Linear Regression, Least Squares & Matrix Multiplication: A Concise Technical Overview

Regression is a time-tested manner for approximating relationships among a given collection of data, and the recipient of unhelpful naming via unfortunate circumstances. Linear regression is a simple algebraic tool which attempts to find the "best" (generally straight) line fitting 2 or more attributes, with one attribute (simple linear regression), or a combination of several (multiple linear regression), being used to predict another, the class attribute. A set of training instances is used to compute the linear model, with one attribute, or a set of attributes, being plotted against another. The model then attempts to identify where new instances would lie on the regression line, given a particular class attribute. It is often confusing for people without a sufficient math background to understand how matrix multiplication fits into linear regression.