Statistical Modeling & Regression · Linear Regression & Diagnostics

Multiple linear regression: Complete matrix formulation

Public introduction · full guide in Eikos

Introduction

What this guide covers

A rigorous and exhaustive breakdown of generalized linear theory, orthogonal projections on Hilbert spaces, and classical parameter estimation.

Overview

Topics covered

  • Introduction
  • Multiple Linear Regression Model
  • Introduction and Fundamentals of the Multiple Model
  • 1.1 Transition to Matrix Algebra
  • 1.2 Model Geometry
  • Classical Assumptions in Matrix Formulation

Related concepts

Main connections

  • Linear algebra & matrices
  • Variance & standard deviation
  • Residual analysis & diagnostics
  • Linear regression
  • Maximum likelihood estimation
  • Hypothesis testing

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

Yi=β0+β1Xi1+β2Xi2+…+βkXik+ϵi
View LaTeX sourceY_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \ldots + \beta_k X_{ik} + \epsilon_i