Statistics Toolbox

Linear and Nonlinear Modeling

The linear and nonlinear models provided in Statistics Toolbox let you model a response variable as a function of one or more predictor variables. These models make predictions, establish relationships between variables, or simplify a problem. For example, linear and nonlinear regression models help establish which variables have the most impact on a response. Robust regression methods can help you find outliers and reduce their effect on the fitted model.

The toolbox provides linear algorithms for:

• Polynomial, stepwise, ridge, robust, and multiple linear regression
• Generalized linear models, including multinomial (discrete-choice) models
• Response surface fitting

The toolbox also provides nonlinear fitting functions. Using nonlinear least squares functions, you can:

• Estimate parameters
• Interactively visualize and predict multi­dimensional nonlinear fitting
• Set confidence intervals for parameters and predicted values

Statistics Toolbox supports a variety of techniques for classification analysis, including:

• Discriminant analysis
• Classification and regression trees

Nonlinear mixed-effect (NLME) models provide a flexible mechanism to model correlations within subgroups contained within a larger data sample.

Statistical learning techniques such as cross-validation and sequential feature selection can be applied to both linear and nonlinear fitting methods.

You can also use the toolbox to work with Hidden Markov models. You can estimate the parameters of a model using the Baum-Welch algorithm, calculate the most likely path through a model using the Viterbi algorithm, and generate random sequences from a given model.

Multivariate Statistics

Multivariate statistics methods let you analyze your data by evaluating groups of variables together. You can:

• Segment data in clusters for further analysis
• Visualize and assess the group-to-group differences in a data set
• Reduce a large set of variables to a more manageable but still representative set

Matrix of scatter plots and histograms comparing automobile performance over three model years. Statistics Toolbox makes it easy to plot multiple variables and compare data.

Nonlinear mixed-effects model of drug absorption and elimination showing intrasubject concentration-versus-time profiles. The nlmefit function in Statistics Toolbox generates a population model using fixed and random effects.

Multivariate statistics tasks supported by Statistics Toolbox include:

• Factor analysis
• Factor rotation and biplots
• Cluster analysis (both hierarchical and k-means)
• Multidimensional scaling (classical, metric, and nonmetric)
• Multivariate plotting (parallel coordinates, glyph plots, and Andrews plots)

Statistics Toolbox also supports data transformation and dimensionality reduction techniques like principal component analysis and partial least squares.

Plots showing how data with similar characteristics can be clustered into groups. Statistics Toolbox includes functions for multivariate analysis and clustering.