Redshift Academy

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Astronomy

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Celestial Coordinates

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Celestial Navigation

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Location of North and South Celestial Poles

Chemistry

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Avogadro's Number

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Balancing Chemical Equations

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The Periodic Table

Classical Physics

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Archimedes Principle

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Bernoulli Principle

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Blackbody (Cavity) Radiation and Planck's Hypothesis

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Center of Mass Frame

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Comparison Between Gravitation and Electrostatics

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Coriolis Effect

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Cyclotron Resonance

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Double Slit Experiment

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Elastic and Inelastic Collisions

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Electric Fields

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Gauss's Law of Universal Gravity

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Gravity - Force and Acceleration

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Ideal and Non-Ideal Gas Laws (van der Waal)

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Kinetic Theory of Gases

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Kirchoff's Laws

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Laplace's and Poisson's Equations

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Lorentz Force Law

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Maxwell's Equations

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Moments and Torque

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One Dimensional Wave Equation

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Pascal's Principle

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Phase and Group Velocity

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Planck Radiation Law

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Poiseuille's Law

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Radioactive Decay

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Refractive Index

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Rotational Dynamics

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Simple Harmonic Motion

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Specific Heat, Latent Heat and Calorimetry

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Stefan-Boltzmann Law

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The Laws of Thermodynamics

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The Zeeman Effect

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Wien's Displacement Law

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Young's Modulus

Climate Change

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Cosmology

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Penrose Diagrams

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Cosmic Background Radiation and Decoupling

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Friedmann-Robertson-Walker Equations

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Geometries of the Universe

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Inflation Theory

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Introduction to Black Holes

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Olbers' Paradox

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Stephen Hawking's Last Paper

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Stephen Hawking's PhD Thesis

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The Big Bang Model

Finance and Accounting

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Brownian Model of Financial Markets

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Capital Structure

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Dividend Discount Formula

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Lecture Notes on International Financial Management

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Periodically and Continuously Compounded Interest

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Repurchase versus Dividend Analysis

General Relativity

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Accelerated Reference Frames - Rindler Coordinates

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Catalog of Spacetimes

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Curvature and Parallel Transport

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Dirac Equation in Curved Spacetime

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Einstein's Field Equations

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Gravitational Time Dilation

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Gravitational Waves

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Quantum Gravity

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Relativistic, Cosmological and Gravitational Redshift

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Ricci Decomposition

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Stress-Energy Tensor

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Stress-Energy-Momentum Tensor

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The Area Metric

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The Equivalence Principal

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The Essential Mathematics of General Relativity

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The Induced Metric

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The Metric Tensor

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Vierbein (Frame) Fields

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World Lines Refresher

Lagrangian and Hamiltonian Mechanics

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Classical Field Theory

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Euler-Lagrange Equation

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Ex: Newtonian, Lagrangian and Hamiltonian Mechanics

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Hamiltonian Formulation

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Liouville's Theorem

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Symmetry and Conservation Laws - Noether's Theorem

Macroeconomics

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Lecture Notes on International Economics

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Lecture Notes on Macroeconomics

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Macroeconomic Policy

Mathematics

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Amplitude, Period and Phase

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Arithmetic and Geometric Sequences and Series

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Augmented Matrices and Cramer's Rule

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Basic Group Theory

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Basic Representation Theory

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Binomial Theorem (Pascal's Triangle)

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Building Groups From Other Groups

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Completing the Square

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Complex Numbers

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Composite Functions

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Conformal Transformations

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Conjugate Pair Theorem

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Contravariant and Covariant Components of a Vector

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Derivatives of Inverse Functions

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Double Angle Formulas

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Eigenvectors and Eigenvalues

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Euler Formula for Polyhedrons

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Factoring of a³ +/- b³

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Fourier Series and Transforms

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Gauss's Divergence Theorem

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Grassmann and Clifford Algebras

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Heron's Formula

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Index Notation (Tensors and Matrices)

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Integration By Parts

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Introduction to Conformal Field Theory

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Inverse of a Function

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Law of Sines and Cosines

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Line Integrals, ∮

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Logarithms and Logarithmic Equations

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Matrices and Determinants

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Matrix Exponential

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Mean Value and Rolle's Theorem

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Modulus Equations

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Orthogonal Curvilinear Coordinates

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Parabolas, Ellipses and Hyperbolas

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Piecewise Functions

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Polar Coordinates

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Polynomial Division

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Regular Polygons

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Sets, Groups, Modules, Rings and Vector Spaces

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Similar Matrices and Diagonalization

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Spherical Trigonometry

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Stirling's Approximation

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Sum and Differences of Squares and Cubes

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Symmetric Groups

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Tangent and Normal Line

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Taylor and Maclaurin Series

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The Essential Mathematics of Lie Groups

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The Integers Modulo n Under + and x

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The Limit Definition of the Exponential Function

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Tic-Tac-Toe Factoring

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Trapezoidal Rule

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Vector Calculus

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Volume Integrals

Microeconomics

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Marginal Revenue and Cost

Particle Physics

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Feynman Diagrams and Loops

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Field Dimensions

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Helicity and Chirality

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Klein-Gordon and Dirac Equations

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Regularization and Renormalization

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Scattering - Mandelstam Variables

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Spin 1 Eigenvectors

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The Vacuum Catastrophe

Probability and Statistics

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Box and Whisker Plots

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Categorical Data - Crosstabs

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Chebyshev's Theorem

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Chi Squared Goodness of Fit

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Conditional Probability

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Confidence Intervals

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Factor Analysis

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Hypothesis Testing

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Linear Regression

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Monte Carlo Methods

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Non Parametric Tests

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Pearson Correlation

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Permutations and Combinations

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Pooled Variance and Standard Error

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Probability Distributions

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Probability Rules

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Sample Size Determination

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Sampling Distributions

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Set Theory - Venn Diagrams

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Stacked and Unstacked Data

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Stem Plots, Histograms and Ogives

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Survey Data - Likert Item and Scale

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Programming and Computer Science

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How this site works ...

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More Programming Topics

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MVC Architecture

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Open Systems Interconnection (OSI) Standard - TCP/IP Protocol

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Public Key Encryption

Quantum Field Theory

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Creation and Annihilation Operators

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Field Operators for Bosons and Fermions

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Lagrangians in Quantum Field Theory

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Path Integral Formulation

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Relativistic Quantum Field Theory

Quantum Mechanics

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Basic Relationships

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Clebsch-Gordan Coefficients

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Electron Orbital Angular Momentum and Spin

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Entangled States

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Heisenberg Uncertainty Principle

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Ladder Operators

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Multi Electron Wavefunctions

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Pauli Exclusion Principle

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Pauli Spin Matrices

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Photoelectric Effect

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Position and Momentum States

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Probability Current

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Schrodinger Equation for Hydrogen Atom

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Schrodinger Wave Equation

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Schrodinger Wave Equation (continued)

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Spin 1/2 Eigenvectors

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The Differential Operator

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The Essential Mathematics of Quantum Mechanics

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The Observer Effect

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The Schrodinger, Heisenberg and Dirac Pictures

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The WKB Approximation

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Time Dependent Perturbation Theory

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Time Evolution and Symmetry Operations

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Time Independent Perturbation Theory

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Semiconductor Reliability

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The Weibull Distribution

Solid State Electronics

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Band Theory of Solids

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Fermi-Dirac Statistics

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Intrinsic and Extrinsic Semiconductors

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The P-N Junction

Special Relativity

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Electromagnetic 4 - Potential

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Energy and Momentum, E = mc²

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Lorentz Invariance

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Lorentz Transform

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Lorentz Transformation of the EM Field

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Newton versus Einstein

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Spinors - Part 1

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Spinors - Part 2

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The Lorentz Group

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Velocity Addition

Statistical Mechanics

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Black Body Radiation

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Entropy and the Partition Function

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The Harmonic Oscillator

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String Theory

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Bosonic Strings

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Extra Dimensions

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Introduction to String Theory

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Kaluza-Klein Compactification of Closed Strings

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Strings in Curved Spacetime

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Toroidal Compactification

Superconductivity

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Introduction to Superconductors

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Superconductivity (Lectures 1 - 10)

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Superconductivity (Lectures 11 - 20)

Supersymmetry (SUSY) and Grand Unified Theory (GUT)

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Chiral Superfields

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Generators of a Supergroup

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Grassmann Numbers

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Introduction to Supersymmetry

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The Gauge Hierarchy Problem

test

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The Standard Model

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Electroweak Unification (Glashow-Weinberg-Salam)

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Gauge Theories (Yang-Mills)

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Gravitational Force and the Planck Scale

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Introduction to the Standard Model

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Isospin, Hypercharge, Weak Isospin and Weak Hypercharge

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Quantum Flavordynamics and Quantum Chromodynamics

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Special Unitary Groups and the Standard Model - Part 1

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Special Unitary Groups and the Standard Model - Part 2

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Special Unitary Groups and the Standard Model - Part 3

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Standard Model Lagrangian

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The Higgs Mechanism

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The Nature of the Weak Interaction

Topology

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Units, Constants and Useful Formulas

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Last modified: January 26, 2018


Factor Analysis
---------------

The key concept of factor analysis is that multiple observed 
variables have similar patterns of responses because they are 
all associated with a latent (i.e. not directly measured) 
variable.

For example, people may respond similarly to questions about 
income, education, and occupation, which are all associated 
with the latent variable socioeconomic status.

When you find a set of variables that are highly correlated 
with each other, it is reasonable to wonder if this mutual 
association may be due to some common underlying cause.  
The purpose of Factor Analysis is to identify a set of 
underlying factors that explain the relationships between 
correlated variables. Generally, there will be fewer 
underlying factors than variables, so the factor analysis 
result is simpler than the original set of variables. 

One of the most useful ways to determine the number of 
factors to use is by means of a SCREE PLOT that shows what 
percentage of the variance is accounted for by each factor.



The horizontal axis shows the number of factors. The 
vertical axis shows the percent of the overall variance 
explained by each factor. A sharp drop off indicates the 
number of factors that should be retained.