Statistical Modeling & Regression · Multivariate Analysis

Multivariate analysis · Linear models and advanced structures

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Advanced Statistics Module

Overview

Topics covered

  • Introduction
  • Multivariate Analysis: Linear Models and Covariance Structures
  • Multivariate matrix algebra and fundamental operators
  • 1.1 Vector of population and sample means
  • 1.2 Population and sample covariance matrix
  • 1.3 Correlation matrix

Related concepts

Main connections

  • Linear algebra & matrices
  • Variance & standard deviation
  • Principal component analysis (PCA)
  • Linear regression
  • Normal (Gaussian) distribution
  • Residual analysis & diagnostics

Compatible notation

Mathematical sample in LaTeX

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

𝐗=(x11x12…x1px21x22…x2p⋮⋮⋱⋮xn1xn2…xnp)=(𝐱1T𝐱2T⋮𝐱nT)
View LaTeX source\mathbf{X} = \begin{pmatrix} x_{11} & x_{12} & \dots & x_{1p} \\ x_{21} & x_{22} & \dots & x_{2p} \\ \vdots & \vdots & \ddots & \vdots \\ x_{n1} & x_{n2} & \dots & x_{np} \end{pmatrix} = \begin{pmatrix} \mathbf{x}_1^T \\ \mathbf{x}_2^T \\ \vdots \\ \mathbf{x}_n^T \end{pmatrix}