====== Regression Analysis ======

The word //regression// implies that the data points were originally lined up neatly.  As time progressed, they drifted off of the line in a random chaotic way.  Now we want to //regress// the points back onto the line.

Knowing the equation of the line gives us a //mathematical model// we can use for understanding the data and making predictions about data points to be discovered in the future.

==== Data Fitting ====
//Data fitting// is the process of finding the line that most closely fits the data.

Terminology:
  * If we try to fit the data to a //straight line// we call it //line fitting// and when successful we say we have a //linear// model.\\
  * If the data fits a curve, we call it //curve fitting// and we say it is a //non-linear model//.
  * If we want to confuse ourselves further, we refer to the curve as a //curved line// and we say we have a //curvilinear// model.  [[Language Alert!]]

==== Types of Regression Analysis ====
We have different types of regression analysis depending on the type of model.
  * [[Linear Regression]] for a straight line.
  * [[Non-linear Regression]] for a curve.

But sometimes we can use use linear regression for a curve.\\

There are also some specialty techniques for uniquely shaped data.
  * [[Logistic Regression]] where the data falls into two classes: yes or no\\

==== Algorithms ====
All regression techniques make use of the idea of [[Least Squares]].\\

==== Notes ====
If at first the data points do not appear to fit any line, it is sometimes possible to transform the data points mathematically until they do fall into a line or curve.