Multiple Linear Regression: Inference and Prediction · Introduction

Introduction

What this guide covers

An exhaustive mathematical and methodological development of the General Linear Model, ranging from the geometric derivation of the estimators to advanced level diagnostic techniques.

Overview

Topics covered

Introduction
The Multiple Linear Regression Model (MRLM) in Matrix Form
Classical Model Assumptions (Gauss-Markov and Normality Assumptions)
Projection Geometry: The Space of Regressors
Estimation by OLS, Maximum Likelihood and Gauss-Markov Theorem
2.1 Analytical derivation of the Ordinary Least Squares (OLS) estimator

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

Y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \cdots + \beta_{P-1} X_{i,P-1} + \varepsilon_i

View LaTeX source

Y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \cdots + \beta_{P-1} X_{i,P-1} + \varepsilon_i