202405171731
Status: #idea
Tags: Statistics, Linear Algebra

Normal Equations

They are a set of equations that are used to find the best parameters for a linear regression. They are so called (Normal) because when put in matrix form, they become equations of the form product of matrix equal to 0, which implies that the matrices involved in the product are orthogonal. In this case the the error vector is orthogonal.

From the normal equations we derive a lot of interesting fact.
For example we can derive that the sum of our residuals is 0 because, when we create the normal equations, the formula we get is equivalent to that.