LinearRegression`
LinearRegression`

# DesignedRegress

As of Version 7.0, DesignedRegress has been superseded by LinearModelFit.

DesignedRegress[matrix,vector]

finds a leastsquares 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

open allclose all

## Basic Examples(1)

Linear regression with one constant and one nonconstant basis function:

## Options(5)

### RegressionReport(1)

Linear regression with a specific list of report values:

### BasisNames(1)

Linear regression with basis functions labeled b1 and b2:

### Weights(2)

Weighted regression with explicit weights for each data element:

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

### ConfidenceLevel(1)

Linear regression with .99 confidence level for confidence intervals:

Wolfram Research (2007), DesignedRegress, Wolfram Language function, https://reference.wolfram.com/language/LinearRegression/ref/DesignedRegress.html.

#### Text

Wolfram Research (2007), DesignedRegress, Wolfram Language function, https://reference.wolfram.com/language/LinearRegression/ref/DesignedRegress.html.

#### CMS

Wolfram Language. 2007. "DesignedRegress." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/LinearRegression/ref/DesignedRegress.html.

#### APA

Wolfram Language. (2007). DesignedRegress. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/LinearRegression/ref/DesignedRegress.html

#### BibTeX

@misc{reference.wolfram_2024_designedregress, author="Wolfram Research", title="{DesignedRegress}", year="2007", howpublished="\url{https://reference.wolfram.com/language/LinearRegression/ref/DesignedRegress.html}", note=[Accessed: 11-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_designedregress, organization={Wolfram Research}, title={DesignedRegress}, year={2007}, url={https://reference.wolfram.com/language/LinearRegression/ref/DesignedRegress.html}, note=[Accessed: 11-September-2024 ]}