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<div class="subTitle">org.apache.commons.math3.stat.regression</div>
<h2 title="Class AbstractMultipleLinearRegression" class="title">Class AbstractMultipleLinearRegression</h2>
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<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</a></dd>
</dl>
<dl>
<dt>Direct Known Subclasses:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/stat/regression/GLSMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">GLSMultipleLinearRegression</a>, <a href="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">OLSMultipleLinearRegression</a></dd>
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<pre>public abstract class <span class="strong">AbstractMultipleLinearRegression</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>
implements <a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</a></pre>
<div class="block">Abstract base class for implementations of MultipleLinearRegression.</div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>2.0</dd>
<dt><span class="strong">Version:</span></dt>
<dd>$Id: AbstractMultipleLinearRegression.java 1547633 2013-12-03 23:03:06Z tn $</dd></dl>
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<th class="colOne" scope="col">Constructor and Description</th>
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<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#AbstractMultipleLinearRegression()">AbstractMultipleLinearRegression</a></strong>()</code>&nbsp;</td>
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<caption><span>Methods</span><span class="tabEnd">&nbsp;</span></caption>
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<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
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<td class="colFirst"><code>protected abstract <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/AbstractMultipleLinearRegression.html#calculateBeta()">calculateBeta</a></strong>()</code>
<div class="block">Calculates the beta of multiple linear regression in matrix notation.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected abstract <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/AbstractMultipleLinearRegression.html#calculateBetaVariance()">calculateBetaVariance</a></strong>()</code>
<div class="block">Calculates the beta variance of multiple linear regression in matrix
notation.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>protected double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateErrorVariance()">calculateErrorVariance</a></strong>()</code>
<div class="block">Calculates the variance of the error term.</div>
</td>
</tr>
<tr class="rowColor">
<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/AbstractMultipleLinearRegression.html#calculateResiduals()">calculateResiduals</a></strong>()</code>
<div class="block">Calculates the residuals of multiple linear regression in matrix
notation.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>protected double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateYVariance()">calculateYVariance</a></strong>()</code>
<div class="block">Calculates the variance of the y values.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateErrorVariance()">estimateErrorVariance</a></strong>()</code>
<div class="block">Estimates the variance of the error.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressandVariance()">estimateRegressandVariance</a></strong>()</code>
<div class="block">Returns the variance of the regressand, ie Var(y).</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionParameters()">estimateRegressionParameters</a></strong>()</code>
<div class="block">Estimates the regression parameters b.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionParametersStandardErrors()">estimateRegressionParametersStandardErrors</a></strong>()</code>
<div class="block">Returns the standard errors of the regression parameters.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[][]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionParametersVariance()">estimateRegressionParametersVariance</a></strong>()</code>
<div class="block">Estimates the variance of the regression parameters, ie Var(b).</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionStandardError()">estimateRegressionStandardError</a></strong>()</code>
<div class="block">Estimates the standard error of the regression.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateResiduals()">estimateResiduals</a></strong>()</code>
<div class="block">Estimates the residuals, ie u = y - X*b.</div>
</td>
</tr>
<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/AbstractMultipleLinearRegression.html#getX()">getX</a></strong>()</code>&nbsp;</td>
</tr>
<tr class="rowColor">
<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/AbstractMultipleLinearRegression.html#getY()">getY</a></strong>()</code>&nbsp;</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#isNoIntercept()">isNoIntercept</a></strong>()</code>&nbsp;</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#newSampleData(double[], int, int)">newSampleData</a></strong>(double[]&nbsp;data,
int&nbsp;nobs,
int&nbsp;nvars)</code>
<div class="block">Loads model x and y sample data from a flat input array, overriding any previous sample.</div>
</td>
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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/AbstractMultipleLinearRegression.html#newXSampleData(double[][])">newXSampleData</a></strong>(double[][]&nbsp;x)</code>
<div class="block">Loads new x sample data, overriding any previous data.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code>protected void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#newYSampleData(double[])">newYSampleData</a></strong>(double[]&nbsp;y)</code>
<div class="block">Loads new y sample data, overriding any previous data.</div>
</td>
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<tr class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#setNoIntercept(boolean)">setNoIntercept</a></strong>(boolean&nbsp;noIntercept)</code>&nbsp;</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#validateCovarianceData(double[][], double[][])">validateCovarianceData</a></strong>(double[][]&nbsp;x,
double[][]&nbsp;covariance)</code>
<div class="block">Validates that the x data and covariance matrix have the same
number of rows and that the covariance matrix is square.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>protected void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#validateSampleData(double[][], double[])">validateSampleData</a></strong>(double[][]&nbsp;x,
double[]&nbsp;y)</code>
<div class="block">Validates sample data.</div>
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<h4>AbstractMultipleLinearRegression</h4>
<pre>public&nbsp;AbstractMultipleLinearRegression()</pre>
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<h4>getX</h4>
<pre>protected&nbsp;<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;getX()</pre>
<dl><dt><span class="strong">Returns:</span></dt><dd>the X sample data.</dd></dl>
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<a name="getY()">
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<h4>getY</h4>
<pre>protected&nbsp;<a href="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;getY()</pre>
<dl><dt><span class="strong">Returns:</span></dt><dd>the Y sample data.</dd></dl>
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<pre>public&nbsp;boolean&nbsp;isNoIntercept()</pre>
<dl><dt><span class="strong">Returns:</span></dt><dd>true if the model has no intercept term; false otherwise</dd><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd></dl>
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<pre>public&nbsp;void&nbsp;setNoIntercept(boolean&nbsp;noIntercept)</pre>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>noIntercept</code> - true means the model is to be estimated without an intercept term</dd><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd></dl>
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<pre>public&nbsp;void&nbsp;newSampleData(double[]&nbsp;data,
int&nbsp;nobs,
int&nbsp;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>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></div>
<dl><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>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if the data array is null</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the length of the data array is not equal
to <code>nobs * (nvars + 1)</code></dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/InsufficientDataException.html" title="class in org.apache.commons.math3.exception">InsufficientDataException</a></code> - if <code>nobs</code> is less than
<code>nvars + 1</code></dd></dl>
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<pre>protected&nbsp;void&nbsp;newYSampleData(double[]&nbsp;y)</pre>
<div class="block">Loads new y sample data, overriding any previous data.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>y</code> - the array representing the y sample</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if y is null</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if y is empty</dd></dl>
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<pre>protected&nbsp;void&nbsp;newXSampleData(double[][]&nbsp;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></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the rectangular array representing the x sample</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if x is null</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if x is empty</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if x is not rectangular</dd></dl>
</li>
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<h4>validateSampleData</h4>
<pre>protected&nbsp;void&nbsp;validateSampleData(double[][]&nbsp;x,
double[]&nbsp;y)
throws <a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre>
<div class="block">Validates sample data. Checks that
<ul><li>Neither x nor y is null or empty;</li>
<li>The length (i.e. number of rows) of x equals the length of y</li>
<li>x has at least one more row than it has columns (i.e. there is
sufficient data to estimate regression coefficients for each of the
columns in x plus an intercept.</li>
</ul></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the [n,k] array representing the x data</dd><dd><code>y</code> - the [n,1] array representing the y data</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>x</code> or <code>y</code> is null</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>x</code> and <code>y</code> do not
have the same length</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>x</code> or <code>y</code> are zero-length</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the number of rows of <code>x</code>
is not larger than the number of columns + 1</dd></dl>
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<a name="validateCovarianceData(double[][], double[][])">
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<h4>validateCovarianceData</h4>
<pre>protected&nbsp;void&nbsp;validateCovarianceData(double[][]&nbsp;x,
double[][]&nbsp;covariance)</pre>
<div class="block">Validates that the x data and covariance matrix have the same
number of rows and that the covariance matrix is square.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the [n,k] array representing the x sample</dd><dd><code>covariance</code> - the [n,n] array representing the covariance matrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the number of rows in x is not equal
to the number of rows in covariance</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if the covariance matrix is not square</dd></dl>
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<h4>estimateRegressionParameters</h4>
<pre>public&nbsp;double[]&nbsp;estimateRegressionParameters()</pre>
<div class="block">Estimates the regression parameters b.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html#estimateRegressionParameters()">estimateRegressionParameters</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>The [k,1] array representing b</dd></dl>
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<h4>estimateResiduals</h4>
<pre>public&nbsp;double[]&nbsp;estimateResiduals()</pre>
<div class="block">Estimates the residuals, ie u = y - X*b.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html#estimateResiduals()">estimateResiduals</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>The [n,1] array representing the residuals</dd></dl>
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<pre>public&nbsp;double[][]&nbsp;estimateRegressionParametersVariance()</pre>
<div class="block">Estimates the variance of the regression parameters, ie Var(b).</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html#estimateRegressionParametersVariance()">estimateRegressionParametersVariance</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>The [k,k] array representing the variance of b</dd></dl>
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<a name="estimateRegressionParametersStandardErrors()">
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<pre>public&nbsp;double[]&nbsp;estimateRegressionParametersStandardErrors()</pre>
<div class="block">Returns the standard errors of the regression parameters.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html#estimateRegressionParametersStandardErrors()">estimateRegressionParametersStandardErrors</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>standard errors of estimated regression parameters</dd></dl>
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<h4>estimateRegressandVariance</h4>
<pre>public&nbsp;double&nbsp;estimateRegressandVariance()</pre>
<div class="block">Returns the variance of the regressand, ie Var(y).</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html#estimateRegressandVariance()">estimateRegressandVariance</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>The double representing the variance of y</dd></dl>
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<pre>public&nbsp;double&nbsp;estimateErrorVariance()</pre>
<div class="block">Estimates the variance of the error.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>estimate of the error variance</dd><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd></dl>
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<pre>public&nbsp;double&nbsp;estimateRegressionStandardError()</pre>
<div class="block">Estimates the standard error of the regression.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>regression standard error</dd><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd></dl>
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<pre>protected abstract&nbsp;<a href="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;calculateBeta()</pre>
<div class="block">Calculates the beta of multiple linear regression in matrix notation.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>beta</dd></dl>
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<pre>protected abstract&nbsp;<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;calculateBetaVariance()</pre>
<div class="block">Calculates the beta variance of multiple linear regression in matrix
notation.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>beta variance</dd></dl>
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<pre>protected&nbsp;double&nbsp;calculateYVariance()</pre>
<div class="block">Calculates the variance of the y values.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>Y variance</dd></dl>
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<pre>protected&nbsp;double&nbsp;calculateErrorVariance()</pre>
<div class="block"><p>Calculates the variance of the error term.</p>
Uses the formula <pre>
var(u) = u &middot; u / (n - k)
</pre>
where n and k are the row and column dimensions of the design
matrix X.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>error variance estimate</dd><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd></dl>
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<h4>calculateResiduals</h4>
<pre>protected&nbsp;<a href="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;calculateResiduals()</pre>
<div class="block">Calculates the residuals of multiple linear regression in matrix
notation.
<pre>
u = y - X * b
</pre></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>The residuals [n,1] matrix</dd></dl>
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