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 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!

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
  

All regression techniques make use of the idea of Least Squares.

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.