/*
    * 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.math4.legacy.stat.regression;
  
  import java.util.Random;
  
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.apache.commons.math4.legacy.exception.OutOfRangeException;
  import org.apache.commons.rng.UniformRandomProvider;
  import org.apache.commons.rng.simple.RandomSource;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  
  /**
   * Test cases for the TestStatistic class.
   *
   */
  
  public final class SimpleRegressionTest {
  
      /*
       * NIST "Norris" reference 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 }
      };
  
      /*
       * From Moore and Mcabe, "Introduction to the Practice of Statistics"
       * Example 10.3
       */
      private double[][] infData = { { 15.6, 5.2 }, {26.8, 6.1 }, {37.8, 8.7 }, {36.4, 8.5 },
              {35.5, 8.8 }, {18.6, 4.9 }, {15.3, 4.5 }, {7.9, 2.5 }, {0.0, 1.1 }
      };
  
      /*
       * Points to remove in the remove tests
       */
      private double[][] removeSingle = {infData[1]};
      private double[][] removeMultiple = { infData[1], infData[2] };
      private double removeX = infData[0][0];
      private double removeY = infData[0][1];
  
  
      /*
       * Data with bad linear fit
       */
      private double[][] infData2 = { { 1, 1 }, {2, 0 }, {3, 5 }, {4, 2 },
              {5, -1 }, {6, 12 }
      };
  
  
      /*
       * Data from NIST NOINT1
       */
      private double[][] noint1 = {
          {130.0,60.0},
          {131.0,61.0},
          {132.0,62.0},
          {133.0,63.0},
          {134.0,64.0},
          {135.0,65.0},
          {136.0,66.0},
          {137.0,67.0},
          {138.0,68.0},
         {139.0,69.0},
         {140.0,70.0}
     };
 
     /*
      * Data from NIST NOINT2
      *
      */
     private double[][] noint2 = {
         {3.0,4},
         {4,5},
         {4,6}
     };
 
 
     /**
      * Test that the SimpleRegression objects generated from combining two
      * SimpleRegression objects created from subsets of data are identical to
      * SimpleRegression objects created from the combined data.
      */
     @Test
     public void testAppend() {
         check(false);
         check(true);
     }
 
     /**
      * Checks that adding data to a single model gives the same result
      * as adding "parts" of the dataset to smaller models and using append
      * to aggregate the smaller models.
      *
      * @param includeIntercept
      */
     private void check(boolean includeIntercept) {
         final int sets = 2;
         final UniformRandomProvider rand = RandomSource.ISAAC.create(10L);// Seed can be changed
         final SimpleRegression whole = new SimpleRegression(includeIntercept);// regression of the whole set
         final SimpleRegression parts = new SimpleRegression(includeIntercept);// regression with parts.
 
         for (int s = 0; s < sets; s++) {// loop through each subset of data.
             final double coef = rand.nextDouble();
             final SimpleRegression sub = new SimpleRegression(includeIntercept);// sub regression
             for (int i = 0; i < 5; i++) { // loop through individual samlpes.
                 final double x = rand.nextDouble();
                 final double y = x * coef + rand.nextDouble();// some noise
                 sub.addData(x, y);
                 whole.addData(x, y);
             }
             parts.append(sub);
             Assert.assertTrue(equals(parts, whole, 1E-6));
         }
     }
 
     /**
      * Returns true iff the statistics reported by model1 are all within tol of
      * those reported by model2.
      *
      * @param model1 first model
      * @param model2 second model
      * @param tol tolerance
      * @return true if the two models report the same regression stats
      */
     private boolean equals(SimpleRegression model1, SimpleRegression model2, double tol) {
         if (model1.getN() != model2.getN()) {
             return false;
         }
         if (JdkMath.abs(model1.getIntercept() - model2.getIntercept()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getInterceptStdErr() - model2.getInterceptStdErr()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getMeanSquareError() - model2.getMeanSquareError()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getR() - model2.getR()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getRegressionSumSquares() - model2.getRegressionSumSquares()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getRSquare() - model2.getRSquare()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getSignificance() - model2.getSignificance()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getSlope() - model2.getSlope()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getSlopeConfidenceInterval() - model2.getSlopeConfidenceInterval()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getSlopeStdErr() - model2.getSlopeStdErr()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getSumOfCrossProducts() - model2.getSumOfCrossProducts()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getSumSquaredErrors() - model2.getSumSquaredErrors()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getTotalSumSquares() - model2.getTotalSumSquares()) > tol) {
             return false;
         }
         if (JdkMath.abs(model1.getXSumSquares() - model2.getXSumSquares()) > tol) {
             return false;
         }
         return true;
     }
 
     @Test
     public void testRegressIfaceMethod(){
         final SimpleRegression regression = new SimpleRegression(true);
         final UpdatingMultipleLinearRegression iface = regression;
         final SimpleRegression regressionNoint = new SimpleRegression( false );
         final SimpleRegression regressionIntOnly= new SimpleRegression( false );
         for (int i = 0; i < data.length; i++) {
             iface.addObservation( new double[]{data[i][1]}, data[i][0]);
             regressionNoint.addData(data[i][1], data[i][0]);
             regressionIntOnly.addData(1.0, data[i][0]);
         }
 
         //should not be null
         final RegressionResults fullReg = iface.regress( );
         Assert.assertNotNull(fullReg);
         Assert.assertEquals("intercept", regression.getIntercept(), fullReg.getParameterEstimate(0), 1.0e-16);
         Assert.assertEquals("intercept std err",regression.getInterceptStdErr(), fullReg.getStdErrorOfEstimate(0),1.0E-16);
         Assert.assertEquals("slope", regression.getSlope(), fullReg.getParameterEstimate(1), 1.0e-16);
         Assert.assertEquals("slope std err",regression.getSlopeStdErr(), fullReg.getStdErrorOfEstimate(1),1.0E-16);
         Assert.assertEquals("number of observations",regression.getN(), fullReg.getN());
         Assert.assertEquals("r-square",regression.getRSquare(), fullReg.getRSquared(), 1.0E-16);
         Assert.assertEquals("SSR", regression.getRegressionSumSquares(), fullReg.getRegressionSumSquares() ,1.0E-16);
         Assert.assertEquals("MSE", regression.getMeanSquareError(), fullReg.getMeanSquareError() ,1.0E-16);
         Assert.assertEquals("SSE", regression.getSumSquaredErrors(), fullReg.getErrorSumSquares() ,1.0E-16);
 
 
         final RegressionResults noInt   = iface.regress( new int[]{1} );
         Assert.assertNotNull(noInt);
         Assert.assertEquals("slope", regressionNoint.getSlope(), noInt.getParameterEstimate(0), 1.0e-12);
         Assert.assertEquals("slope std err",regressionNoint.getSlopeStdErr(), noInt.getStdErrorOfEstimate(0),1.0E-16);
         Assert.assertEquals("number of observations",regressionNoint.getN(), noInt.getN());
         Assert.assertEquals("r-square",regressionNoint.getRSquare(), noInt.getRSquared(), 1.0E-16);
         Assert.assertEquals("SSR", regressionNoint.getRegressionSumSquares(), noInt.getRegressionSumSquares() ,1.0E-8);
         Assert.assertEquals("MSE", regressionNoint.getMeanSquareError(), noInt.getMeanSquareError() ,1.0E-16);
         Assert.assertEquals("SSE", regressionNoint.getSumSquaredErrors(), noInt.getErrorSumSquares() ,1.0E-16);
 
         final RegressionResults onlyInt = iface.regress( new int[]{0} );
         Assert.assertNotNull(onlyInt);
         Assert.assertEquals("slope", regressionIntOnly.getSlope(), onlyInt.getParameterEstimate(0), 1.0e-12);
         Assert.assertEquals("slope std err",regressionIntOnly.getSlopeStdErr(), onlyInt.getStdErrorOfEstimate(0),1.0E-12);
         Assert.assertEquals("number of observations",regressionIntOnly.getN(), onlyInt.getN());
         Assert.assertEquals("r-square",regressionIntOnly.getRSquare(), onlyInt.getRSquared(), 1.0E-14);
         Assert.assertEquals("SSE", regressionIntOnly.getSumSquaredErrors(), onlyInt.getErrorSumSquares() ,1.0E-8);
         Assert.assertEquals("SSR", regressionIntOnly.getRegressionSumSquares(), onlyInt.getRegressionSumSquares() ,1.0E-8);
         Assert.assertEquals("MSE", regressionIntOnly.getMeanSquareError(), onlyInt.getMeanSquareError() ,1.0E-8);
     }
 
     /**
      * Verify that regress generates exceptions as advertised for bad model specifications.
      */
     @Test
     public void testRegressExceptions() {
         // No intercept
         final SimpleRegression noIntRegression = new SimpleRegression(false);
         noIntRegression.addData(noint2[0][1], noint2[0][0]);
         noIntRegression.addData(noint2[1][1], noint2[1][0]);
         noIntRegression.addData(noint2[2][1], noint2[2][0]);
         try { // null array
             noIntRegression.regress(null);
             Assert.fail("Expecting MathIllegalArgumentException for null array");
         } catch (MathIllegalArgumentException ex) {
             // Expected
         }
         try { // empty array
             noIntRegression.regress(new int[] {});
             Assert.fail("Expecting MathIllegalArgumentException for empty array");
         } catch (MathIllegalArgumentException ex) {
             // Expected
         }
         try { // more than 1 regressor
             noIntRegression.regress(new int[] {0, 1});
             Assert.fail("Expecting ModelSpecificationException - too many regressors");
         } catch (ModelSpecificationException ex) {
             // Expected
         }
         try { // invalid regressor
             noIntRegression.regress(new int[] {1});
             Assert.fail("Expecting OutOfRangeException - invalid regression");
         } catch (OutOfRangeException ex) {
             // Expected
         }
 
         // With intercept
         final SimpleRegression regression = new SimpleRegression(true);
         regression.addData(noint2[0][1], noint2[0][0]);
         regression.addData(noint2[1][1], noint2[1][0]);
         regression.addData(noint2[2][1], noint2[2][0]);
         try { // null array
             regression.regress(null);
             Assert.fail("Expecting MathIllegalArgumentException for null array");
         } catch (MathIllegalArgumentException ex) {
             // Expected
         }
         try { // empty array
             regression.regress(new int[] {});
             Assert.fail("Expecting MathIllegalArgumentException for empty array");
         } catch (MathIllegalArgumentException ex) {
             // Expected
         }
         try { // more than 2 regressors
             regression.regress(new int[] {0, 1, 2});
             Assert.fail("Expecting ModelSpecificationException - too many regressors");
         } catch (ModelSpecificationException ex) {
             // Expected
         }
         try { // wrong order
             regression.regress(new int[] {1,0});
             Assert.fail("Expecting ModelSpecificationException - invalid regression");
         } catch (ModelSpecificationException ex) {
             // Expected
         }
         try { // out of range
             regression.regress(new int[] {3,4});
             Assert.fail("Expecting OutOfRangeException");
         } catch (OutOfRangeException ex) {
             // Expected
         }
         try { // out of range
             regression.regress(new int[] {0,2});
             Assert.fail("Expecting OutOfRangeException");
         } catch (OutOfRangeException ex) {
             // Expected
         }
         try { // out of range
             regression.regress(new int[] {2});
             Assert.fail("Expecting OutOfRangeException");
         } catch (OutOfRangeException ex) {
             // Expected
         }
     }
 
     @Test
     public void testNoInterceot_noint2(){
          SimpleRegression regression = new SimpleRegression(false);
          regression.addData(noint2[0][1], noint2[0][0]);
          regression.addData(noint2[1][1], noint2[1][0]);
          regression.addData(noint2[2][1], noint2[2][0]);
          Assert.assertEquals("intercept", 0, regression.getIntercept(), 0);
          Assert.assertEquals("slope", 0.727272727272727,
                  regression.getSlope(), 10E-12);
          Assert.assertEquals("slope std err", 0.420827318078432E-01,
                 regression.getSlopeStdErr(),10E-12);
         Assert.assertEquals("number of observations", 3, regression.getN());
         Assert.assertEquals("r-square", 0.993348115299335,
             regression.getRSquare(), 10E-12);
         Assert.assertEquals("SSR", 40.7272727272727,
             regression.getRegressionSumSquares(), 10E-9);
         Assert.assertEquals("MSE", 0.136363636363636,
             regression.getMeanSquareError(), 10E-10);
         Assert.assertEquals("SSE", 0.272727272727273,
             regression.getSumSquaredErrors(),10E-9);
     }
 
     @Test
     public void testNoIntercept_noint1(){
         SimpleRegression regression = new SimpleRegression(false);
         for (int i = 0; i < noint1.length; i++) {
             regression.addData(noint1[i][1], noint1[i][0]);
         }
         Assert.assertEquals("intercept", 0, regression.getIntercept(), 0);
         Assert.assertEquals("slope", 2.07438016528926, regression.getSlope(), 10E-12);
         Assert.assertEquals("slope std err", 0.165289256198347E-01,
                 regression.getSlopeStdErr(),10E-12);
         Assert.assertEquals("number of observations", 11, regression.getN());
         Assert.assertEquals("r-square", 0.999365492298663,
             regression.getRSquare(), 10E-12);
         Assert.assertEquals("SSR", 200457.727272727,
             regression.getRegressionSumSquares(), 10E-9);
         Assert.assertEquals("MSE", 12.7272727272727,
             regression.getMeanSquareError(), 10E-10);
         Assert.assertEquals("SSE", 127.272727272727,
             regression.getSumSquaredErrors(),10E-9);
     }
 
     @Test
     public void testNorris() {
         SimpleRegression regression = new SimpleRegression();
         for (int i = 0; i < data.length; i++) {
             regression.addData(data[i][1], data[i][0]);
         }
         // Tests against certified values from
         // http://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA/Norris.dat
         Assert.assertEquals("slope", 1.00211681802045, regression.getSlope(), 10E-12);
         Assert.assertEquals("slope std err", 0.429796848199937E-03,
                 regression.getSlopeStdErr(),10E-12);
         Assert.assertEquals("number of observations", 36, regression.getN());
         Assert.assertEquals( "intercept", -0.262323073774029,
             regression.getIntercept(),10E-12);
         Assert.assertEquals("std err intercept", 0.232818234301152,
             regression.getInterceptStdErr(),10E-12);
         Assert.assertEquals("r-square", 0.999993745883712,
             regression.getRSquare(), 10E-12);
         Assert.assertEquals("SSR", 4255954.13232369,
             regression.getRegressionSumSquares(), 10E-9);
         Assert.assertEquals("MSE", 0.782864662630069,
             regression.getMeanSquareError(), 10E-10);
         Assert.assertEquals("SSE", 26.6173985294224,
             regression.getSumSquaredErrors(),10E-9);
         // ------------  End certified data tests
 
         Assert.assertEquals( "predict(0)",  -0.262323073774029,
             regression.predict(0), 10E-12);
         Assert.assertEquals("predict(1)", 1.00211681802045 - 0.262323073774029,
             regression.predict(1), 10E-12);
     }
 
     @Test
     public void testCorr() {
         SimpleRegression regression = new SimpleRegression();
         regression.addData(corrData);
         Assert.assertEquals("number of observations", 17, regression.getN());
         Assert.assertEquals("r-square", .896123, regression.getRSquare(), 10E-6);
         Assert.assertEquals("r", -0.94663767742, regression.getR(), 1E-10);
     }
 
     @Test
     public void testNaNs() {
         SimpleRegression regression = new SimpleRegression();
         Assert.assertTrue("intercept not NaN", Double.isNaN(regression.getIntercept()));
         Assert.assertTrue("slope not NaN", Double.isNaN(regression.getSlope()));
         Assert.assertTrue("slope std err not NaN", Double.isNaN(regression.getSlopeStdErr()));
         Assert.assertTrue("intercept std err not NaN", Double.isNaN(regression.getInterceptStdErr()));
         Assert.assertTrue("MSE not NaN", Double.isNaN(regression.getMeanSquareError()));
         Assert.assertTrue("e not NaN", Double.isNaN(regression.getR()));
         Assert.assertTrue("r-square not NaN", Double.isNaN(regression.getRSquare()));
         Assert.assertTrue( "RSS not NaN", Double.isNaN(regression.getRegressionSumSquares()));
         Assert.assertTrue("SSE not NaN",Double.isNaN(regression.getSumSquaredErrors()));
         Assert.assertTrue("SSTO not NaN", Double.isNaN(regression.getTotalSumSquares()));
         Assert.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...
         Assert.assertTrue("intercept not NaN", Double.isNaN(regression.getIntercept()));
         Assert.assertTrue("slope not NaN", Double.isNaN(regression.getSlope()));
         Assert.assertTrue("slope std err not NaN", Double.isNaN(regression.getSlopeStdErr()));
         Assert.assertTrue("intercept std err not NaN", Double.isNaN(regression.getInterceptStdErr()));
         Assert.assertTrue("MSE not NaN", Double.isNaN(regression.getMeanSquareError()));
         Assert.assertTrue("e not NaN", Double.isNaN(regression.getR()));
         Assert.assertTrue("r-square not NaN", Double.isNaN(regression.getRSquare()));
         Assert.assertTrue("RSS not NaN", Double.isNaN(regression.getRegressionSumSquares()));
         Assert.assertTrue("SSE not NaN", Double.isNaN(regression.getSumSquaredErrors()));
         Assert.assertTrue("predict not NaN", Double.isNaN(regression.predict(0)));
 
         // but SSTO should be OK
         Assert.assertFalse("SSTO NaN", Double.isNaN(regression.getTotalSumSquares()));
 
         regression = new SimpleRegression();
 
         regression.addData(1, 2);
         regression.addData(3, 3);
 
         // All should be OK except MSE, s(b0), s(b1) which need one more df
         Assert.assertFalse("interceptNaN", Double.isNaN(regression.getIntercept()));
         Assert.assertFalse("slope NaN", Double.isNaN(regression.getSlope()));
         Assert.assertTrue("slope std err not NaN", Double.isNaN(regression.getSlopeStdErr()));
         Assert.assertTrue("intercept std err not NaN", Double.isNaN(regression.getInterceptStdErr()));
         Assert.assertTrue("MSE not NaN", Double.isNaN(regression.getMeanSquareError()));
         Assert.assertFalse("r NaN", Double.isNaN(regression.getR()));
         Assert.assertFalse("r-square NaN", Double.isNaN(regression.getRSquare()));
         Assert.assertFalse("RSS NaN", Double.isNaN(regression.getRegressionSumSquares()));
         Assert.assertFalse("SSE NaN", Double.isNaN(regression.getSumSquaredErrors()));
         Assert.assertFalse("SSTO NaN", Double.isNaN(regression.getTotalSumSquares()));
         Assert.assertFalse("predict NaN", Double.isNaN(regression.predict(0)));
 
         regression.addData(1, 4);
 
         // MSE, MSE, s(b0), s(b1) should all be OK now
         Assert.assertFalse("MSE NaN", Double.isNaN(regression.getMeanSquareError()));
         Assert.assertFalse("slope std err NaN", Double.isNaN(regression.getSlopeStdErr()));
         Assert.assertFalse("intercept std err NaN", Double.isNaN(regression.getInterceptStdErr()));
     }
 
     @Test
     public void testClear() {
         SimpleRegression regression = new SimpleRegression();
         regression.addData(corrData);
         Assert.assertEquals("number of observations", 17, regression.getN());
         regression.clear();
         Assert.assertEquals("number of observations", 0, regression.getN());
         regression.addData(corrData);
         Assert.assertEquals("r-square", .896123, regression.getRSquare(), 10E-6);
         regression.addData(data);
         Assert.assertEquals("number of observations", 53, regression.getN());
     }
 
     @Test
     public void testInference() {
         //----------  verified against R, version 1.8.1 -----
         // infData
         SimpleRegression regression = new SimpleRegression();
         regression.addData(infData);
         Assert.assertEquals("slope std err", 0.011448491,
                 regression.getSlopeStdErr(), 1E-10);
         Assert.assertEquals("std err intercept", 0.286036932,
                 regression.getInterceptStdErr(),1E-8);
         Assert.assertEquals("significance", 4.596e-07,
                 regression.getSignificance(),1E-8);
         Assert.assertEquals("slope conf interval half-width", 0.0270713794287,
                 regression.getSlopeConfidenceInterval(),1E-8);
         // infData2
         regression = new SimpleRegression();
         regression.addData(infData2);
         Assert.assertEquals("slope std err", 1.07260253,
                 regression.getSlopeStdErr(), 1E-8);
         Assert.assertEquals("std err intercept",4.17718672,
                 regression.getInterceptStdErr(),1E-8);
         Assert.assertEquals("significance", 0.261829133982,
                 regression.getSignificance(),1E-11);
         Assert.assertEquals("slope conf interval half-width", 2.97802204827,
                 regression.getSlopeConfidenceInterval(),1E-8);
         //------------- End R-verified tests -------------------------------
 
         //FIXME: get a real example to test against with alpha = .01
         Assert.assertTrue("tighter means wider",
                 regression.getSlopeConfidenceInterval() < regression.getSlopeConfidenceInterval(0.01));
 
         try {
             regression.getSlopeConfidenceInterval(1);
             Assert.fail("expecting MathIllegalArgumentException for alpha = 1");
         } catch (MathIllegalArgumentException ex) {
             // ignored
         }
     }
 
     @Test
     public void testPerfect() {
         SimpleRegression regression = new SimpleRegression();
         int n = 100;
         for (int i = 0; i < n; i++) {
             regression.addData(((double) i) / (n - 1), i);
         }
         Assert.assertEquals(0.0, regression.getSignificance(), 1.0e-5);
         Assert.assertTrue(regression.getSlope() > 0.0);
         Assert.assertTrue(regression.getSumSquaredErrors() >= 0.0);
     }
 
     @Test
     public void testPerfect2() {
         SimpleRegression regression = new SimpleRegression();
         regression.addData(0, 0);
         regression.addData(1, 1);
         regression.addData(2, 2);
         Assert.assertEquals(0.0, regression.getSlopeStdErr(), 0.0);
         Assert.assertEquals(0.0, regression.getSignificance(), Double.MIN_VALUE);
         Assert.assertEquals(1, regression.getRSquare(), Double.MIN_VALUE);
     }
 
     @Test
     public void testPerfectNegative() {
         SimpleRegression regression = new SimpleRegression();
         int n = 100;
         for (int i = 0; i < n; i++) {
             regression.addData(- ((double) i) / (n - 1), i);
         }
 
         Assert.assertEquals(0.0, regression.getSignificance(), 1.0e-5);
         Assert.assertTrue(regression.getSlope() < 0.0);
     }
 
     @Test
     public void testRandom() {
         SimpleRegression regression = new SimpleRegression();
         Random random = new Random(1);
         int n = 100;
         for (int i = 0; i < n; i++) {
             regression.addData(((double) i) / (n - 1), random.nextDouble());
         }
 
         Assert.assertTrue( 0.0 < regression.getSignificance()
                     && regression.getSignificance() < 1.0);
     }
 
 
     // Jira MATH-85 = Bugzilla 39432
     @Test
     public void testSSENonNegative() {
         double[] y = { 8915.102, 8919.302, 8923.502 };
         double[] x = { 1.107178495E2, 1.107264895E2, 1.107351295E2 };
         SimpleRegression reg = new SimpleRegression();
         for (int i = 0; i < x.length; i++) {
             reg.addData(x[i], y[i]);
         }
         Assert.assertTrue(reg.getSumSquaredErrors() >= 0.0);
     }
 
     // Test remove X,Y (single observation)
     @Test
     public void testRemoveXY() {
         // Create regression with inference data then remove to test
         SimpleRegression regression = new SimpleRegression();
         regression.addData(infData);
         regression.removeData(removeX, removeY);
         regression.addData(removeX, removeY);
         // Use the inference assertions to make sure that everything worked
         Assert.assertEquals("slope std err", 0.011448491,
                 regression.getSlopeStdErr(), 1E-10);
         Assert.assertEquals("std err intercept", 0.286036932,
                 regression.getInterceptStdErr(),1E-8);
         Assert.assertEquals("significance", 4.596e-07,
                 regression.getSignificance(),1E-8);
         Assert.assertEquals("slope conf interval half-width", 0.0270713794287,
                 regression.getSlopeConfidenceInterval(),1E-8);
      }
 
 
     // Test remove single observation in array
     @Test
     public void testRemoveSingle() {
         // Create regression with inference data then remove to test
         SimpleRegression regression = new SimpleRegression();
         regression.addData(infData);
         regression.removeData(removeSingle);
         regression.addData(removeSingle);
         // Use the inference assertions to make sure that everything worked
         Assert.assertEquals("slope std err", 0.011448491,
                 regression.getSlopeStdErr(), 1E-10);
         Assert.assertEquals("std err intercept", 0.286036932,
                 regression.getInterceptStdErr(),1E-8);
         Assert.assertEquals("significance", 4.596e-07,
                 regression.getSignificance(),1E-8);
         Assert.assertEquals("slope conf interval half-width", 0.0270713794287,
                 regression.getSlopeConfidenceInterval(),1E-8);
      }
 
     // Test remove multiple observations
     @Test
     public void testRemoveMultiple() {
         // Create regression with inference data then remove to test
         SimpleRegression regression = new SimpleRegression();
         regression.addData(infData);
         regression.removeData(removeMultiple);
         regression.addData(removeMultiple);
         // Use the inference assertions to make sure that everything worked
         Assert.assertEquals("slope std err", 0.011448491,
                 regression.getSlopeStdErr(), 1E-10);
         Assert.assertEquals("std err intercept", 0.286036932,
                 regression.getInterceptStdErr(),1E-8);
         Assert.assertEquals("significance", 4.596e-07,
                 regression.getSignificance(),1E-8);
         Assert.assertEquals("slope conf interval half-width", 0.0270713794287,
                 regression.getSlopeConfidenceInterval(),1E-8);
      }
 
     // Remove observation when empty
     @Test
     public void testRemoveObsFromEmpty() {
         SimpleRegression regression = new SimpleRegression();
         regression.removeData(removeX, removeY);
         Assert.assertEquals(regression.getN(), 0);
     }
 
     // Remove single observation to empty
     @Test
     public void testRemoveObsFromSingle() {
         SimpleRegression regression = new SimpleRegression();
         regression.addData(removeX, removeY);
         regression.removeData(removeX, removeY);
         Assert.assertEquals(regression.getN(), 0);
     }
 
     // Remove multiple observations to empty
     @Test
     public void testRemoveMultipleToEmpty() {
         SimpleRegression regression = new SimpleRegression();
         regression.addData(removeMultiple);
         regression.removeData(removeMultiple);
         Assert.assertEquals(regression.getN(), 0);
     }
 
     // Remove multiple observations past empty (i.e. size of array > n)
     @Test
     public void testRemoveMultiplePastEmpty() {
         SimpleRegression regression = new SimpleRegression();
         regression.addData(removeX, removeY);
         regression.removeData(removeMultiple);
         Assert.assertEquals(regression.getN(), 0);
     }
 }