Statistical Methods with MATLAB
Overview
MATLAB is an integrated technical computing environment from the MathWorks that combines array-based numeric computation, advanced graphics and visualization, and a high-level programming language. Separately licensed toolboxes provide additional domain-specific functionality.
Matlab Academy: Statistics Onramp
Documentation: Statistics and Machine Learning Toolbox (help page)
Documentation: Statistics and Machine Learning Toolbox (product page)
Course Overview
This video from the MATLAB academy provides ample introductory information to follow along on this tutorial.
Video: Statistical Methods with Matlab
Exploring Data
How do we know what our data looks like? This section aims to show you how to explore your data and get to know what kind of information you are dealing with.
Visualizing Data Sets
The following section displays appropriate uses of histograms, boxplots, and scatter plots as a way to quantitatively assess your data before you continue your analysis in MATLAB.
Documentation: histogram boxplot scatter
Measures of Centrality and Spread
This section explores statistical measures such as mean, median, mode, variance, and interquartile range to summarize data.
Documentation: mean median mode trimmean
Documentation: std iqr range var
Distributions
This section covers different types probability distributions and how to visualize and analyze them in MATLAB.
Documentation: normpdf unifpdf randn rand
Summary
These figures summarize the key concepts and visualizations discussed in the previous sections.
Fitting a Curve to Data
Linear Regression
This section demonstrates how to fit linear models to data and interpret the results.
Evaluating Goodness of Fit
Here we evaluate how well linear models fit the data using various statistical metrics, including residual analysis.
Nonlinear Regression
This section shows how to fit nonlinear models to data and compare them to linear models.
Summary
These figures summarize the results and insights gained from regression analyses and how to fit a curve to data.
Interpolating Data
This section disucusses how we can create new data as an estimate based off our current data, and implement it in MATLAB
Linear Interpolation
Linear interpolation techniques are used to estimate values between known data points.
Nonlinear Interpolation
This section demonstrates nonlinear interpolation methods for more complex datasets.
Summary
Figures here summarize the interpolation methods and results and how they can be applied using MATLAB.
Additional Resources
This section provides links to additional MATLAB tools, tutorials, and support resources.
MATLAB Central MathWorks Support
Exercises
The resource computing team has kindly accumulated exercises to practice on, based on your MATLAB needs. All exercises are provided through the MATLAB Help Center
Visualizing Data sets
Practice exercises to reinforce techniques for visualizing height and weight data.
Exercise: Visualize Height and Weight Data
Measure of Centrality and Spread
Exercises to calculate and interpret mean, median, standard deviation, and other centrality measures.
Exercise: Find the Mean and Median
Exercise: Find the Standard Deviation and IQR
Distributions
Exercises to explore probability distributions and generate data using MATLAB functions.
Exercise: Fit and Plot a Normal Distribution
Exercise: Generating Random Numbers
Review: Exploring Data
Exercises reviewing data visualization and analysis skills from previous sections.
Linear Regression
Exercises to practice fitting lines and polynomials to datasets.
Exercise: Fit a Polynomial to Data
Evaluating the Goodness of Fit
Exercises to evaluate and improve the fit of models to your data.
Exercise: Evaluate and Improve the Fit
Nonlinear Regression
Exercises focused on fitting nonlinear models to data and interpreting results.
Exercise: Fit a Nonlinear Model
Review: Fitting a Curve to Data
Exercises reviewing linear and nonlinear regression techniques applied to sample datasets.
Exercise: Temperature Fluctuations
Linear Interpolation
Exercises to practice estimating values using linear interpolation.
Exercise: Fill in Missing Data
Nonlinear Interpolation
Exercises applying nonlinear interpolation methods to datasets.
Exercise: Resample Data with Different Interpolation Methods
Review: Interpolation
Exercises reviewing both linear and nonlinear interpolation techniques.