MathIsimple
Multivariate Analysis

Multivariate Statistical Analysis

Master the analysis of high-dimensional data: from multivariate distributions to dimensionality reduction, classification, and correlation analysis

8 Core Topics45-60 Hours Study TimeIntermediate to Advanced

Core Topics

Eight comprehensive modules covering essential multivariate statistical methods

New!
Intermediate
Multivariate Statistics Fundamentals
Master the foundations of multivariate analysis: random vectors, covariance matrices, and sample statistics for high-dimensional data
8 lessons
4-6 hours

Key Content:

  • Multivariate data representation
  • Matrix algebra review
  • Random vectors and mean vectors
  • Covariance and correlation matrices
  • Sample statistics and Mahalanobis distance
New!
Intermediate
Multivariate Normal Distribution
Explore the multivariate normal distribution: properties, marginal and conditional distributions, MLE, and sampling distributions
10 lessons
5-7 hours

Key Content:

  • Multivariate normal PDF and properties
  • Linear transformations
  • Marginal and conditional distributions
  • Maximum likelihood estimation
  • Wishart distribution and Hotelling's T²
New!
Intermediate to Advanced
Inference on Mean Vectors
Master hypothesis testing for multivariate means: Hotelling's T², two-sample tests, MANOVA, and profile analysis
10 lessons
5-7 hours

Key Content:

  • One-sample Hotelling's T² test
  • Two-sample mean vector comparison
  • Paired comparisons
  • MANOVA: Wilks' Lambda and other statistics
  • Profile analysis
New!
Intermediate
Principal Component Analysis (PCA)
Learn dimensionality reduction through PCA: eigenvalue decomposition, variance explanation, and practical applications
12 lessons
6-8 hours

Key Content:

  • PCA goals and geometric interpretation
  • Eigenvalue decomposition of covariance matrix
  • Variance explained and component selection
  • Scree plots and Kaiser criterion
  • Biplots and practical applications
New!
Intermediate to Advanced
Factor Analysis
Understand latent variable modeling: factor models, estimation methods, rotation techniques, and factor scores
12 lessons
6-8 hours

Key Content:

  • Orthogonal factor model
  • Principal component and ML estimation
  • Factor rotation: Varimax and Oblimin
  • Communalities and uniqueness
  • Factor scores and model evaluation
New!
Intermediate to Advanced
Discriminant Analysis
Master classification methods: Fisher's LDA, Bayesian classification, QDA, and model evaluation techniques
12 lessons
6-8 hours

Key Content:

  • Fisher's Linear Discriminant Analysis
  • Classification rules and boundaries
  • Multiple group discrimination
  • Quadratic Discriminant Analysis (QDA)
  • Cross-validation and ROC curves
New!
Intermediate
Cluster Analysis
Learn unsupervised classification: distance measures, hierarchical clustering, K-means, and cluster validation
12 lessons
6-8 hours

Key Content:

  • Distance and similarity measures
  • Hierarchical clustering and dendrograms
  • K-means algorithm and optimization
  • Choosing optimal number of clusters
  • Cluster validation metrics
New!
Advanced
Canonical Correlation Analysis
Explore relationships between variable sets: canonical variates, correlations, and statistical inference
10 lessons
5-7 hours

Key Content:

  • Canonical variates and correlations
  • Eigenvalue formulation
  • Canonical loadings interpretation
  • Redundancy analysis
  • Statistical significance testing

Learning Path

Follow the recommended sequence to build comprehensive multivariate analysis skills

Recommended Learning Path
Learn multivariate statistical analysis topics in suggested order
Estimated study time: 45-60 hours

Learning Sequence:

  1. 1Multivariate Statistics Fundamentals
  2. 2Multivariate Normal Distribution
  3. 3Inference on Mean Vectors
  4. 4Principal Component Analysis (PCA)
  5. 5Factor Analysis
  6. 6Discriminant Analysis
  7. 7Cluster Analysis
  8. 8Canonical Correlation Analysis

💡 Learning Tip: Start with fundamentals, progress through distribution theory, then explore dimensionality reduction and classification methods

Learning Features

Comprehensive multivariate analysis learning experience

Dimensionality Reduction

Master PCA and Factor Analysis to extract meaningful patterns from high-dimensional data

Classification Methods

Learn discriminant analysis and clustering for supervised and unsupervised classification

Practical Applications

Apply multivariate methods to real-world problems in data science, psychology, and biology

Prerequisites

Before starting this course, you should have a solid understanding of:

Probability Theory

  • • Random variables and distributions
  • • Expected value and variance
  • • Normal distribution properties

Mathematical Statistics

  • • Point estimation (MLE, MoM)
  • • Hypothesis testing basics
  • • Confidence intervals

Linear Algebra

  • • Matrix operations
  • • Eigenvalues and eigenvectors
  • • Matrix decomposition

Calculus

  • • Partial derivatives
  • • Optimization methods
  • • Multiple integrals

Start Your Multivariate Analysis Journey

We recommend starting with "Multivariate Statistics Fundamentals" to build a strong foundation in random vectors, covariance matrices, and sample statistics before exploring advanced topics.

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