Advanced linear regression · Qualitative variables and interaction effects

Introduction

What this guide covers

Linear regression analysis constitutes the core of predictive and inferential modeling in empirical and methodological sciences. Although the simplest formulation of the model assumes additive relationships between strictly continuous variables, real-world scenarios require the inclusion of categorical factors (qualitative variables) and the modeling of cross-conditional dependencies.

Overview

Topics covered

• Introduction
• Linear Regression: Qualitative and Interactions
• Algebraic and Geometric Fundamentals of the General Linear Model (GLM)
• The Geometry of Ordinary Least Squares
• The Gauss-Markov Theorem in Context
• Coding of Qualitative Variables

Related concepts

Main connections

• Linear algebra & matrices
• Variance & standard deviation
• Residual analysis & diagnostics
• Linear regression
• Collinearity & VIF
• Mean & expected value

Compatible notation

Mathematical sample in LaTeX

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