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.