Derivation of Coefficients:
- OLS derives the coefficients by setting the partial derivatives of the SSE with respect to each coefficient to zero. This results in a set of normal equations that can be solved to find the optimal coefficients.
- In matrix form, the solution can be expressed as:
- Here, is the matrix of input features (including a column of ones for the intercept), is the vector of observed values, and is the vector of coefficients.
Ordinary Least Squares
The Ordinary Least Squares method is used to minimize SSE. It achieves this by finding the values of that minimize the sum of squared differences between the observed and predicted values. The formulas for are derived by setting partial derivatives of SSE with respect to each coefficient to zero.
OLS is an analytical method
