Statistics Toolbox: Math, Statistics, and Optimization employing  MATLAB and performing statistical modeling and analysis

Statistics Toolbox renders algorithms and tools for modeling, analyzing and organizing data. Developers can employ classification or regression for predictive modeling, bring forth random numbers for Monte Carlo simulations, employ statistical plots for explorative data analysis and execute hypothesis tests.

For canvassing multidimensional data, Statistics Toolbox comprises algorithms that permit developers distinguish key variables that strike the model with successive characteristic choice, metamorphose the data with principal component analysis, employ partial least squares or  enforce regularization and shrinkage.

Statistics Toolbox comprises differentiated data types for preparing and getting at heterogenous data. Dataset arrays store text,  metadata,  numeric data, in a single data container. Built-in methods perlits developers to mix datasets employing  a common key, compute sum-up statistics on grouped data and change over among wide and tall data representations. Categorical arrays render a memory-efficient data container for laying in data drawn from a finite, discrete set of classes.

Cardinal Prominent Attributes

Statistical arrays for laying in categorical and heterogeneous data

Regression techniques, comprising nonlinear,  linear, ridge,  robust, and nonlinear mixed-effects models.

Classification algorithms, comprising bagged and boosted decision trees, linear discriminant analysis and  k-Nearest Neighbor.

Analysis of variance (ANOVA)

Probability distributions, comprising Gaussian  and copulas mixtures.

Random number generation.

Hypothesis testing.

Blueprint of statistical  and experiments procedure control.

Data Organization and Management

Statistics Toolbox renders two differentiated arrays for managing  and storing statistical data. They are categorical arrays  and  dataset arrays.

Dataset Arrays

Dataset arrays permits commodious analysis and organization of heterogeneous metadata and statistical data. Dataset arrays render columns to constitute evaluated variables and rows to constitute reflections. With dataset arrays, developers can:

Lay in various forms of data in a single container.

Label columns and rows of data and address that data employing  placeable names.

To show and modify data in an nonrational tabular format.

Make use of  metadata to   store data, describe data and define units.

Statistics Toolbox renders differentiated functions to operate on dataset arrays. With these differentiated functions, developers can:

Add together different elements of the  datasets by aggregating fields employing  common keys.

Export data into standard file formats, comprising comma-separated value (CSV) and Microsoft® Excel®.

Compute sum-up statistics on grouped data.

Change over data among wide  and tall representations.

Categorical Arrays
Categorical arrays permits developers to process  and organize  ordinal  and nominal data that emplys values from a finite set of discrete categories or  levels. With categorical arrays, developers can:

Classification, Regression and ANOVA

Regression

With regression, developers can model a continuous response variable as a function of one or more forecasters. Statistics Toolbox permits a broad form of regression algorithms, comprising:

Nonlinear regression

Linear regression

Logistic regression and other extrapolated linear models.

Robust regression

Developers can measure goodness of fit employing  a diversity of metrics, comprising:

Akaike data criterion (AIC) and Bayesian data criterion (BIC)

Cross-validated mean squared error

R2 and adjusted R2

With the toolbox, developers can compute confidence intervals for both predicted values and regression coefficients. Statistics Toolbox affirms more brought forward proficiencies to meliorate prognosticative truth when the dataset comprises prominent numbers of correlated variables. The toolbox affirms:

Subset choice techniques, comprising consecutive prominent attributes choice and stepwise regression.

Regularization methods, comprising lasso, elastic net and ridge regression.

Statistics Toolbox in addition, corroborates nonparametric regression techniques for bringing forth an accurate fit without assigning a model that delineates the relationship among the response and  the predictor. Nonparametric regression techniques establish boosted and bagged regression trees as well as  decision trees. In addition,, Statistics Toolbox corroborates nonlinear mixed-effect (NLME) models in which some  of the parameters of a nonlinear function alter across groups or individuals.

Cardinal Prominent Attributes of Statistics Toolbox

Multivariate Statistics

Design of Experiments and Statistical Process Control.

Data Administration and Direction

Classification, ANOVA and Regression.

Exploration Data Analysis

Hypothesis Testing

Probability Distributions

Classification algorithms permits developers to model a unconditional response variable as a function of one or more predictors. Statistics Toolbox permits a broad diversity of  algorithms,  nonparametric and parametric classification, such as:

Naive Bayes classification

Boosted and bagged classification trees, comprising  LogitBoost, AdaBoost, RobustBoost and GentleBoost.

Linear discriminant analysis

k-Nearest Neighbor (kNN) classification.

Developers can assess goodness of fit for the leading classification models employing  techniques such as:

Confusion matrices

Cross-validated deprivation

Receiver operating characteristic (ROC) curves or Performance curves

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