Java tutorial
/* * 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.math3.stat.regression; import java.io.Serializable; import java.util.Arrays; import org.apache.commons.math3.util.FastMath; import org.apache.commons.math3.util.MathArrays; import org.apache.commons.math3.exception.OutOfRangeException; /** * Results of a Multiple Linear Regression model fit. * * @version $Id: RegressionResults.java 1392342 2012-10-01 14:08:52Z psteitz $ * @since 3.0 */ public class RegressionResults implements Serializable { /** INDEX of Sum of Squared Errors */ private static final int SSE_IDX = 0; /** INDEX of Sum of Squares of Model */ private static final int SST_IDX = 1; /** INDEX of R-Squared of regression */ private static final int RSQ_IDX = 2; /** INDEX of Mean Squared Error */ private static final int MSE_IDX = 3; /** INDEX of Adjusted R Squared */ private static final int ADJRSQ_IDX = 4; /** UID */ private static final long serialVersionUID = 1l; /** regression slope parameters */ private final double[] parameters; /** variance covariance matrix of parameters */ private final double[][] varCovData; /** boolean flag for variance covariance matrix in symm compressed storage */ private final boolean isSymmetricVCD; /** rank of the solution */ @SuppressWarnings("unused") private final int rank; /** number of observations on which results are based */ private final long nobs; /** boolean flag indicator of whether a constant was included*/ private final boolean containsConstant; /** array storing global results, SSE, MSE, RSQ, adjRSQ */ private final double[] globalFitInfo; /** * Set the default constructor to private access * to prevent inadvertent instantiation */ @SuppressWarnings("unused") private RegressionResults() { this.parameters = null; this.varCovData = null; this.rank = -1; this.nobs = -1; this.containsConstant = false; this.isSymmetricVCD = false; this.globalFitInfo = null; } /** * Constructor for Regression Results. * * @param parameters a double array with the regression slope estimates * @param varcov the variance covariance matrix, stored either in a square matrix * or as a compressed * @param isSymmetricCompressed a flag which denotes that the variance covariance * matrix is in symmetric compressed format * @param nobs the number of observations of the regression estimation * @param rank the number of independent variables in the regression * @param sumy the sum of the independent variable * @param sumysq the sum of the squared independent variable * @param sse sum of squared errors * @param containsConstant true model has constant, false model does not have constant * @param copyData if true a deep copy of all input data is made, if false only references * are copied and the RegressionResults become mutable */ public RegressionResults(final double[] parameters, final double[][] varcov, final boolean isSymmetricCompressed, final long nobs, final int rank, final double sumy, final double sumysq, final double sse, final boolean containsConstant, final boolean copyData) { if (copyData) { this.parameters = MathArrays.copyOf(parameters); this.varCovData = new double[varcov.length][]; for (int i = 0; i < varcov.length; i++) { this.varCovData[i] = MathArrays.copyOf(varcov[i]); } } else { this.parameters = parameters; this.varCovData = varcov; } this.isSymmetricVCD = isSymmetricCompressed; this.nobs = nobs; this.rank = rank; this.containsConstant = containsConstant; this.globalFitInfo = new double[5]; Arrays.fill(this.globalFitInfo, Double.NaN); if (rank > 0) { this.globalFitInfo[SST_IDX] = containsConstant ? (sumysq - sumy * sumy / nobs) : sumysq; } this.globalFitInfo[SSE_IDX] = sse; this.globalFitInfo[MSE_IDX] = this.globalFitInfo[SSE_IDX] / (nobs - rank); this.globalFitInfo[RSQ_IDX] = 1.0 - this.globalFitInfo[SSE_IDX] / this.globalFitInfo[SST_IDX]; if (!containsConstant) { this.globalFitInfo[ADJRSQ_IDX] = 1.0 - (1.0 - this.globalFitInfo[RSQ_IDX]) * ((double) nobs / ((double) (nobs - rank))); } else { this.globalFitInfo[ADJRSQ_IDX] = 1.0 - (sse * (nobs - 1.0)) / (globalFitInfo[SST_IDX] * (nobs - rank)); } } /** * <p>Returns the parameter estimate for the regressor at the given index.</p> * * <p>A redundant regressor will have its redundancy flag set, as well as * a parameters estimated equal to {@code Double.NaN}</p> * * @param index Index. * @return the parameters estimated for regressor at index. * @throws OutOfRangeException if {@code index} is not in the interval * {@code [0, number of parameters)}. */ public double getParameterEstimate(int index) throws OutOfRangeException { if (parameters == null) { return Double.NaN; } if (index < 0 || index >= this.parameters.length) { throw new OutOfRangeException(index, 0, this.parameters.length - 1); } return this.parameters[index]; } /** * <p>Returns a copy of the regression parameters estimates.</p> * * <p>The parameter estimates are returned in the natural order of the data.</p> * * <p>A redundant regressor will have its redundancy flag set, as will * a parameter estimate equal to {@code Double.NaN}.</p> * * @return array of parameter estimates, null if no estimation occurred */ public double[] getParameterEstimates() { if (this.parameters == null) { return null; } return MathArrays.copyOf(parameters); } /** * Returns the <a href="http://www.xycoon.com/standerrorb(1).htm">standard * error of the parameter estimate at index</a>, * usually denoted s(b<sub>index</sub>). * * @param index Index. * @return the standard errors associated with parameters estimated at index. * @throws OutOfRangeException if {@code index} is not in the interval * {@code [0, number of parameters)}. */ public double getStdErrorOfEstimate(int index) throws OutOfRangeException { if (parameters == null) { return Double.NaN; } if (index < 0 || index >= this.parameters.length) { throw new OutOfRangeException(index, 0, this.parameters.length - 1); } double var = this.getVcvElement(index, index); if (!Double.isNaN(var) && var > Double.MIN_VALUE) { return FastMath.sqrt(var); } return Double.NaN; } /** * <p>Returns the <a href="http://www.xycoon.com/standerrorb(1).htm">standard * error of the parameter estimates</a>, * usually denoted s(b<sub>i</sub>).</p> * * <p>If there are problems with an ill conditioned design matrix then the regressor * which is redundant will be assigned <code>Double.NaN</code>. </p> * * @return an array standard errors associated with parameters estimates, * null if no estimation occurred */ public double[] getStdErrorOfEstimates() { if (parameters == null) { return null; } double[] se = new double[this.parameters.length]; for (int i = 0; i < this.parameters.length; i++) { double var = this.getVcvElement(i, i); if (!Double.isNaN(var) && var > Double.MIN_VALUE) { se[i] = FastMath.sqrt(var); continue; } se[i] = Double.NaN; } return se; } /** * <p>Returns the covariance between regression parameters i and j.</p> * * <p>If there are problems with an ill conditioned design matrix then the covariance * which involves redundant columns will be assigned {@code Double.NaN}. </p> * * @param i {@code i}th regression parameter. * @param j {@code j}th regression parameter. * @return the covariance of the parameter estimates. * @throws OutOfRangeException if {@code i} or {@code j} is not in the * interval {@code [0, number of parameters)}. */ public double getCovarianceOfParameters(int i, int j) throws OutOfRangeException { if (parameters == null) { return Double.NaN; } if (i < 0 || i >= this.parameters.length) { throw new OutOfRangeException(i, 0, this.parameters.length - 1); } if (j < 0 || j >= this.parameters.length) { throw new OutOfRangeException(j, 0, this.parameters.length - 1); } return this.getVcvElement(i, j); } /** * <p>Returns the number of parameters estimated in the model.</p> * * <p>This is the maximum number of regressors, some techniques may drop * redundant parameters</p> * * @return number of regressors, -1 if not estimated */ public int getNumberOfParameters() { if (this.parameters == null) { return -1; } return this.parameters.length; } /** * Returns the number of observations added to the regression model. * * @return Number of observations, -1 if an error condition prevents estimation */ public long getN() { return this.nobs; } /** * <p>Returns the sum of squared deviations of the y values about their mean.</p> * * <p>This is defined as SSTO * <a href="http://www.xycoon.com/SumOfSquares.htm">here</a>.</p> * * <p>If {@code n < 2}, this returns {@code Double.NaN}.</p> * * @return sum of squared deviations of y values */ public double getTotalSumSquares() { return this.globalFitInfo[SST_IDX]; } /** * <p>Returns the sum of squared deviations of the predicted y values about * their mean (which equals the mean of y).</p> * * <p>This is usually abbreviated SSR or SSM. It is defined as SSM * <a href="http://www.xycoon.com/SumOfSquares.htm">here</a></p> * * <p><strong>Preconditions</strong>: <ul> * <li>At least two observations (with at least two different x values) * must have been added before invoking this method. If this method is * invoked before a model can be estimated, <code>Double.NaN</code> is * returned. * </li></ul></p> * * @return sum of squared deviations of predicted y values */ public double getRegressionSumSquares() { return this.globalFitInfo[SST_IDX] - this.globalFitInfo[SSE_IDX]; } /** * <p>Returns the <a href="http://www.xycoon.com/SumOfSquares.htm"> * sum of squared errors</a> (SSE) associated with the regression * model.</p> * * <p>The return value is constrained to be non-negative - i.e., if due to * rounding errors the computational formula returns a negative result, * 0 is returned.</p> * * <p><strong>Preconditions</strong>: <ul> * <li>numberOfParameters data pairs * must have been added before invoking this method. If this method is * invoked before a model can be estimated, <code>Double,NaN</code> is * returned. * </li></ul></p> * * @return sum of squared errors associated with the regression model */ public double getErrorSumSquares() { return this.globalFitInfo[SSE_IDX]; } /** * <p>Returns the sum of squared errors divided by the degrees of freedom, * usually abbreviated MSE.</p> * * <p>If there are fewer than <strong>numberOfParameters + 1</strong> data pairs in the model, * or if there is no variation in <code>x</code>, this returns * <code>Double.NaN</code>.</p> * * @return sum of squared deviations of y values */ public double getMeanSquareError() { return this.globalFitInfo[MSE_IDX]; } /** * <p>Returns the <a href="http://www.xycoon.com/coefficient1.htm"> * coefficient of multiple determination</a>, * usually denoted r-square.</p> * * <p><strong>Preconditions</strong>: <ul> * <li>At least numberOfParameters observations (with at least numberOfParameters different x values) * must have been added before invoking this method. If this method is * invoked before a model can be estimated, {@code Double,NaN} is * returned. * </li></ul></p> * * @return r-square, a double in the interval [0, 1] */ public double getRSquared() { return this.globalFitInfo[RSQ_IDX]; } /** * <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 sum of squared residuals}, * SSTO is the total sum of squares}, 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 - {@link #getRSquared()} ) * (n / (n - p)) </code> * </pre></p> * * @return adjusted R-Squared statistic */ public double getAdjustedRSquared() { return this.globalFitInfo[ADJRSQ_IDX]; } /** * Returns true if the regression model has been computed including an intercept. * In this case, the coefficient of the intercept is the first element of the * {@link #getParameterEstimates() parameter estimates}. * @return true if the model has an intercept term */ public boolean hasIntercept() { return this.containsConstant; } /** * Gets the i-jth element of the variance-covariance matrix. * * @param i first variable index * @param j second variable index * @return the requested variance-covariance matrix entry */ private double getVcvElement(int i, int j) { if (this.isSymmetricVCD) { if (this.varCovData.length > 1) { //could be stored in upper or lower triangular if (i == j) { return varCovData[i][i]; } else if (i >= varCovData[j].length) { return varCovData[i][j]; } else { return varCovData[j][i]; } } else {//could be in single array if (i > j) { return varCovData[0][(i + 1) * i / 2 + j]; } else { return varCovData[0][(j + 1) * j / 2 + i]; } } } else { return this.varCovData[i][j]; } } }