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<div class="subTitle">org.apache.commons.math3.stat.regression</div>
<h2 title="Class OLSMultipleLinearRegression" class="title">Class OLSMultipleLinearRegression</h2>
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<li><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">org.apache.commons.math3.stat.regression.AbstractMultipleLinearRegression</a></li>
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<dd><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</a></dd>
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<pre>public class <span class="strong">OLSMultipleLinearRegression</span>
extends <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">AbstractMultipleLinearRegression</a></pre>
<div class="block"><p>Implements ordinary least squares (OLS) to estimate the parameters of a
multiple linear regression model.</p>
<p>The regression coefficients, <code>b</code>, satisfy the normal equations:
<pre><code> X<sup>T</sup> X b = X<sup>T</sup> y </code></pre></p>
<p>To solve the normal equations, this implementation uses QR decomposition
of the <code>X</code> matrix. (See <a href="../../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear"><code>QRDecomposition</code></a> for details on the
decomposition algorithm.) The <code>X</code> matrix, also known as the <i>design matrix,</i>
has rows corresponding to sample observations and columns corresponding to independent
variables. When the model is estimated using an intercept term (i.e. when
<a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#isNoIntercept()"><code>isNoIntercept</code></a> is false as it is by default), the <code>X</code>
matrix includes an initial column identically equal to 1. We solve the normal equations
as follows:
<pre><code> X<sup>T</sup>X b = X<sup>T</sup> y
(QR)<sup>T</sup> (QR) b = (QR)<sup>T</sup>y
R<sup>T</sup> (Q<sup>T</sup>Q) R b = R<sup>T</sup> Q<sup>T</sup> y
R<sup>T</sup> R b = R<sup>T</sup> Q<sup>T</sup> y
(R<sup>T</sup>)<sup>-1</sup> R<sup>T</sup> R b = (R<sup>T</sup>)<sup>-1</sup> R<sup>T</sup> Q<sup>T</sup> y
R b = Q<sup>T</sup> y </code></pre></p>
<p>Given <code>Q</code> and <code>R</code>, the last equation is solved by back-substitution.</p></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>2.0</dd></dl>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#OLSMultipleLinearRegression()">OLSMultipleLinearRegression</a></strong>()</code>
<div class="block">Create an empty OLSMultipleLinearRegression instance.</div>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#OLSMultipleLinearRegression(double)">OLSMultipleLinearRegression</a></strong>(double threshold)</code>
<div class="block">Create an empty OLSMultipleLinearRegression instance, using the given
singularity threshold for the QR decomposition.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateAdjustedRSquared()">calculateAdjustedRSquared</a></strong>()</code>
<div class="block">Returns the adjusted R-squared statistic, defined by the formula</div>
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<td class="colFirst"><code>protected <a href="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateBeta()">calculateBeta</a></strong>()</code>
<div class="block">Calculates the regression coefficients using OLS.</div>
</td>
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<tr class="altColor">
<td class="colFirst"><code>protected <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateBetaVariance()">calculateBetaVariance</a></strong>()</code>
<div class="block">Calculates the variance-covariance matrix of the regression parameters.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateHat()">calculateHat</a></strong>()</code>
<div class="block">Compute the "hat" matrix.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateResidualSumOfSquares()">calculateResidualSumOfSquares</a></strong>()</code>
<div class="block">Returns the sum of squared residuals.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateRSquared()">calculateRSquared</a></strong>()</code>
<div class="block">Returns the R-Squared statistic, defined by the formula</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateTotalSumOfSquares()">calculateTotalSumOfSquares</a></strong>()</code>
<div class="block">Returns the sum of squared deviations of Y from its mean.</div>
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<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#newSampleData(double[],%20double[][])">newSampleData</a></strong>(double[] y,
double[][] x)</code>
<div class="block">Loads model x and y sample data, overriding any previous sample.</div>
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<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#newSampleData(double[],%20int,%20int)">newSampleData</a></strong>(double[] data,
int nobs,
int nvars)</code>
<div class="block">Loads model x and y sample data from a flat input array, overriding any previous sample.</div>
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<td class="colFirst"><code>protected void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#newXSampleData(double[][])">newXSampleData</a></strong>(double[][] x)</code>
<div class="block">Loads new x sample data, overriding any previous data.</div>
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<h3>Methods inherited from class org.apache.commons.math3.stat.regression.<a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">AbstractMultipleLinearRegression</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateErrorVariance()">calculateErrorVariance</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateResiduals()">calculateResiduals</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateYVariance()">calculateYVariance</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateErrorVariance()">estimateErrorVariance</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressandVariance()">estimateRegressandVariance</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionParameters()">estimateRegressionParameters</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionParametersStandardErrors()">estimateRegressionParametersStandardErrors</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionParametersVariance()">estimateRegressionParametersVariance</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionStandardError()">estimateRegressionStandardError</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateResiduals()">estimateResiduals</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#getX()">getX</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#getY()">getY</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#isNoIntercept()">isNoIntercept</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#newYSampleData(double[])">newYSampleData</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#setNoIntercept(boolean)">setNoIntercept</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#validateCovarianceData(double[][],%20double[][])">validateCovarianceData</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#validateSampleData(double[][],%20double[])">validateSampleData</a></code></li>
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<h4>OLSMultipleLinearRegression</h4>
<pre>public OLSMultipleLinearRegression()</pre>
<div class="block">Create an empty OLSMultipleLinearRegression instance.</div>
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<h4>OLSMultipleLinearRegression</h4>
<pre>public OLSMultipleLinearRegression(double threshold)</pre>
<div class="block">Create an empty OLSMultipleLinearRegression instance, using the given
singularity threshold for the QR decomposition.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>threshold</code> - the singularity threshold</dd><dt><span class="strong">Since:</span></dt>
<dd>3.3</dd></dl>
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<h4>newSampleData</h4>
<pre>public void newSampleData(double[] y,
double[][] x)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre>
<div class="block">Loads model x and y sample data, overriding any previous sample.
Computes and caches QR decomposition of the X matrix.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>y</code> - the [n,1] array representing the y sample</dd><dd><code>x</code> - the [n,k] array representing the x sample</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the x and y array data are not
compatible for the regression</dd></dl>
</li>
</ul>
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<h4>newSampleData</h4>
<pre>public void newSampleData(double[] data,
int nobs,
int nvars)</pre>
<div class="block"><p>Loads model x and y sample data from a flat input array, overriding any previous sample.
</p>
<p>Assumes that rows are concatenated with y values first in each row. For example, an input
<code>data</code> array containing the sequence of values (1, 2, 3, 4, 5, 6, 7, 8, 9) with
<code>nobs = 3</code> and <code>nvars = 2</code> creates a regression dataset with two
independent variables, as below:
<pre>
y x[0] x[1]
--------------
1 2 3
4 5 6
7 8 9
</pre>
</p>
<p>Note that there is no need to add an initial unitary column (column of 1's) when
specifying a model including an intercept term. If <a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#isNoIntercept()"><code>AbstractMultipleLinearRegression.isNoIntercept()</code></a> is <code>true</code>,
the X matrix will be created without an initial column of "1"s; otherwise this column will
be added.
</p>
<p>Throws IllegalArgumentException if any of the following preconditions fail:
<ul><li><code>data</code> cannot be null</li>
<li><code>data.length = nobs * (nvars + 1)</li>
<li><code>nobs > nvars</code></li></ul>
</p>
<p>This implementation computes and caches the QR decomposition of the X matrix.</p></div>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#newSampleData(double[],%20int,%20int)">newSampleData</a></code> in class <code><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">AbstractMultipleLinearRegression</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - input data array</dd><dd><code>nobs</code> - number of observations (rows)</dd><dd><code>nvars</code> - number of independent variables (columns, not counting y)</dd></dl>
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<a name="calculateHat()">
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<h4>calculateHat</h4>
<pre>public <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> calculateHat()</pre>
<div class="block"><p>Compute the "hat" matrix.
</p>
<p>The hat matrix is defined in terms of the design matrix X
by X(X<sup>T</sup>X)<sup>-1</sup>X<sup>T</sup>
</p>
<p>The implementation here uses the QR decomposition to compute the
hat matrix as Q I<sub>p</sub>Q<sup>T</sup> where I<sub>p</sub> is the
p-dimensional identity matrix augmented by 0's. This computational
formula is from "The Hat Matrix in Regression and ANOVA",
David C. Hoaglin and Roy E. Welsch,
<i>The American Statistician</i>, Vol. 32, No. 1 (Feb., 1978), pp. 17-22.
</p>
<p>Data for the model must have been successfully loaded using one of
the <code>newSampleData</code> methods before invoking this method; otherwise
a <code>NullPointerException</code> will be thrown.</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the hat matrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - unless method <code>newSampleData</code> has been
called beforehand.</dd></dl>
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<h4>calculateTotalSumOfSquares</h4>
<pre>public double calculateTotalSumOfSquares()</pre>
<div class="block"><p>Returns the sum of squared deviations of Y from its mean.</p>
<p>If the model has no intercept term, <code>0</code> is used for the
mean of Y - i.e., what is returned is the sum of the squared Y values.</p>
<p>The value returned by this method is the SSTO value used in
the <a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateRSquared()"><code>R-squared</code></a> computation.</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>SSTO - the total sum of squares</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - if the sample has not been set</dd><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#isNoIntercept()"><code>AbstractMultipleLinearRegression.isNoIntercept()</code></a></dd></dl>
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<pre>public double calculateResidualSumOfSquares()</pre>
<div class="block">Returns the sum of squared residuals.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>residual sum of squares</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the design matrix is singular</dd>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - if the data for the model have not been loaded</dd><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd></dl>
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<pre>public double calculateRSquared()</pre>
<div class="block">Returns the R-Squared statistic, defined by the formula <pre>
R<sup>2</sup> = 1 - SSR / SSTO
</pre>
where SSR is the <a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateResidualSumOfSquares()"><code>sum of squared residuals</code></a>
and SSTO is the <a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateTotalSumOfSquares()"><code>total sum of squares</code></a>
<p>If there is no variance in y, i.e., SSTO = 0, NaN is returned.</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>R-square statistic</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - if the sample has not been set</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the design matrix is singular</dd><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd></dl>
</li>
</ul>
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<pre>public double calculateAdjustedRSquared()</pre>
<div class="block"><p>Returns the adjusted R-squared statistic, defined by the formula <pre>
R<sup>2</sup><sub>adj</sub> = 1 - [SSR (n - 1)] / [SSTO (n - p)]
</pre>
where SSR is the <a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateResidualSumOfSquares()"><code>sum of squared residuals</code></a>,
SSTO is the <a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateTotalSumOfSquares()"><code>total sum of squares</code></a>, n is the number
of observations and p is the number of parameters estimated (including the intercept).</p>
<p>If the regression is estimated without an intercept term, what is returned is <pre>
<code> 1 - (1 - <a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#calculateRSquared()"><code>calculateRSquared()</code></a>) * (n / (n - p)) </code>
</pre></p>
<p>If there is no variance in y, i.e., SSTO = 0, NaN is returned.</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>adjusted R-Squared statistic</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - if the sample has not been set</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the design matrix is singular</dd><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#isNoIntercept()"><code>AbstractMultipleLinearRegression.isNoIntercept()</code></a></dd></dl>
</li>
</ul>
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<pre>protected void newXSampleData(double[][] x)</pre>
<div class="block"><p>Loads new x sample data, overriding any previous data.
</p>
The input <code>x</code> array should have one row for each sample
observation, with columns corresponding to independent variables.
For example, if <pre>
<code> x = new double[][] {{1, 2}, {3, 4}, {5, 6}} </code></pre>
then <code>setXSampleData(x) </code> results in a model with two independent
variables and 3 observations:
<pre>
x[0] x[1]
----------
1 2
3 4
5 6
</pre>
</p>
<p>Note that there is no need to add an initial unitary column (column of 1's) when
specifying a model including an intercept term.
</p>
<p>This implementation computes and caches the QR decomposition of the X matrix
once it is successfully loaded.</p></div>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#newXSampleData(double[][])">newXSampleData</a></code> in class <code><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">AbstractMultipleLinearRegression</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the rectangular array representing the x sample</dd></dl>
</li>
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<a name="calculateBeta()">
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<h4>calculateBeta</h4>
<pre>protected <a href="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> calculateBeta()</pre>
<div class="block">Calculates the regression coefficients using OLS.
<p>Data for the model must have been successfully loaded using one of
the <code>newSampleData</code> methods before invoking this method; otherwise
a <code>NullPointerException</code> will be thrown.</p></div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateBeta()">calculateBeta</a></code> in class <code><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">AbstractMultipleLinearRegression</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>beta</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the design matrix is singular</dd>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - if the data for the model have not been loaded</dd></dl>
</li>
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<a name="calculateBetaVariance()">
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<h4>calculateBetaVariance</h4>
<pre>protected <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> calculateBetaVariance()</pre>
<div class="block"><p>Calculates the variance-covariance matrix of the regression parameters.
</p>
<p>Var(b) = (X<sup>T</sup>X)<sup>-1</sup>
</p>
<p>Uses QR decomposition to reduce (X<sup>T</sup>X)<sup>-1</sup>
to (R<sup>T</sup>R)<sup>-1</sup>, with only the top p rows of
R included, where p = the length of the beta vector.</p>
<p>Data for the model must have been successfully loaded using one of
the <code>newSampleData</code> methods before invoking this method; otherwise
a <code>NullPointerException</code> will be thrown.</p></div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateBetaVariance()">calculateBetaVariance</a></code> in class <code><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">AbstractMultipleLinearRegression</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>The beta variance-covariance matrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the design matrix is singular</dd>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - if the data for the model have not been loaded</dd></dl>
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