

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