Linear regression: Variable selection and cross-validation

Introduction

What this guide covers

Variable selection and model validation constitute the cornerstones of contemporary predictive modeling. In the context of linear regression, estimating coefficients by ordinary least squares is usually insufficient or infeasible when the number of predictors is high or exceeds the number of observations. This document addresses the problem of optimizing prediction error.

Overview

Topics covered

• Introduction
• Linear Regression: Selection and Validation
• The problem of high-dimensional variable selection
• Classical subset selection methods
• 1. Best Subset Selection (best subset selection)
• 2. Forward Stepwise Selection (forward stepwise selection)

Related concepts

Main connections

• Regularization (Lasso / Ridge / Elastic Net)
• Linear algebra & matrices
• Variance & standard deviation
• Cross-validation & train/test splits
• Overfitting & cross-validation
• Linear regression

Compatible notation

Mathematical sample in LaTeX

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