Ordinary Least Squares (OLS) › Summary

Ordinary Least Squares (OLS) gives a direct and computationally efficient method for linear regression. By minimizing the sum of squared errors, OLS finds the linear relationship between features and target variables that best fits the training data, with interpretable coefficients and clear assumptions.

The method's closed-form solution $\hat{\beta} = (X^TX)^{-1}X^Ty$ makes it computationally attractive, while its linear coefficient interpretation makes it valuable for applications requiring model transparency. However, OLS requires careful attention to its assumptions about linearity, error distribution, and feature relationships to ensure reliable results.

While OLS has limitations in handling nonlinear relationships and high-dimensional data, it remains a useful tool in the data science toolkit, particularly as a baseline model and in applications where interpretability matters. Understanding OLS deeply gives the basis for grasping more sophisticated regression techniques and regularization methods.