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From tobr...@apache.org
Subject cvs commit: jakarta-commons-sandbox/math/src/test/org/apache/commons/math BivariateRegressionTest.java
Date Mon, 26 May 2003 02:11:50 GMT
tobrien     2003/05/25 19:11:50

  Added:       math/src/java/org/apache/commons/math
                        BivariateRegression.java
               math/src/test/org/apache/commons/math
                        BivariateRegressionTest.java
  Log:
  An implementation of ordinary least squares regression with one independent
  variable. The implementation uses running sums and does not require the data
  to be stored in memory.  Since I could not conceive of any significantly
  different implementation strategies that did not amount to just improving
  efficiency or numerical accuracy of what I am submitting, I did not abstract
  the interface.
  
  The test cases validate the computations against NIST reference data and
  verified computations. The slope, intercept, their standard errors and
  r-square estimates are accurate to within 10E-12 against the reference data
  set.  MSE and other ANOVA stats are good at least to within 10E-8. -- Phil S.
  
  PR: Issue #20224
  Obtained from: Bugzilla
  Submitted by: Phil Steitz
  Reviewed by: Tim O'Brien
  
  Revision  Changes    Path
  1.1                  jakarta-commons-sandbox/math/src/java/org/apache/commons/math/BivariateRegression.java
  
  Index: BivariateRegression.java
  ===================================================================
  /* ====================================================================
   * The Apache Software License, Version 1.1
   *
   * Copyright (c) 2003 The Apache Software Foundation.  All rights
   * reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   *
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   *
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in
   *    the documentation and/or other materials provided with the
   *    distribution.
   *
   * 3. The end-user documentation included with the redistribution, if
   *    any, must include the following acknowlegement:
   *       "This product includes software developed by the
   *        Apache Software Foundation (http://www.apache.org/)."
   *    Alternately, this acknowlegement may appear in the software itself,
   *    if and wherever such third-party acknowlegements normally appear.
   *
   * 4. The names "The Jakarta Project", "Commons", and "Apache Software
   *    Foundation" must not be used to endorse or promote products derived
   *    from this software without prior written permission. For written
   *    permission, please contact apache@apache.org.
   *
   * 5. Products derived from this software may not be called "Apache"
   *    nor may "Apache" appear in their names without prior written
   *    permission of the Apache Software Foundation.
   *
   * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
   * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
   * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   * DISCLAIMED.  IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
   * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
   * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
   * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
   * USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
   * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
   * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
   * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   * SUCH DAMAGE.
   * ====================================================================
   *
   * This software consists of voluntary contributions made by many
   * individuals on behalf of the Apache Software Foundation.  For more
   * information on the Apache Software Foundation, please see
   * <http://www.apache.org/>.
   *
   */
  
  package org.apache.commons.math;
  
  /**
   * Estimates an ordinary least squares regression model
   * with one independent variable: <p>
   *
   * y = intercept + slope * x  </code><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>
   *
   * 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>
   *
   * <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>
   *
   * @author  Phil Steitz
   * @version $Revision: 1.1 $ $Date: 2003/05/26 02:11:50 $
   */
  public class BivariateRegression {
      
      /** sum of x values */
      private double sumX = 0d;
      
      /** sum of squared x values */
      private double sumSqX = 0d;
      
      /** sum of y values */
      private double sumY = 0d;
      
      /** sum of squared y values */
      private double sumSqY = 0d;
      
      /** sum of products */
      private double sumXY = 0d;
      
      /** number of observations */
      private long n = 0;
      
      // ---------------------Public methods--------------------------------------
      
      /**
       * Adds the observation (x,y) to the regression data set
       *
       * @param x independent variable value
       * @param y dependent variable value
       */
      public void addData(double x, double y) {
          sumX += x;
          sumSqX += x*x;
          sumY += y;
          sumSqY += y*y;
          sumXY += x*y;
          n++;
      } 
      
      /**
       * 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> 
       * 
       * This method does not replace data that has already been added.  
       * To replace all data, use <code>clear()</code> before adding the new data.
       * 
       * @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]);
         }
      }
      
      /*
       * Clears all data from the model
       */
      public void clear() {
          sumX = 0d;
          sumSqX = 0d;
          sumY = 0d;
          sumSqY = 0d;
          sumXY = 0d;
          n = 0;
      }
            
      /**
       * Returns the number of observations that have been added to the model
       *
       * @return n
       */
      public long getN() {
          return n;
      }
      
      /**
       * Returns the "predicted" <code>y</code> value associated with the 
       * supplied <code>x</code> value. Specifically, <p>
       *
       * <code> predict(x) = intercept + slope * x </code> <p>
       *
       * 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.
       *
       * @param x input <code>x</code> value
       * @return predicted <code>y</code> value
       */
      public double predict(double x) {
          double b1 = getSlope();
          if (b1 == Double.NaN) {
              return b1;
          }
          return getIntercept(b1) + b1*x;
      }
      
      /**
       * Returns the intercept of the estimated regression line.
       * The least squares estimate of the intercept is computed using the normal
       * equations, as described 
       * <a href=http://www.xycoon.com/estimation4.htm>here</a>.
       * The intercept is sometimes denoted b0. <p>
       *
       * At least two distinct data pairs (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.
       *
       * @return the intercept of the regression line
       */
       public double getIntercept() {
           return getIntercept(getSlope());
       }
       
       /**
       * Returns the slope of the estimated regression line.  
       * The least squares estimate of the slope is computed using the normal
       * equations, as described 
       * <a href=http://www.xycoon.com/estimation4.htm>here</a>.
       * The slope is sometimes denoted b1. <p>
       *
       * 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.
       *
       * @return the slope of the regression line
       */
       public double getSlope() {
           if (n < 2) {
               return Double.NaN;  //not enough data 
           }
           double dn = (double) n;
           double denom = sumSqX - (sumX*sumX/dn);
           if (Math.abs(denom)< 10*Double.MIN_VALUE) { 
               return Double.NaN; //not enough variation in x
           }
           return (sumXY - (sumX*sumY/dn))/denom;
       }
       
       /**
        * Returns the sum of squared errors</a> associated with the regression 
        * model. This is defined as SSE 
        * <a href=http://www.xycoon.com/SumOfSquares.htm>here</a>. <p>
        *
        * At least two distinct data pairs (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.
        *
        * @return sum of squared errors associated with the regression model
        */
       public double getSumSquaredErrors() {
           return getSumSquaredErrors(getSlope());
       }
       
       /**
        * Returns the sum of squared deviations of the y values about their mean.
        * This is defined as SSTO 
        * <a href=http://www.xycoon.com/SumOfSquares.htm>here</a>.
        * <p>
        * If n < 2, this returns NaN.
        *
        * @return sum of squared deviations of y values
        */
       public double getTotalSumSquares() {
           if (n < 2) {
               return Double.NaN;
           }
           return sumSqY - sumY*sumY/(double) n;
       }
           
       /**
        * Returns the sum of squared deviations of the predicted y values about 
        * their mean (which equals the mean of y).
        * This is usually abbreviated SSR or SSM.  It is defined as SSM 
        * <a href=http://www.xycoon.com/SumOfSquares.htm>here</a><p>
        *
        * At least two distinct data pairs (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.
        *
        * @return sum of squared deviations of y values
        */
       public double getRegressionSumSquares() {
           double b1 = getSlope();
           if (b1 == Double.NaN) {
               return b1;
           }
           return b1*(sumXY - sumX*sumY/(double) n);
       }
       
       /**
        * Returns the sum of squared errors divided by the degrees of freedom.
        * This is usually abbreviated MSE. <p>
        *
        * If there are fewer than <strong>three</strong> data pairs in the model,
        * or if there is no variation in x, this returns <code>NaN</code>.
        *
        * @return sum of squared deviations of y values
        */
       public double getMeanSquareError() {
           if (n < 3) {
               return Double.NaN;
           }
           double sse = getSumSquaredErrors();
           if (sse == Double.NaN) {
               return sse;
           }
           return sse/(double) (n - 2);
       }
       
       /**
        * Returns <a href=http://www.stt.msu.edu/~xiaoyimi/STT200/Lecture5.pdf>
        * Pearson's product moment correlation coefficient</a>.
        * This is usually denoted r. <p>
        *
        * 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.
        *
        * @return Pearson's r
        */
       public double getR() {
           double b1 = getSlope();
           if (b1 == Double.NaN) {
               return b1;
           }
           double result = Math.sqrt(getRSquare(b1));
           if (b1 < 0) {
               result = -result;
           }
           return result;
       }
               
       /** 
        * Returns the <a href=http://www.xycoon.com/coefficient1.htm> coefficient
        * of determination</a>.
        * This is usually denoted r-square. <p>
        *
        * At least two observaions (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.
        *
        * @return r-square
        */
       public double getRSquare() {
           return getRSquare(getSlope());
       }
       
           
       /**
        * Returns the <a href=http://www.xycoon.com/standarderrorb0.htm>standard
        * error of the intercept estimate</a>.
        * This is 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>NaN</code>.
        *
        * @return standard error associated with intercept estimate
        */
       public double getInterceptStdErr() {
           double ssx = getSumSquaresX();
           if (ssx == Double.NaN) {
               return ssx;
           }
           return Math.sqrt(getMeanSquareError()*sumSqX/(((double) n)*ssx));
       }
               
       /**
        * Returns the <a http://www.xycoon.com/standerrorb(1).htm>standard
        * error of the slope estimate</a>.
        * This is 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>NaN</code>.
        *
        * @return standard error associated with slope estimate
        */
       public double getSlopeStdErr() {
           double ssx = getSumSquaresX();
           if (ssx == Double.NaN) {
               return ssx;
           }
           return Math.sqrt(getMeanSquareError()/ssx);
       }
       
       // ---------------------Private methods-----------------------------------
       
       /**
       * Returns the intercept of the estimated regression line, given the slope.
       * Will return <code>NaN</code> if slope is <code>NaN</code>.
       *
       * @param slope current slope
       * @return the intercept of the regression line
       */
       private double getIntercept(double slope) {
           if (slope == Double.NaN) {
               return slope;
           }
           return (sumY - slope*sumX)/((double) n);
       }
         
       /**
        * Returns the sum of squared errors</a> associated with the regression 
        * model, using the slope of the regression line.  Returns NaN if the slope
        * is NaN.
        *
        * @return sum of squared errors associated with the regression model
        */
       private double getSumSquaredErrors(double b1) {
           if (b1 == Double.NaN) {
               return b1;
           }
           double b0 = getIntercept(b1);
           return sumSqY - b0*sumY - b1*sumXY;
       } 
       
       /**
        * Returns the sum of squared deviations of the x values about their mean.
        * <p>
        * If n < 2, this returns NaN.
        *
        * @return sum of squared deviations of x values
        */
       private double getSumSquaresX() {
           if (n < 2) {
               return Double.NaN;
           }
           return sumSqX - sumX*sumX/(double) n;
       }
       
       /** 
        * Computes r-square from the slope.
        * will return NaN if slope is Nan
        *
        * @return r-square
        */
       private double getRSquare(double b1) {
           if (b1 == Double.NaN) {
               return b1;
           }
           double ssto = getTotalSumSquares();
           if (ssto == Double.NaN) {
               return ssto;
           }
           return (ssto - getSumSquaredErrors(b1))/ssto;
       }
  }
  
  
  
  
  1.1                  jakarta-commons-sandbox/math/src/test/org/apache/commons/math/BivariateRegressionTest.java
  
  Index: BivariateRegressionTest.java
  ===================================================================
  /* ====================================================================
   * The Apache Software License, Version 1.1
   *
   * Copyright (c) 2003 The Apache Software Foundation.  All rights
   * reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   *
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   *
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in
   *    the documentation and/or other materials provided with the
   *    distribution.
   *
   * 3. The end-user documentation included with the redistribution, if
   *    any, must include the following acknowlegement:
   *       "This product includes software developed by the
   *        Apache Software Foundation (http://www.apache.org/)."
   *    Alternately, this acknowlegement may appear in the software itself,
   *    if and wherever such third-party acknowlegements normally appear.
   *
   * 4. The names "The Jakarta Project", "Commons", and "Apache Software
   *    Foundation" must not be used to endorse or promote products derived
   *    from this software without prior written permission. For written
   *    permission, please contact apache@apache.org.
   *
   * 5. Products derived from this software may not be called "Apache"
   *    nor may "Apache" appear in their names without prior written
   *    permission of the Apache Software Foundation.
   *
   * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
   * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
   * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   * DISCLAIMED.  IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
   * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
   * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
   * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
   * USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
   * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
   * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
   * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   * SUCH DAMAGE.
   * ====================================================================
   *
   * This software consists of voluntary contributions made by many
   * individuals on behalf of the Apache Software Foundation.  For more
   * information on the Apache Software Foundation, please see
   * <http://www.apache.org/>.
   */
  package org.apache.commons.math;
  
  import junit.framework.Test;
  import junit.framework.TestCase;
  import junit.framework.TestSuite;
  /**
   * Test cases for the TestStatistic class.
   *
   * @author Phil Steitz
   * @version $Revision: 1.1 $ $Date: 2003/05/26 02:11:50 $
   */
  
  public final class BivariateRegressionTest extends TestCase {
  
      /* 
       * NIST "Norris" refernce data set from 
       * http://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA/Norris.dat
       * Strangely, order is {y,x}
       */
      private double[][] data = {{0.1,0.2},{338.8,337.4},{118.1,118.2},
          {888.0,884.6},{9.2,10.1},{228.1,226.5},{668.5,666.3},{998.5,996.3},
          {449.1,448.6},{778.9,777.0},{559.2,558.2},{0.3,0.4},{0.1,0.6},
          {778.1,775.5},{668.8,666.9},{339.3,338.0},{448.9,447.5},{10.8,11.6},
          {557.7,556.0},{228.3,228.1},{998.0,995.8},{888.8,887.6},{119.6,120.2},
          {0.3,0.3},{0.6,0.3},{557.6,556.8},{339.3,339.1},{888.0,887.2},
          {998.5,999.0},{778.9,779.0},{10.2,11.1},{117.6,118.3},{228.9,229.2},
          {668.4,669.1},{449.2,448.9},{0.2,0.5}}; 
          
      /* 
       * Correlation example from 
       * http://www.xycoon.com/correlation.htm
       */
      private double[][] corrData = {{101.0,99.2},{100.1,99.0},{100.0,100.0},
          {90.6,111.6},{86.5,122.2},{89.7,117.6},{90.6,121.1},{82.8,136.0},
          {70.1,154.2},{65.4,153.6},{61.3,158.5},{62.5,140.6},{63.6,136.2},
          {52.6,168.0},{59.7,154.3},{59.5,149.0},{61.3,165.5}};
      
      public BivariateRegressionTest(String name) {
          super(name);
      }
      
      public void setUp() { 
      }
  
      public static Test suite() {
          TestSuite suite = new TestSuite(BivariateRegressionTest.class);
          suite.setName("BivariateRegression Tests");
          return suite;
      }
      
      public void testNorris() {
         BivariateRegression regression = new BivariateRegression();
         for (int i = 0; i < data.length; i++) {
             regression.addData(data[i][1],data[i][0]);
         }
         assertEquals("slope",1.00211681802045, 
              regression.getSlope(),10E-12);
         assertEquals("slope std err",0.429796848199937E-03, 
              regression.getSlopeStdErr(),10E-12);
         assertEquals("number of observations",36,regression.getN());
         assertEquals("intercept", -0.262323073774029,
              regression.getIntercept(),10E-12);
         assertEquals("std err intercept", 0.232818234301152, 
              regression.getInterceptStdErr(),10E-12);
         assertEquals("r-square",0.999993745883712,
              regression.getRSquare(),10E-12);
         assertEquals("SSR",4255954.13232369, 
              regression.getRegressionSumSquares(),10E-8);
         assertEquals("MSE",0.782864662630069, 
              regression.getMeanSquareError(),10E-8);
         assertEquals("SSE",26.6173985294224, 
              regression.getSumSquaredErrors(),10E-8);
         assertEquals("predict(0)",-0.262323073774029,
              regression.predict(0),10E-12);
         assertEquals("predict(1)",1.00211681802045-0.262323073774029,
              regression.predict(1),10E-11);
      }
      
      public void testCorr() {
         BivariateRegression regression = new BivariateRegression();
         regression.addData(corrData);
         assertEquals("number of observations",17,regression.getN());
         assertEquals("r-square",.896123,
              regression.getRSquare(),10E-6);
         assertEquals("r",-.946638, 
              regression.getR(),10E-6);
      }  
      
      public void testNaNs() {
          
          BivariateRegression regression = new BivariateRegression();
          
          assertTrue("intercept not NaN",Double.isNaN(regression.getIntercept()));
          assertTrue("slope not NaN",Double.isNaN(regression.getSlope()));
          assertTrue("slope std err not NaN",
              Double.isNaN(regression.getSlopeStdErr()));
          assertTrue("intercept std err not NaN",
              Double.isNaN(regression.getInterceptStdErr()));
          assertTrue("MSE not NaN",Double.isNaN(regression.getMeanSquareError()));
          assertTrue("e not NaN",Double.isNaN(regression.getR()));
          assertTrue("r-square not NaN",Double.isNaN(regression.getRSquare()));
          assertTrue("RSS not NaN",
              Double.isNaN(regression.getRegressionSumSquares()));
          assertTrue("SSE not NaN",Double.isNaN(regression.getSumSquaredErrors()));
          assertTrue("SSTO not NaN",Double.isNaN(regression.getTotalSumSquares()));
          assertTrue("predict not NaN",Double.isNaN(regression.predict(0)));
          
          regression.addData(1,2);
          regression.addData(1,3);
          
          // No x variation, so these should still blow...
          assertTrue("intercept not NaN",Double.isNaN(regression.getIntercept()));
          assertTrue("slope not NaN",Double.isNaN(regression.getSlope()));
          assertTrue("slope std err not NaN",
              Double.isNaN(regression.getSlopeStdErr()));
          assertTrue("intercept std err not NaN",
              Double.isNaN(regression.getInterceptStdErr()));
          assertTrue("MSE not NaN",Double.isNaN(regression.getMeanSquareError()));
          assertTrue("e not NaN",Double.isNaN(regression.getR()));
          assertTrue("r-square not NaN",Double.isNaN(regression.getRSquare()));
          assertTrue("RSS not NaN",
              Double.isNaN(regression.getRegressionSumSquares()));
          assertTrue("SSE not NaN",Double.isNaN(regression.getSumSquaredErrors()));
          assertTrue("predict not NaN",Double.isNaN(regression.predict(0)));
          
          // but SSTO should be OK
           assertTrue("SSTO NaN",!Double.isNaN(regression.getTotalSumSquares()));
          
          regression = new BivariateRegression();
          
          regression.addData(1,2);
          regression.addData(3,3);
          
          // All should be OK except MSE, s(b0), s(b1) which need one more df 
          assertTrue("interceptNaN",!Double.isNaN(regression.getIntercept()));
          assertTrue("slope NaN",!Double.isNaN(regression.getSlope()));
          assertTrue("slope std err not NaN",
              Double.isNaN(regression.getSlopeStdErr()));
          assertTrue("intercept std err not NaN",
              Double.isNaN(regression.getInterceptStdErr()));
          assertTrue("MSE not NaN",Double.isNaN(regression.getMeanSquareError()));
          assertTrue("r NaN",!Double.isNaN(regression.getR()));
          assertTrue("r-square NaN",!Double.isNaN(regression.getRSquare()));
          assertTrue("RSS NaN",
              !Double.isNaN(regression.getRegressionSumSquares()));
          assertTrue("SSE NaN",!Double.isNaN(regression.getSumSquaredErrors()));
          assertTrue("SSTO NaN",!Double.isNaN(regression.getTotalSumSquares()));
          assertTrue("predict NaN",!Double.isNaN(regression.predict(0)));
          
          regression.addData(1,4);
          
          // MSE, MSE, s(b0), s(b1) should all be OK now
          assertTrue("MSE NaN",!Double.isNaN(regression.getMeanSquareError()));
          assertTrue("slope std err NaN",
              !Double.isNaN(regression.getSlopeStdErr()));
          assertTrue("intercept std err NaN",
              !Double.isNaN(regression.getInterceptStdErr()));
      }
      
      public void testClear() {
         BivariateRegression regression = new BivariateRegression();
         regression.addData(corrData);
         assertEquals("number of observations",17,regression.getN());
         regression.clear();
         assertEquals("number of observations",0,regression.getN());
         regression.addData(corrData);
         assertEquals("r-square",.896123,regression.getRSquare(),10E-6);
         regression.addData(data);
         assertEquals("number of observations",53,regression.getN());
      }
                      
  }
  
  
  
  

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