LinearRegression`

Regress

As of Version 7.0, Regress has been superseded by LinearModelFit.

Regress[data,funs,vars]

finds a least–squares fit to a list of data as a linear combination of the functions funs of variables vars.

Details and Options

To use Regress, you first need to load the Linear Regression Package using Needs["LinearRegression`"].
The data can have the form {{x₁,y₁,…,f₁},{x₂,y₂,…,f₂},…}, where the number of coordinates x,y,… is equal to the number of variables in the list vars.
The data can also be of the form {f₁,f₂,…}, with a single coordinate assumed to take values 1,2,….
The argument funs can be any list of functions that depend only on the variables vars.
Regress returns a list of rules for results and diagnostics specified by the option RegressionReport.
Regress always finds the linear combination of the functions in the list funs that minimize the sum of the squares of deviations from the values f_i.
Exact numbers given as input to Regress are converted to approximate numbers with machine precision.
The following options can be given:

RegressionReport	SummaryReport	results to be included in output
IncludeConstant	True	whether to automatically include a constant as one of the functions
BasisNames	Automatic	names of basis elements for table headings
Weights	Automatic	weights for each data point
Method	Automatic	method used to compute singular values
Tolerance	Automatic	tolerance to use in computing singular values
ConfidenceLevel	0.95	confidence level used for confidence intervals

With the option IncludeConstant->False, Regress gives the same fit as Fit does.
Possible settings for Weights are Automatic, a list of numbers with the same length as the data, or a pure function.
With the default setting Weights->Automatic, each data point is given a weight of 1.

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Linear regression for a straight line:

Linear regression for a constant plus a sinusoid:

Linear regression for a straight line with basis functions labeled b1 and b2:

Linear regression with .99 confidence level for confidence intervals:

Linear regression with constant term assumed to be 0:

Linear regression with a specific list of report values:

Weighted regression with explicit weights for each data element:

Weighted regression with weights equal to the squares of the measured responses:

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