Upgrading from:

LinearRegression`

Regress and DesignedRegress are now available using the built-in function LinearModelFit.
The function DesignMatrix has been added to the built-in Mathematica kernel.
The option BasisNames is now an optional argument to LinearModelFit.
The option IncludeConstant has been renamed to IncludeConstantBasis.

New system functions

LinearModelFit is part of the built-in Mathematica kernel:

Version 6.0 << LinearRegression`; Regress[{{1, 2}, {2, 4}, {3, 2}, {4, -1}}, {Sin[x]}, x]

The result is returned as a FittedModel object, of which properties can be returned:

For a list of available properties, use "Properties":

Version 6.0 << LinearRegression`; RegressionReportValues

To get the functional form of the FittedModel object, use Normal:

DesignedRegress has also been superseded by LinearModelFit:

Version 6.0 << LinearRegression`; DesignedRegress[{{1, 0}, {1, 1}, {1, 2}}, {1, 2, 4}]

Calculate the parameter table and property values:

DesignMatrix is part of the built-in Mathematica kernel:

Version 6.0 << LinearRegression`; DesignMatrix[{2, 3, 4, 6}, x, x]

BasisNames is now an optional argument to LinearModelFit:

Version 6.0 << LinearRegression`; DesignedRegress[{{1, 1}, {1, 2}, {1, 3}, {1, 4}}, {2, 3, 4, 6}, BasisNames -> {"b1", "b2"}]

IncludeConstant has been renamed to IncludeConstantBasis:

Version 6.0 << LinearRegression`; DesignMatrix[{1, 2, 3, 4}, {x}, x, IncludeConstant -> False]

Some of the properties previously available to Regress and related functions have been renamed:

RegressLinearModelFit
BestFitParametersDelta"BetaDifferences"
CookD"CookDistances"
CovarianceMatrixDetRatio"CovarianceRatios"
JackknifedVariance"SingleDeletionVariances"
MeanPredictionCITable"MeanPredictionConfidenceIntervalTable"
ParameterCITable"ParameterConfidenceIntervalTable"
PredictedResponseDelta"FitDifferences"
SinglePredictionCITable"SinglePredictionConfidenceIntervalTable"
SummaryReport{"ParameterTable", "RSquared", "AdjustedRSquared", "EstimatedVariance", "ANOVATable"}
VarianceInflation"VarianceInflationFactors"