LinearRegression`

LinearRegression`

DesignedRegress

As of Version 7.0, DesignedRegress has been superseded by LinearModelFit.

DesignedRegress[matrix,vector]

finds a least–squares fit given the design matrix matrix and response vector vector.

DesignedRegress[svd,vector]

finds a fit given the singular value decomposition svd of a design matrix.

Details and Options

To use DesignedRegress, you first need to load the Linear Regression Package using Needs["LinearRegression`"].
A design matrix is a list containing the basis functions evaluated at the observed values of the independent variables, as returned by DesignMatrix.
DesignedRegress returns a list of rules for results and diagnostics specified by the option RegressionReport.
The argument svd is of the same form as that returned by SingularValueDecomposition.
Exact numbers given as input to DesignedRegress are converted to approximate numbers with machine precision.
The following options can be given:

	RegressionReport	SummaryReport	results to be included in output
	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

Examples

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Basic Examples (1)Summary of the most common use cases

In[1]:=1

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-bzuif4

Linear regression with one constant and one nonconstant basis function:

In[2]:=2

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-3w5t8

Out[2]=2

Options (5)Common values & functionality for each option

RegressionReport (1)

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-gh9znz

Linear regression with a specific list of report values:

In[2]:=2

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-utiu5

Out[2]=2

BasisNames (1)

In[1]:=1

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-b9lg7g

Linear regression with basis functions labeled b1 and b2:

In[2]:=2

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-gx2563

Out[2]=2

Weights (2)

In[1]:=1

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-k1nru

Weighted regression with explicit weights for each data element:

In[2]:=2

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-c6zfy3

Out[2]=2

In[1]:=1

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-hh6ecm

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

In[2]:=2

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-bopk88

Out[2]=2

ConfidenceLevel (1)

In[1]:=1

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-hthas

Linear regression with .99 confidence level for confidence intervals:

In[2]:=2

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https://wolfram.com/xid/0doyoimi5pq7czywctu4m-jy5r7q

Out[2]=2

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