Simple linear regression between 2 samples. Takes two vectors Y={yi} and X={xi} and returns (alpha, beta) such that Y = alpha + beta*X

Simple linear regression between 2 samples. Takes two vectors Y={yi} and X={xi} and returns (alpha, beta, r*r) such that Y = alpha + beta*X and where r is the Pearson product-moment correlation coefficient

Total Least Squares (TLS) linear regression. Assumes x-axis values (and not just y-axis values) are random variables and that both variables have similar distributions. interface is the same as linearRegression.

Pearson's product-moment correlation coefficient

Covariance of two samples

The error (or residual) mean square of a sample w.r.t. an estimated regression line. This serves as an estimate for the variance of the sampled data. Accepts the regression parameters (alpha,beta) and the sample vectors X and Y.

The estimated distributions of the regression parameters (alpha and beta) assuming normal, identical distributions of Y, the sampled data. These can serve to get confidence intervals for the regression parameters. Accepts the regression parameters (alpha,beta) and the sample vectors X and Y. The distributions are StudnetT distributions centered at the estimated (alpha,beta) respectively, with parameter numbers n-2 (where n is the initial sample size) and with standard deviations that are extracted from the sampled data based on its MSE. See chapter 2 of reference [3] for details.

Finding a robust fit linear estimate between two samples. The procedure requires randomization and is based on the procedure described in the reference.

A wrapper that executes robustFit using a default random generator (meaning it is only pseudo-random)

Robust fit yielding also the R-square value of the "clean" dataset.

The robust fit algorithm used has various parameters that can be specified using the EstimationParameters record.

An ErrorFunction is a function that computes the error of a given point from an estimate. This module provides two error functions correspoinding to the two Estimator functions it defines:

• Vertical distance squared via linearRegressionError that should be used with linearRegression
• Total distance squared vie linearRegressionTLSError that should be used with linearRegressionTLS

An Estimator is a function that generates an estimated linear regression based on 2 samples. This module provides two estimator functions: linearRegression and linearRegressionTLS

An estimated linear relation between 2 samples is (alpha,beta) such that Y = alpha + beta*X.

Default set of parameters to use (see reference for details).

linearRegression error function is the square of the vertical distance of a point from the line.

linearRegressionTLS error function is the square of the total distance of a point from the line.

Calculate the optimal (local minimum) estimate based on an initial estimate. The local minimum may not be the global (a.k.a. best) estimate but starting from enough different initial estimates should yield the global optimum eventually.