The aim of this post is to explain how a linear regression is calculated with a very simple example. Assume we want to approximate a cloud of point with the following line :
as illustrated bellow :
We want to minimize the error given by the square of the difference between points and the line :
By expending each term, the equation becomes :
As we want to minimize the error, the value of we are looking for is necessary a zero of the derivative of the error. Let’s calculate the derivative :
The error is minimized when :
It is now easy to calculate :
Download

Linear regression example for Matlab 0.40 KB