Statistics.LinearRegression

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.