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Commons Math example source code file (OLSMultipleLinearRegression.java)

This example Commons Math source code file (OLSMultipleLinearRegression.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

abstractmultiplelinearregression, array2drowrealmatrix, array2drowrealmatrix, olsmultiplelinearregression, override, override, q, qrdecomposition, qrdecompositionimpl, qrdecompositionimpl, raug, realmatrix, realmatrix, realvector

The Commons Math OLSMultipleLinearRegression.java source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math.stat.regression;

import org.apache.commons.math.linear.Array2DRowRealMatrix;
import org.apache.commons.math.linear.LUDecompositionImpl;
import org.apache.commons.math.linear.QRDecomposition;
import org.apache.commons.math.linear.QRDecompositionImpl;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.linear.RealVector;

/**
 * <p>Implements ordinary least squares (OLS) to estimate the parameters of a
 * multiple linear regression model.</p>
 *
 * <p>OLS assumes the covariance matrix of the error to be diagonal and with
 * equal variance.</p>
 * <p>
 * u ~ N(0, ?<sup>2I)
 * </p>
 *
 * <p>The regression coefficients, b, satisfy the normal equations:
 * <p>
 * X<sup>T X b = XT y
 * </p>
 *
 * <p>To solve the normal equations, this implementation uses QR decomposition
 * of the X matrix. (See {@link QRDecompositionImpl} for details on the
 * decomposition algorithm.)
 * </p>
 * <p>XTX b = XT y 
* (QR)<sup>T (QR) b = (QR)Ty
* R<sup>T (QTQ) R b = RT QT y
* R<sup>T R b = RT QT y
* (R<sup>T)-1 RT R b = (RT)-1 RT QT y
* R b = Q<sup>T y * </p> * Given Q and R, the last equation is solved by back-subsitution.</p> * * @version $Revision: 825925 $ $Date: 2009-10-16 11:11:47 -0400 (Fri, 16 Oct 2009) $ * @since 2.0 */ public class OLSMultipleLinearRegression extends AbstractMultipleLinearRegression { /** Cached QR decomposition of X matrix */ private QRDecomposition qr = null; /** * Loads model x and y sample data, overriding any previous sample. * * Computes and caches QR decomposition of the X matrix. * @param y the [n,1] array representing the y sample * @param x the [n,k] array representing the x sample * @throws IllegalArgumentException if the x and y array data are not * compatible for the regression */ public void newSampleData(double[] y, double[][] x) { validateSampleData(x, y); newYSampleData(y); newXSampleData(x); } /** * {@inheritDoc} * * Computes and caches QR decomposition of the X matrix */ @Override public void newSampleData(double[] data, int nobs, int nvars) { super.newSampleData(data, nobs, nvars); qr = new QRDecompositionImpl(X); } /** * <p>Compute the "hat" matrix. * </p> * <p>The hat matrix is defined in terms of the design matrix X * by X(X<sup>TX)-1XT * </p> * <p>The implementation here uses the QR decomposition to compute the * hat matrix as Q I<sub>pQT where Ip 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, Vol. 32, No. 1 (Feb., 1978), pp. 17-22. * * @return the hat matrix */ public RealMatrix calculateHat() { // Create augmented identity matrix RealMatrix Q = qr.getQ(); final int p = qr.getR().getColumnDimension(); final int n = Q.getColumnDimension(); Array2DRowRealMatrix augI = new Array2DRowRealMatrix(n, n); double[][] augIData = augI.getDataRef(); for (int i = 0; i < n; i++) { for (int j =0; j < n; j++) { if (i == j && i < p) { augIData[i][j] = 1d; } else { augIData[i][j] = 0d; } } } // Compute and return Hat matrix return Q.multiply(augI).multiply(Q.transpose()); } /** * Loads new x sample data, overriding any previous sample * * @param x the [n,k] array representing the x sample */ @Override protected void newXSampleData(double[][] x) { this.X = new Array2DRowRealMatrix(x); qr = new QRDecompositionImpl(X); } /** * Calculates regression coefficients using OLS. * * @return beta */ @Override protected RealVector calculateBeta() { return qr.getSolver().solve(Y); } /** * <p>Calculates the variance on the beta by OLS. * </p> * <p>Var(b) = (XTX)-1 * </p> * <p>Uses QR decomposition to reduce (XTX)-1 * to (R<sup>TR)-1, with only the top p rows of * R included, where p = the length of the beta vector.</p> * * @return The beta variance */ @Override protected RealMatrix calculateBetaVariance() { int p = X.getColumnDimension(); RealMatrix Raug = qr.getR().getSubMatrix(0, p - 1 , 0, p - 1); RealMatrix Rinv = new LUDecompositionImpl(Raug).getSolver().getInverse(); return Rinv.multiply(Rinv.transpose()); } /** * <p>Calculates the variance on the Y by OLS. * </p> * <p> Var(y) = Tr(uTu)/(n - k) * </p> * @return The Y variance */ @Override protected double calculateYVariance() { RealVector residuals = calculateResiduals(); return residuals.dotProduct(residuals) / (X.getRowDimension() - X.getColumnDimension()); } }

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