Course Description

This 2-day hands-on workshop provides engineers, researchers, financial analysts, and statisticians a headstart in using MATLAB and the Statistics Toolbox for data analysis.

Topics include data file input and output, handling large and incommensurate data sets, computing descriptive statistics, statistical plotting and visualization, fitting distributions to data, bivariate and multivariate regression, random number generators, simulation, and basic inferential methods.

The workshop is packed with examples and exercises that cover a cross-section of application areas in science, engineering, and finance.

Prerequisites

Working knowledge of the MATLAB language and basic statistics

Course Outline

Introduction
Objective:

• Obtain a quick overview of The MathWorks and the family of products
• Discuss course set-up, materials, and logistics
• Provide a “big picture” view of the course ahead

Data and Statistics
Objective: Learn to work with data in the MATLAB environment, compute basic descriptive statistics, and visualize data in a variety of ways

What is Statistics?

• Statistical sampling and modeling
• Statistical questions
• Data analysis

Working with data

• Data I/O
• Tabular data and case lists
• Incommensurate data
• Missing data

Descriptive statistics

• Measures of center, spread and shape

Statistical plotting

• Histograms, scatter plots, and box plots
• Grouped data
• Preprocessing and reexpression

Exercise

• Time series

Probability and Distributions
Objective: Review the basics of probability and random variables and explore the variety of probability distributions available in the Statistics Toolbox

Probability concepts

• Probability measures
• Random variables
• Probability distributions

Distribution concepts

• Discrete distributions
• Continuous distributions
• Distributions in the Statistic Toolbox
• Distribution parameters
• Computing probabilities

Data and distributions

• Sampling distributions
• Choosing a distribution
• Parameter estimation
• Nonparametric density functions
• Bootstrapping and simulation
• Distribution testing

Exercise

• Distribution in diagnostics

Regression Analysis
Objective: Explore regression analysis for bivariate data

Regression concepts

• Predictors and responses
• Linear and nonlinear models
• Scatter plots
• Correlation and covariance

Linear methods

• Quantiles and quantile plots
• Solving systems of linear equations with the backslash operator
• Linear least squares
• Polynomial fitting
• Graphical user interface tools for linear regression
• Curve Fitting Toolbox
• Generalized linear models

Nonlinear methods

• Nonlinear fitting
• Graphical user interface tools for nonlinear regression
• Using the Curve Fitting Toolbox for nonlinear regression

Exercise

• National debt

Multivariate Statistics
Objective: Extend the concepts of the previous section to data sets with many variables and introduce specialized techniques for multivariate analysis and visualization

Multivariate plotting

• 3-D scatter plots
• Response surfaces

Principal component analysis

• Concepts
• Set-up and analysis

Factor analysis

• Concepts
• Set-up and analysis

Cluster analysis

• Concepts
• Set-up and analysis
• Hierarchical clustering and k-means clustering

Exercise

• Winning the decathlon

Random Numbers and Simulation
Objective: Understand the random number generators in MATLAB and the Statistics Toolbox and their use in Monte Carlo methods

Pseudorandom numbers

• Randomness
• Multiplicative congruential algorithms

Uniform random numbers

• rand and its algorithm

Gaussian random numbers

• randn and its algorithm

Writing new generators

• Inverse transform method
• Acceptance-rejection method
• Random number generators in the Statistics Toolbox

Monte Carlo methods

• Integration
• Simulation

Exercises

• Writing a random number generator
• Monte Carlo integration

Inferential Statistics
Objective: Explore hypothesis testing and its application to analysis of variance

Hypothesis tests

• Terminology
• Assumptions
• Tests in the Statistics Toolbox

One-way analysis of variance

• Set-up and analysis

Two-way analysis of variance

• Set-up and analysis

N-way analysis of variance

• Set-up and analysis

Multivariate analysis of variance

• Set-up and analysis

Exercise

• Nutritional data