Bivariate Class 
Namespace: Meta.Numerics.Statistics
The Bivariate type exposes the following members.
Name  Description  

CorrelationCoefficient 
Computes the correlation coefficient between the two variables.
 
Covariance 
Computes the covariance of the two variables.
 
CrosstabsR, C 
Produces a crosstabulation.
 
KendallTauTest 
Performs a Kendall concordance test for association.
 
LinearLogisticRegression 
Computes the bestfit linear logistic regression from the data.
 
LinearRegression 
Computes the bestfit 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 ttest.
 
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 rankorder test of association between the two variables.
 
WilcoxonSignedRankTest 
Performs a Wilcoxon signed rank test.

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 multisample 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.