Bivariate Class

Contains methods for analyzing on bivariate samples.

Inheritance Hierarchy

SystemObject
Meta.Numerics.StatisticsBivariate

Namespace: Meta.Numerics.Statistics
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 4.1.4

Syntax

C++

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public static class Bivariate

<ExtensionAttribute>
Public NotInheritable Class Bivariate

[ExtensionAttribute]
public ref class Bivariate abstract sealed

[<AbstractClassAttribute>]
[<SealedAttribute>]
[<ExtensionAttribute>]
type Bivariate =  class end

The Bivariate type exposes the following members.

Methods

	Name	Description
	CorrelationCoefficient	Computes the correlation coefficient between the two variables.
	Covariance	Computes the covariance of the two variables.
	CrosstabsR, C	Produces a cross-tabulation.
	KendallTauTest	Performs a Kendall concordance test for association.
	LinearLogisticRegression	Computes the best-fit linear logistic regression from the data.
	LinearRegression	Computes the best-fit linear regression from the data.
	NonlinearRegression(IReadOnlyListDouble, IReadOnlyListDouble, FuncIReadOnlyDictionaryString, Double, Double, Double, IReadOnlyDictionaryString, Double)	Finds the parameterized function that best fits the data.
	NonlinearRegression(IReadOnlyListDouble, IReadOnlyListDouble, FuncIReadOnlyListDouble, Double, Double, IReadOnlyListDouble)	Finds the parameterized function that best fits the data.
	PairedStudentTTest	Performs a paired Student t-test.
	PearsonRTest	Performs a Pearson correlation test for association.
	PolynomialRegression	Computes the polynomial of given degree which best fits the data.
	PopulationCovariance	Estimates the covariance of the two variables in the population.
	SpearmanRhoTest	Performs a Spearman rank-order test of association between the two variables.
	WilcoxonSignedRankTest	Performs a Wilcoxon signed rank test.

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Remarks

A bivariate sample is a sample in which each observation contains measurements of two quantities. A data set with height and weight measured for each person in the sample, for example, is bivariate. A data set with height measured for each person in two different groups, for example, is not bivariate. The first data set can be analyzed with the methods here. The second, which is just two independent univariate samples, should be analyzed with the multi-sample methods of the Univariate class.

One common task with bivariate data is to determine whether some association exists between the two measured quantities. This can be accomplished with the PearsonRTest, the SpearmanRhoTest, or the KendallTauTest. Simpler than testing for the statistical significance of any association is simply to measure it by reporting the CorrelationCoefficient(IReadOnlyListDouble, IReadOnlyListDouble).

Another common operation on bivariate data is to try to predict one variable on the basis of the other. There are many types of models you can construct to make such predictions, including LinearRegression(IReadOnlyListDouble, IReadOnlyListDouble), PolynomialRegression(IReadOnlyListDouble, IReadOnlyListDouble, Int32), and NonlinearRegression(IReadOnlyListDouble, IReadOnlyListDouble, FuncIReadOnlyListDouble, Double, Double, IReadOnlyListDouble). If the dependent variable is Boolean, you can use LinearLogisticRegression(IReadOnlyListBoolean, IReadOnlyListDouble) instead.

Reference

Meta.Numerics.Statistics Namespace