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diff --git a/src/main/java/org/apache/commons/math/stat/regression/SimpleRegression.java b/src/main/java/org/apache/commons/math/stat/regression/SimpleRegression.java new file mode 100644 index 0000000..d950541 --- /dev/null +++ b/src/main/java/org/apache/commons/math/stat/regression/SimpleRegression.java @@ -0,0 +1,639 @@ +/* + * 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 java.io.Serializable; + +import org.apache.commons.math.MathException; +import org.apache.commons.math.MathRuntimeException; +import org.apache.commons.math.distribution.TDistribution; +import org.apache.commons.math.distribution.TDistributionImpl; +import org.apache.commons.math.exception.util.LocalizedFormats; +import org.apache.commons.math.util.FastMath; + +/** + * Estimates an ordinary least squares regression model + * with one independent variable. + * <p> + * <code> y = intercept + slope * x </code></p> + * <p> + * Standard errors for <code>intercept</code> and <code>slope</code> are + * available as well as ANOVA, r-square and Pearson's r statistics.</p> + * <p> + * Observations (x,y pairs) can be added to the model one at a time or they + * can be provided in a 2-dimensional array. The observations are not stored + * in memory, so there is no limit to the number of observations that can be + * added to the model.</p> + * <p> + * <strong>Usage Notes</strong>: <ul> + * <li> When there are fewer than two observations in the model, or when + * there is no variation in the x values (i.e. all x values are the same) + * all statistics return <code>NaN</code>. At least two observations with + * different x coordinates are requred to estimate a bivariate regression + * model. + * </li> + * <li> getters for the statistics always compute values based on the current + * set of observations -- i.e., you can get statistics, then add more data + * and get updated statistics without using a new instance. There is no + * "compute" method that updates all statistics. Each of the getters performs + * the necessary computations to return the requested statistic.</li> + * </ul></p> + * + * @version $Revision: 1042336 $ $Date: 2010-12-05 13:40:48 +0100 (dim. 05 déc. 2010) $ + */ +public class SimpleRegression implements Serializable { + + /** Serializable version identifier */ + private static final long serialVersionUID = -3004689053607543335L; + + /** the distribution used to compute inference statistics. */ + private TDistribution distribution; + + /** sum of x values */ + private double sumX = 0d; + + /** total variation in x (sum of squared deviations from xbar) */ + private double sumXX = 0d; + + /** sum of y values */ + private double sumY = 0d; + + /** total variation in y (sum of squared deviations from ybar) */ + private double sumYY = 0d; + + /** sum of products */ + private double sumXY = 0d; + + /** number of observations */ + private long n = 0; + + /** mean of accumulated x values, used in updating formulas */ + private double xbar = 0; + + /** mean of accumulated y values, used in updating formulas */ + private double ybar = 0; + + // ---------------------Public methods-------------------------------------- + + /** + * Create an empty SimpleRegression instance + */ + public SimpleRegression() { + this(new TDistributionImpl(1.0)); + } + + /** + * Create an empty SimpleRegression using the given distribution object to + * compute inference statistics. + * @param t the distribution used to compute inference statistics. + * @since 1.2 + * @deprecated in 2.2 (to be removed in 3.0). Please use the {@link + * #SimpleRegression(int) other constructor} instead. + */ + @Deprecated + public SimpleRegression(TDistribution t) { + super(); + setDistribution(t); + } + + /** + * Create an empty SimpleRegression. + * + * @param degrees Number of degrees of freedom of the distribution + * used to compute inference statistics. + * @since 2.2 + */ + public SimpleRegression(int degrees) { + setDistribution(new TDistributionImpl(degrees)); + } + + /** + * Adds the observation (x,y) to the regression data set. + * <p> + * Uses updating formulas for means and sums of squares defined in + * "Algorithms for Computing the Sample Variance: Analysis and + * Recommendations", Chan, T.F., Golub, G.H., and LeVeque, R.J. + * 1983, American Statistician, vol. 37, pp. 242-247, referenced in + * Weisberg, S. "Applied Linear Regression". 2nd Ed. 1985.</p> + * + * + * @param x independent variable value + * @param y dependent variable value + */ + public void addData(double x, double y) { + if (n == 0) { + xbar = x; + ybar = y; + } else { + double dx = x - xbar; + double dy = y - ybar; + sumXX += dx * dx * (double) n / (n + 1d); + sumYY += dy * dy * (double) n / (n + 1d); + sumXY += dx * dy * (double) n / (n + 1d); + xbar += dx / (n + 1.0); + ybar += dy / (n + 1.0); + } + sumX += x; + sumY += y; + n++; + + if (n > 2) { + distribution.setDegreesOfFreedom(n - 2); + } + } + + + /** + * Removes the observation (x,y) from the regression data set. + * <p> + * Mirrors the addData method. This method permits the use of + * SimpleRegression instances in streaming mode where the regression + * is applied to a sliding "window" of observations, however the caller is + * responsible for maintaining the set of observations in the window.</p> + * + * The method has no effect if there are no points of data (i.e. n=0) + * + * @param x independent variable value + * @param y dependent variable value + */ + public void removeData(double x, double y) { + if (n > 0) { + double dx = x - xbar; + double dy = y - ybar; + sumXX -= dx * dx * (double) n / (n - 1d); + sumYY -= dy * dy * (double) n / (n - 1d); + sumXY -= dx * dy * (double) n / (n - 1d); + xbar -= dx / (n - 1.0); + ybar -= dy / (n - 1.0); + sumX -= x; + sumY -= y; + n--; + + if (n > 2) { + distribution.setDegreesOfFreedom(n - 2); + } + } + } + + /** + * Adds the observations represented by the elements in + * <code>data</code>. + * <p> + * <code>(data[0][0],data[0][1])</code> will be the first observation, then + * <code>(data[1][0],data[1][1])</code>, etc.</p> + * <p> + * This method does not replace data that has already been added. The + * observations represented by <code>data</code> are added to the existing + * dataset.</p> + * <p> + * To replace all data, use <code>clear()</code> before adding the new + * data.</p> + * + * @param data array of observations to be added + */ + public void addData(double[][] data) { + for (int i = 0; i < data.length; i++) { + addData(data[i][0], data[i][1]); + } + } + + + /** + * Removes observations represented by the elements in <code>data</code>. + * <p> + * If the array is larger than the current n, only the first n elements are + * processed. This method permits the use of SimpleRegression instances in + * streaming mode where the regression is applied to a sliding "window" of + * observations, however the caller is responsible for maintaining the set + * of observations in the window.</p> + * <p> + * To remove all data, use <code>clear()</code>.</p> + * + * @param data array of observations to be removed + */ + public void removeData(double[][] data) { + for (int i = 0; i < data.length && n > 0; i++) { + removeData(data[i][0], data[i][1]); + } + } + + /** + * Clears all data from the model. + */ + public void clear() { + sumX = 0d; + sumXX = 0d; + sumY = 0d; + sumYY = 0d; + sumXY = 0d; + n = 0; + } + + /** + * Returns the number of observations that have been added to the model. + * + * @return n number of observations that have been added. + */ + public long getN() { + return n; + } + + /** + * Returns the "predicted" <code>y</code> value associated with the + * supplied <code>x</code> value, based on the data that has been + * added to the model when this method is activated. + * <p> + * <code> predict(x) = intercept + slope * x </code></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> + * + * @param x input <code>x</code> value + * @return predicted <code>y</code> value + */ + public double predict(double x) { + double b1 = getSlope(); + return getIntercept(b1) + b1 * x; + } + + /** + * Returns the intercept of the estimated regression line. + * <p> + * The least squares estimate of the intercept is computed using the + * <a href="http://www.xycoon.com/estimation4.htm">normal equations</a>. + * The intercept is sometimes denoted b0.</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 the intercept of the regression line + */ + public double getIntercept() { + return getIntercept(getSlope()); + } + + /** + * Returns the slope of the estimated regression line. + * <p> + * The least squares estimate of the slope is computed using the + * <a href="http://www.xycoon.com/estimation4.htm">normal equations</a>. + * The slope is sometimes denoted b1.</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 the slope of the regression line + */ + public double getSlope() { + if (n < 2) { + return Double.NaN; //not enough data + } + if (FastMath.abs(sumXX) < 10 * Double.MIN_VALUE) { + return Double.NaN; //not enough variation in x + } + return sumXY / sumXX; + } + + /** + * Returns the <a href="http://www.xycoon.com/SumOfSquares.htm"> + * sum of squared errors</a> (SSE) associated with the regression + * model. + * <p> + * The sum is computed using the computational formula</p> + * <p> + * <code>SSE = SYY - (SXY * SXY / SXX)</code></p> + * <p> + * where <code>SYY</code> is the sum of the squared deviations of the y + * values about their mean, <code>SXX</code> is similarly defined and + * <code>SXY</code> is the sum of the products of x and y mean deviations. + * </p><p> + * The sums are accumulated using the updating algorithm referenced in + * {@link #addData}.</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>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 errors associated with the regression model + */ + public double getSumSquaredErrors() { + return FastMath.max(0d, sumYY - sumXY * sumXY / sumXX); + } + + /** + * Returns the sum of squared deviations of the y values about their mean. + * <p> + * This is defined as SSTO + * <a href="http://www.xycoon.com/SumOfSquares.htm">here</a>.</p> + * <p> + * If <code>n < 2</code>, this returns <code>Double.NaN</code>.</p> + * + * @return sum of squared deviations of y values + */ + public double getTotalSumSquares() { + if (n < 2) { + return Double.NaN; + } + return sumYY; + } + + /** + * Returns the sum of squared deviations of the x values about their mean. + * + * If <code>n < 2</code>, this returns <code>Double.NaN</code>.</p> + * + * @return sum of squared deviations of x values + */ + public double getXSumSquares() { + if (n < 2) { + return Double.NaN; + } + return sumXX; + } + + /** + * Returns the sum of crossproducts, x<sub>i</sub>*y<sub>i</sub>. + * + * @return sum of cross products + */ + public double getSumOfCrossProducts() { + return sumXY; + } + + /** + * Returns the sum of squared deviations of the predicted y values about + * their mean (which equals the mean of y). + * <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 getRegressionSumSquares(getSlope()); + } + + /** + * Returns the sum of squared errors divided by the degrees of freedom, + * usually abbreviated MSE. + * <p> + * If there are fewer than <strong>three</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() { + if (n < 3) { + return Double.NaN; + } + return getSumSquaredErrors() / (n - 2); + } + + /** + * Returns <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html"> + * Pearson's product moment correlation coefficient</a>, + * usually denoted r. + * <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 Pearson's r + */ + public double getR() { + double b1 = getSlope(); + double result = FastMath.sqrt(getRSquare()); + if (b1 < 0) { + result = -result; + } + return result; + } + + /** + * Returns the <a href="http://www.xycoon.com/coefficient1.htm"> + * coefficient of determination</a>, + * usually denoted r-square. + * <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 r-square + */ + public double getRSquare() { + double ssto = getTotalSumSquares(); + return (ssto - getSumSquaredErrors()) / ssto; + } + + /** + * Returns the <a href="http://www.xycoon.com/standarderrorb0.htm"> + * standard error of the intercept estimate</a>, + * usually denoted s(b0). + * <p> + * If there are fewer that <strong>three</strong> observations in the + * model, or if there is no variation in x, this returns + * <code>Double.NaN</code>.</p> + * + * @return standard error associated with intercept estimate + */ + public double getInterceptStdErr() { + return FastMath.sqrt( + getMeanSquareError() * ((1d / (double) n) + (xbar * xbar) / sumXX)); + } + + /** + * Returns the <a href="http://www.xycoon.com/standerrorb(1).htm">standard + * error of the slope estimate</a>, + * usually denoted s(b1). + * <p> + * If there are fewer that <strong>three</strong> data pairs in the model, + * or if there is no variation in x, this returns <code>Double.NaN</code>. + * </p> + * + * @return standard error associated with slope estimate + */ + public double getSlopeStdErr() { + return FastMath.sqrt(getMeanSquareError() / sumXX); + } + + /** + * Returns the half-width of a 95% confidence interval for the slope + * estimate. + * <p> + * The 95% confidence interval is</p> + * <p> + * <code>(getSlope() - getSlopeConfidenceInterval(), + * getSlope() + getSlopeConfidenceInterval())</code></p> + * <p> + * If there are fewer that <strong>three</strong> observations in the + * model, or if there is no variation in x, this returns + * <code>Double.NaN</code>.</p> + * <p> + * <strong>Usage Note</strong>:<br> + * The validity of this statistic depends on the assumption that the + * observations included in the model are drawn from a + * <a href="http://mathworld.wolfram.com/BivariateNormalDistribution.html"> + * Bivariate Normal Distribution</a>.</p> + * + * @return half-width of 95% confidence interval for the slope estimate + * @throws MathException if the confidence interval can not be computed. + */ + public double getSlopeConfidenceInterval() throws MathException { + return getSlopeConfidenceInterval(0.05d); + } + + /** + * Returns the half-width of a (100-100*alpha)% confidence interval for + * the slope estimate. + * <p> + * The (100-100*alpha)% confidence interval is </p> + * <p> + * <code>(getSlope() - getSlopeConfidenceInterval(), + * getSlope() + getSlopeConfidenceInterval())</code></p> + * <p> + * To request, for example, a 99% confidence interval, use + * <code>alpha = .01</code></p> + * <p> + * <strong>Usage Note</strong>:<br> + * The validity of this statistic depends on the assumption that the + * observations included in the model are drawn from a + * <a href="http://mathworld.wolfram.com/BivariateNormalDistribution.html"> + * Bivariate Normal Distribution</a>.</p> + * <p> + * <strong> Preconditions:</strong><ul> + * <li>If there are fewer that <strong>three</strong> observations in the + * model, or if there is no variation in x, this returns + * <code>Double.NaN</code>. + * </li> + * <li><code>(0 < alpha < 1)</code>; otherwise an + * <code>IllegalArgumentException</code> is thrown. + * </li></ul></p> + * + * @param alpha the desired significance level + * @return half-width of 95% confidence interval for the slope estimate + * @throws MathException if the confidence interval can not be computed. + */ + public double getSlopeConfidenceInterval(double alpha) + throws MathException { + if (alpha >= 1 || alpha <= 0) { + throw MathRuntimeException.createIllegalArgumentException( + LocalizedFormats.OUT_OF_BOUND_SIGNIFICANCE_LEVEL, + alpha, 0.0, 1.0); + } + return getSlopeStdErr() * + distribution.inverseCumulativeProbability(1d - alpha / 2d); + } + + /** + * Returns the significance level of the slope (equiv) correlation. + * <p> + * Specifically, the returned value is the smallest <code>alpha</code> + * such that the slope confidence interval with significance level + * equal to <code>alpha</code> does not include <code>0</code>. + * On regression output, this is often denoted <code>Prob(|t| > 0)</code> + * </p><p> + * <strong>Usage Note</strong>:<br> + * The validity of this statistic depends on the assumption that the + * observations included in the model are drawn from a + * <a href="http://mathworld.wolfram.com/BivariateNormalDistribution.html"> + * Bivariate Normal Distribution</a>.</p> + * <p> + * If there are fewer that <strong>three</strong> observations in the + * model, or if there is no variation in x, this returns + * <code>Double.NaN</code>.</p> + * + * @return significance level for slope/correlation + * @throws MathException if the significance level can not be computed. + */ + public double getSignificance() throws MathException { + return 2d * (1.0 - distribution.cumulativeProbability( + FastMath.abs(getSlope()) / getSlopeStdErr())); + } + + // ---------------------Private methods----------------------------------- + + /** + * Returns the intercept of the estimated regression line, given the slope. + * <p> + * Will return <code>NaN</code> if slope is <code>NaN</code>.</p> + * + * @param slope current slope + * @return the intercept of the regression line + */ + private double getIntercept(double slope) { + return (sumY - slope * sumX) / n; + } + + /** + * Computes SSR from b1. + * + * @param slope regression slope estimate + * @return sum of squared deviations of predicted y values + */ + private double getRegressionSumSquares(double slope) { + return slope * slope * sumXX; + } + + /** + * Modify the distribution used to compute inference statistics. + * @param value the new distribution + * @since 1.2 + * @deprecated in 2.2 (to be removed in 3.0). + */ + @Deprecated + public void setDistribution(TDistribution value) { + distribution = value; + + // modify degrees of freedom + if (n > 2) { + distribution.setDegreesOfFreedom(n - 2); + } + } +} |