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Java example source code file (OLSMultipleLinearRegressionTest.java)

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

Learn more about this Java project at its project page.

Java - Java tags/keywords

before, defaultrealmatrixchangingvisitor, multiplelinearregressionabstracttest, olsmultiplelinearregression, olsmultiplelinearregressiontest, override, realmatrix, realvector, test

The OLSMultipleLinearRegressionTest.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.stat.regression;


import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.apache.commons.math3.linear.DefaultRealMatrixChangingVisitor;
import org.apache.commons.math3.linear.MatrixUtils;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.RealVector;
import org.apache.commons.math3.stat.StatUtils;
import org.junit.Assert;
import org.junit.Before;
import org.junit.Test;

public class OLSMultipleLinearRegressionTest extends MultipleLinearRegressionAbstractTest {

    private double[] y;
    private double[][] x;

    @Before
    @Override
    public void setUp(){
        y = new double[]{11.0, 12.0, 13.0, 14.0, 15.0, 16.0};
        x = new double[6][];
        x[0] = new double[]{0, 0, 0, 0, 0};
        x[1] = new double[]{2.0, 0, 0, 0, 0};
        x[2] = new double[]{0, 3.0, 0, 0, 0};
        x[3] = new double[]{0, 0, 4.0, 0, 0};
        x[4] = new double[]{0, 0, 0, 5.0, 0};
        x[5] = new double[]{0, 0, 0, 0, 6.0};
        super.setUp();
    }

    @Override
    protected OLSMultipleLinearRegression createRegression() {
        OLSMultipleLinearRegression regression = new OLSMultipleLinearRegression();
        regression.newSampleData(y, x);
        return regression;
    }

    @Override
    protected int getNumberOfRegressors() {
        return x[0].length + 1;
    }

    @Override
    protected int getSampleSize() {
        return y.length;
    }

    @Test(expected=IllegalArgumentException.class)
    public void cannotAddSampleDataWithSizeMismatch() {
        double[] y = new double[]{1.0, 2.0};
        double[][] x = new double[1][];
        x[0] = new double[]{1.0, 0};
        createRegression().newSampleData(y, x);
    }

    @Test
    public void testPerfectFit() {
        double[] betaHat = regression.estimateRegressionParameters();
        TestUtils.assertEquals(betaHat,
                               new double[]{ 11.0, 1.0 / 2.0, 2.0 / 3.0, 3.0 / 4.0, 4.0 / 5.0, 5.0 / 6.0 },
                               1e-14);
        double[] residuals = regression.estimateResiduals();
        TestUtils.assertEquals(residuals, new double[]{0d,0d,0d,0d,0d,0d},
                               1e-14);
        RealMatrix errors =
            new Array2DRowRealMatrix(regression.estimateRegressionParametersVariance(), false);
        final double[] s = { 1.0, -1.0 /  2.0, -1.0 /  3.0, -1.0 /  4.0, -1.0 /  5.0, -1.0 /  6.0 };
        RealMatrix referenceVariance = new Array2DRowRealMatrix(s.length, s.length);
        referenceVariance.walkInOptimizedOrder(new DefaultRealMatrixChangingVisitor() {
            @Override
            public double visit(int row, int column, double value) {
                if (row == 0) {
                    return s[column];
                }
                double x = s[row] * s[column];
                return (row == column) ? 2 * x : x;
            }
        });
       Assert.assertEquals(0.0,
                     errors.subtract(referenceVariance).getNorm(),
                     5.0e-16 * referenceVariance.getNorm());
       Assert.assertEquals(1, ((OLSMultipleLinearRegression) regression).calculateRSquared(), 1E-12);
    }


    /**
     * Test Longley dataset against certified values provided by NIST.
     * Data Source: J. Longley (1967) "An Appraisal of Least Squares
     * Programs for the Electronic Computer from the Point of View of the User"
     * Journal of the American Statistical Association, vol. 62. September,
     * pp. 819-841.
     *
     * Certified values (and data) are from NIST:
     * http://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA/Longley.dat
     */
    @Test
    public void testLongly() {
        // Y values are first, then independent vars
        // Each row is one observation
        double[] design = new double[] {
            60323,83.0,234289,2356,1590,107608,1947,
            61122,88.5,259426,2325,1456,108632,1948,
            60171,88.2,258054,3682,1616,109773,1949,
            61187,89.5,284599,3351,1650,110929,1950,
            63221,96.2,328975,2099,3099,112075,1951,
            63639,98.1,346999,1932,3594,113270,1952,
            64989,99.0,365385,1870,3547,115094,1953,
            63761,100.0,363112,3578,3350,116219,1954,
            66019,101.2,397469,2904,3048,117388,1955,
            67857,104.6,419180,2822,2857,118734,1956,
            68169,108.4,442769,2936,2798,120445,1957,
            66513,110.8,444546,4681,2637,121950,1958,
            68655,112.6,482704,3813,2552,123366,1959,
            69564,114.2,502601,3931,2514,125368,1960,
            69331,115.7,518173,4806,2572,127852,1961,
            70551,116.9,554894,4007,2827,130081,1962
        };

        final int nobs = 16;
        final int nvars = 6;

        // Estimate the model
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        model.newSampleData(design, nobs, nvars);

        // Check expected beta values from NIST
        double[] betaHat = model.estimateRegressionParameters();
        TestUtils.assertEquals(betaHat,
          new double[]{-3482258.63459582, 15.0618722713733,
                -0.358191792925910E-01,-2.02022980381683,
                -1.03322686717359,-0.511041056535807E-01,
                 1829.15146461355}, 2E-8); //

        // Check expected residuals from R
        double[] residuals = model.estimateResiduals();
        TestUtils.assertEquals(residuals, new double[]{
                267.340029759711,-94.0139423988359,46.28716775752924,
                -410.114621930906,309.7145907602313,-249.3112153297231,
                -164.0489563956039,-13.18035686637081,14.30477260005235,
                 455.394094551857,-17.26892711483297,-39.0550425226967,
                -155.5499735953195,-85.6713080421283,341.9315139607727,
                -206.7578251937366},
                      1E-8);

        // Check standard errors from NIST
        double[] errors = model.estimateRegressionParametersStandardErrors();
        TestUtils.assertEquals(new double[] {890420.383607373,
                       84.9149257747669,
                       0.334910077722432E-01,
                       0.488399681651699,
                       0.214274163161675,
                       0.226073200069370,
                       455.478499142212}, errors, 1E-6);

        // Check regression standard error against R
        Assert.assertEquals(304.8540735619638, model.estimateRegressionStandardError(), 1E-10);

        // Check R-Square statistics against R
        Assert.assertEquals(0.995479004577296, model.calculateRSquared(), 1E-12);
        Assert.assertEquals(0.992465007628826, model.calculateAdjustedRSquared(), 1E-12);

        checkVarianceConsistency(model);

        // Estimate model without intercept
        model.setNoIntercept(true);
        model.newSampleData(design, nobs, nvars);

        // Check expected beta values from R
        betaHat = model.estimateRegressionParameters();
        TestUtils.assertEquals(betaHat,
          new double[]{-52.99357013868291, 0.07107319907358,
                -0.42346585566399,-0.57256866841929,
                -0.41420358884978, 48.41786562001326}, 1E-11);

        // Check standard errors from R
        errors = model.estimateRegressionParametersStandardErrors();
        TestUtils.assertEquals(new double[] {129.54486693117232, 0.03016640003786,
                0.41773654056612, 0.27899087467676, 0.32128496193363,
                17.68948737819961}, errors, 1E-11);

        // Check expected residuals from R
        residuals = model.estimateResiduals();
        TestUtils.assertEquals(residuals, new double[]{
                279.90274927293092, -130.32465380836874, 90.73228661967445, -401.31252201634948,
                -440.46768772620027, -543.54512853774793, 201.32111639536299, 215.90889365977932,
                73.09368242049943, 913.21694494481869, 424.82484953610174, -8.56475876776709,
                -361.32974610842876, 27.34560497213464, 151.28955976355002, -492.49937355336846},
                      1E-10);

        // Check regression standard error against R
        Assert.assertEquals(475.1655079819517, model.estimateRegressionStandardError(), 1E-10);

        // Check R-Square statistics against R
        Assert.assertEquals(0.9999670130706, model.calculateRSquared(), 1E-12);
        Assert.assertEquals(0.999947220913, model.calculateAdjustedRSquared(), 1E-12);

    }

    /**
     * Test R Swiss fertility dataset against R.
     * Data Source: R datasets package
     */
    @Test
    public void testSwissFertility() {
        double[] design = new double[] {
            80.2,17.0,15,12,9.96,
            83.1,45.1,6,9,84.84,
            92.5,39.7,5,5,93.40,
            85.8,36.5,12,7,33.77,
            76.9,43.5,17,15,5.16,
            76.1,35.3,9,7,90.57,
            83.8,70.2,16,7,92.85,
            92.4,67.8,14,8,97.16,
            82.4,53.3,12,7,97.67,
            82.9,45.2,16,13,91.38,
            87.1,64.5,14,6,98.61,
            64.1,62.0,21,12,8.52,
            66.9,67.5,14,7,2.27,
            68.9,60.7,19,12,4.43,
            61.7,69.3,22,5,2.82,
            68.3,72.6,18,2,24.20,
            71.7,34.0,17,8,3.30,
            55.7,19.4,26,28,12.11,
            54.3,15.2,31,20,2.15,
            65.1,73.0,19,9,2.84,
            65.5,59.8,22,10,5.23,
            65.0,55.1,14,3,4.52,
            56.6,50.9,22,12,15.14,
            57.4,54.1,20,6,4.20,
            72.5,71.2,12,1,2.40,
            74.2,58.1,14,8,5.23,
            72.0,63.5,6,3,2.56,
            60.5,60.8,16,10,7.72,
            58.3,26.8,25,19,18.46,
            65.4,49.5,15,8,6.10,
            75.5,85.9,3,2,99.71,
            69.3,84.9,7,6,99.68,
            77.3,89.7,5,2,100.00,
            70.5,78.2,12,6,98.96,
            79.4,64.9,7,3,98.22,
            65.0,75.9,9,9,99.06,
            92.2,84.6,3,3,99.46,
            79.3,63.1,13,13,96.83,
            70.4,38.4,26,12,5.62,
            65.7,7.7,29,11,13.79,
            72.7,16.7,22,13,11.22,
            64.4,17.6,35,32,16.92,
            77.6,37.6,15,7,4.97,
            67.6,18.7,25,7,8.65,
            35.0,1.2,37,53,42.34,
            44.7,46.6,16,29,50.43,
            42.8,27.7,22,29,58.33
        };

        final int nobs = 47;
        final int nvars = 4;

        // Estimate the model
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        model.newSampleData(design, nobs, nvars);

        // Check expected beta values from R
        double[] betaHat = model.estimateRegressionParameters();
        TestUtils.assertEquals(betaHat,
                new double[]{91.05542390271397,
                -0.22064551045715,
                -0.26058239824328,
                -0.96161238456030,
                 0.12441843147162}, 1E-12);

        // Check expected residuals from R
        double[] residuals = model.estimateResiduals();
        TestUtils.assertEquals(residuals, new double[]{
                7.1044267859730512,1.6580347433531366,
                4.6944952770029644,8.4548022690166160,13.6547432343186212,
               -9.3586864458500774,7.5822446330520386,15.5568995563859289,
                0.8113090736598980,7.1186762732484308,7.4251378771228724,
                2.6761316873234109,0.8351584810309354,7.1769991119615177,
               -3.8746753206299553,-3.1337779476387251,-0.1412575244091504,
                1.1186809170469780,-6.3588097346816594,3.4039270429434074,
                2.3374058329820175,-7.9272368576900503,-7.8361010968497959,
               -11.2597369269357070,0.9445333697827101,6.6544245101380328,
               -0.9146136301118665,-4.3152449403848570,-4.3536932047009183,
               -3.8907885169304661,-6.3027643926302188,-7.8308982189289091,
               -3.1792280015332750,-6.7167298771158226,-4.8469946718041754,
               -10.6335664353633685,11.1031134362036958,6.0084032641811733,
                5.4326230830188482,-7.2375578629692230,2.1671550814448222,
                15.0147574652763112,4.8625103516321015,-7.1597256413907706,
                -0.4515205619767598,-10.2916870903837587,-15.7812984571900063},
                1E-12);

        // Check standard errors from R
        double[] errors = model.estimateRegressionParametersStandardErrors();
        TestUtils.assertEquals(new double[] {6.94881329475087,
                0.07360008972340,
                0.27410957467466,
                0.19454551679325,
                0.03726654773803}, errors, 1E-10);

        // Check regression standard error against R
        Assert.assertEquals(7.73642194433223, model.estimateRegressionStandardError(), 1E-12);

        // Check R-Square statistics against R
        Assert.assertEquals(0.649789742860228, model.calculateRSquared(), 1E-12);
        Assert.assertEquals(0.6164363850373927, model.calculateAdjustedRSquared(), 1E-12);

        checkVarianceConsistency(model);

        // Estimate the model with no intercept
        model = new OLSMultipleLinearRegression();
        model.setNoIntercept(true);
        model.newSampleData(design, nobs, nvars);

        // Check expected beta values from R
        betaHat = model.estimateRegressionParameters();
        TestUtils.assertEquals(betaHat,
                new double[]{0.52191832900513,
                  2.36588087917963,
                  -0.94770353802795,
                  0.30851985863609}, 1E-12);

        // Check expected residuals from R
        residuals = model.estimateResiduals();
        TestUtils.assertEquals(residuals, new double[]{
                44.138759883538249, 27.720705122356215, 35.873200836126799,
                34.574619581211977, 26.600168342080213, 15.074636243026923, -12.704904871199814,
                1.497443824078134, 2.691972687079431, 5.582798774291231, -4.422986561283165,
                -9.198581600334345, 4.481765170730647, 2.273520207553216, -22.649827853221336,
                -17.747900013943308, 20.298314638496436, 6.861405135329779, -8.684712790954924,
                -10.298639278062371, -9.896618896845819, 4.568568616351242, -15.313570491727944,
                -13.762961360873966, 7.156100301980509, 16.722282219843990, 26.716200609071898,
                -1.991466398777079, -2.523342564719335, 9.776486693095093, -5.297535127628603,
                -16.639070567471094, -10.302057295211819, -23.549487860816846, 1.506624392156384,
                -17.939174438345930, 13.105792202765040, -1.943329906928462, -1.516005841666695,
                -0.759066561832886, 20.793137744128977, -2.485236153005426, 27.588238710486976,
                2.658333257106881, -15.998337823623046, -5.550742066720694, -14.219077806826615},
                1E-12);

        // Check standard errors from R
        errors = model.estimateRegressionParametersStandardErrors();
        TestUtils.assertEquals(new double[] {0.10470063765677, 0.41684100584290,
                0.43370143099691, 0.07694953606522}, errors, 1E-10);

        // Check regression standard error against R
        Assert.assertEquals(17.24710630547, model.estimateRegressionStandardError(), 1E-10);

        // Check R-Square statistics against R
        Assert.assertEquals(0.946350722085, model.calculateRSquared(), 1E-12);
        Assert.assertEquals(0.9413600915813, model.calculateAdjustedRSquared(), 1E-12);
    }

    /**
     * Test hat matrix computation
     *
     */
    @Test
    public void testHat() {

        /*
         * This example is from "The Hat Matrix in Regression and ANOVA",
         * David C. Hoaglin and Roy E. Welsch,
         * The American Statistician, Vol. 32, No. 1 (Feb., 1978), pp. 17-22.
         *
         */
        double[] design = new double[] {
                11.14, .499, 11.1,
                12.74, .558, 8.9,
                13.13, .604, 8.8,
                11.51, .441, 8.9,
                12.38, .550, 8.8,
                12.60, .528, 9.9,
                11.13, .418, 10.7,
                11.7, .480, 10.5,
                11.02, .406, 10.5,
                11.41, .467, 10.7
        };

        int nobs = 10;
        int nvars = 2;

        // Estimate the model
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        model.newSampleData(design, nobs, nvars);

        RealMatrix hat = model.calculateHat();

        // Reference data is upper half of symmetric hat matrix
        double[] referenceData = new double[] {
                .418, -.002,  .079, -.274, -.046,  .181,  .128,  .222,  .050,  .242,
                       .242,  .292,  .136,  .243,  .128, -.041,  .033, -.035,  .004,
                              .417, -.019,  .273,  .187, -.126,  .044, -.153,  .004,
                                     .604,  .197, -.038,  .168, -.022,  .275, -.028,
                                            .252,  .111, -.030,  .019, -.010, -.010,
                                                   .148,  .042,  .117,  .012,  .111,
                                                          .262,  .145,  .277,  .174,
                                                                 .154,  .120,  .168,
                                                                        .315,  .148,
                                                                               .187
        };

        // Check against reference data and verify symmetry
        int k = 0;
        for (int i = 0; i < 10; i++) {
            for (int j = i; j < 10; j++) {
                Assert.assertEquals(referenceData[k], hat.getEntry(i, j), 10e-3);
                Assert.assertEquals(hat.getEntry(i, j), hat.getEntry(j, i), 10e-12);
                k++;
            }
        }

        /*
         * Verify that residuals computed using the hat matrix are close to
         * what we get from direct computation, i.e. r = (I - H) y
         */
        double[] residuals = model.estimateResiduals();
        RealMatrix I = MatrixUtils.createRealIdentityMatrix(10);
        double[] hatResiduals = I.subtract(hat).operate(model.getY()).toArray();
        TestUtils.assertEquals(residuals, hatResiduals, 10e-12);
    }

    /**
     * test calculateYVariance
     */
    @Test
    public void testYVariance() {

        // assumes: y = new double[]{11.0, 12.0, 13.0, 14.0, 15.0, 16.0};

        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        model.newSampleData(y, x);
        TestUtils.assertEquals(model.calculateYVariance(), 3.5, 0);
    }

    /**
     * Verifies that calculateYVariance and calculateResidualVariance return consistent
     * values with direct variance computation from Y, residuals, respectively.
     */
    protected void checkVarianceConsistency(OLSMultipleLinearRegression model) {
        // Check Y variance consistency
        TestUtils.assertEquals(StatUtils.variance(model.getY().toArray()), model.calculateYVariance(), 0);

        // Check residual variance consistency
        double[] residuals = model.calculateResiduals().toArray();
        RealMatrix X = model.getX();
        TestUtils.assertEquals(
                StatUtils.variance(model.calculateResiduals().toArray()) * (residuals.length - 1),
                model.calculateErrorVariance() * (X.getRowDimension() - X.getColumnDimension()), 1E-20);

    }

    /**
     * Verifies that setting X and Y separately has the same effect as newSample(X,Y).
     */
    @Test
    public void testNewSample2() {
        double[] y = new double[] {1, 2, 3, 4};
        double[][] x = new double[][] {
          {19, 22, 33},
          {20, 30, 40},
          {25, 35, 45},
          {27, 37, 47}
        };
        OLSMultipleLinearRegression regression = new OLSMultipleLinearRegression();
        regression.newSampleData(y, x);
        RealMatrix combinedX = regression.getX().copy();
        RealVector combinedY = regression.getY().copy();
        regression.newXSampleData(x);
        regression.newYSampleData(y);
        Assert.assertEquals(combinedX, regression.getX());
        Assert.assertEquals(combinedY, regression.getY());

        // No intercept
        regression.setNoIntercept(true);
        regression.newSampleData(y, x);
        combinedX = regression.getX().copy();
        combinedY = regression.getY().copy();
        regression.newXSampleData(x);
        regression.newYSampleData(y);
        Assert.assertEquals(combinedX, regression.getX());
        Assert.assertEquals(combinedY, regression.getY());
    }

    @Test(expected=IllegalArgumentException.class)
    public void testNewSampleDataYNull() {
        createRegression().newSampleData(null, new double[][] {});
    }

    @Test(expected=IllegalArgumentException.class)
    public void testNewSampleDataXNull() {
        createRegression().newSampleData(new double[] {}, null);
    }

     /*
     * This is a test based on the Wampler1 data set
     * http://www.itl.nist.gov/div898/strd/lls/data/Wampler1.shtml
     */
    @Test
    public void testWampler1() {
        double[] data = new double[]{
            1, 0,
            6, 1,
            63, 2,
            364, 3,
            1365, 4,
            3906, 5,
            9331, 6,
            19608, 7,
            37449, 8,
            66430, 9,
            111111, 10,
            177156, 11,
            271453, 12,
            402234, 13,
            579195, 14,
            813616, 15,
            1118481, 16,
            1508598, 17,
            2000719, 18,
            2613660, 19,
            3368421, 20};
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();


        final int nvars = 5;
        final int nobs = 21;
        double[] tmp = new double[(nvars + 1) * nobs];
        int off = 0;
        int off2 = 0;
        for (int i = 0; i < nobs; i++) {
            tmp[off2] = data[off];
            tmp[off2 + 1] = data[off + 1];
            tmp[off2 + 2] = tmp[off2 + 1] * tmp[off2 + 1];
            tmp[off2 + 3] = tmp[off2 + 1] * tmp[off2 + 2];
            tmp[off2 + 4] = tmp[off2 + 1] * tmp[off2 + 3];
            tmp[off2 + 5] = tmp[off2 + 1] * tmp[off2 + 4];
            off2 += (nvars + 1);
            off += 2;
        }
        model.newSampleData(tmp, nobs, nvars);
        double[] betaHat = model.estimateRegressionParameters();
        TestUtils.assertEquals(betaHat,
                new double[]{1.0,
                    1.0, 1.0,
                    1.0, 1.0,
                    1.0}, 1E-8);

        double[] se = model.estimateRegressionParametersStandardErrors();
        TestUtils.assertEquals(se,
                new double[]{0.0,
                    0.0, 0.0,
                    0.0, 0.0,
                    0.0}, 1E-8);

        TestUtils.assertEquals(1.0, model.calculateRSquared(), 1.0e-10);
        TestUtils.assertEquals(0, model.estimateErrorVariance(), 1.0e-7);
        TestUtils.assertEquals(0.00, model.calculateResidualSumOfSquares(), 1.0e-6);

        return;
    }

    /*
     * This is a test based on the Wampler2 data set
     * http://www.itl.nist.gov/div898/strd/lls/data/Wampler2.shtml
     */
    @Test
    public void testWampler2() {
        double[] data = new double[]{
            1.00000, 0,
            1.11111, 1,
            1.24992, 2,
            1.42753, 3,
            1.65984, 4,
            1.96875, 5,
            2.38336, 6,
            2.94117, 7,
            3.68928, 8,
            4.68559, 9,
            6.00000, 10,
            7.71561, 11,
            9.92992, 12,
            12.75603, 13,
            16.32384, 14,
            20.78125, 15,
            26.29536, 16,
            33.05367, 17,
            41.26528, 18,
            51.16209, 19,
            63.00000, 20};
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();


        final int nvars = 5;
        final int nobs = 21;
        double[] tmp = new double[(nvars + 1) * nobs];
        int off = 0;
        int off2 = 0;
        for (int i = 0; i < nobs; i++) {
            tmp[off2] = data[off];
            tmp[off2 + 1] = data[off + 1];
            tmp[off2 + 2] = tmp[off2 + 1] * tmp[off2 + 1];
            tmp[off2 + 3] = tmp[off2 + 1] * tmp[off2 + 2];
            tmp[off2 + 4] = tmp[off2 + 1] * tmp[off2 + 3];
            tmp[off2 + 5] = tmp[off2 + 1] * tmp[off2 + 4];
            off2 += (nvars + 1);
            off += 2;
        }
        model.newSampleData(tmp, nobs, nvars);
        double[] betaHat = model.estimateRegressionParameters();
        TestUtils.assertEquals(betaHat,
                new double[]{
                    1.0,
                    1.0e-1,
                    1.0e-2,
                    1.0e-3, 1.0e-4,
                    1.0e-5}, 1E-8);

        double[] se = model.estimateRegressionParametersStandardErrors();
        TestUtils.assertEquals(se,
                new double[]{0.0,
                    0.0, 0.0,
                    0.0, 0.0,
                    0.0}, 1E-8);
        TestUtils.assertEquals(1.0, model.calculateRSquared(), 1.0e-10);
        TestUtils.assertEquals(0, model.estimateErrorVariance(), 1.0e-7);
        TestUtils.assertEquals(0.00, model.calculateResidualSumOfSquares(), 1.0e-6);
        return;
    }

    /*
     * This is a test based on the Wampler3 data set
     * http://www.itl.nist.gov/div898/strd/lls/data/Wampler3.shtml
     */
    @Test
    public void testWampler3() {
        double[] data = new double[]{
            760, 0,
            -2042, 1,
            2111, 2,
            -1684, 3,
            3888, 4,
            1858, 5,
            11379, 6,
            17560, 7,
            39287, 8,
            64382, 9,
            113159, 10,
            175108, 11,
            273291, 12,
            400186, 13,
            581243, 14,
            811568, 15,
            1121004, 16,
            1506550, 17,
            2002767, 18,
            2611612, 19,
            3369180, 20};

        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        final int nvars = 5;
        final int nobs = 21;
        double[] tmp = new double[(nvars + 1) * nobs];
        int off = 0;
        int off2 = 0;
        for (int i = 0; i < nobs; i++) {
            tmp[off2] = data[off];
            tmp[off2 + 1] = data[off + 1];
            tmp[off2 + 2] = tmp[off2 + 1] * tmp[off2 + 1];
            tmp[off2 + 3] = tmp[off2 + 1] * tmp[off2 + 2];
            tmp[off2 + 4] = tmp[off2 + 1] * tmp[off2 + 3];
            tmp[off2 + 5] = tmp[off2 + 1] * tmp[off2 + 4];
            off2 += (nvars + 1);
            off += 2;
        }
        model.newSampleData(tmp, nobs, nvars);
        double[] betaHat = model.estimateRegressionParameters();
        TestUtils.assertEquals(betaHat,
                new double[]{
                    1.0,
                    1.0,
                    1.0,
                    1.0,
                    1.0,
                    1.0}, 1E-8);

        double[] se = model.estimateRegressionParametersStandardErrors();
        TestUtils.assertEquals(se,
                new double[]{2152.32624678170,
                    2363.55173469681, 779.343524331583,
                    101.475507550350, 5.64566512170752,
                    0.112324854679312}, 1E-8); //

        TestUtils.assertEquals(.999995559025820, model.calculateRSquared(), 1.0e-10);
        TestUtils.assertEquals(5570284.53333333, model.estimateErrorVariance(), 1.0e-6);
        TestUtils.assertEquals(83554268.0000000, model.calculateResidualSumOfSquares(), 1.0e-5);
        return;
    }

    /*
     * This is a test based on the Wampler4 data set
     * http://www.itl.nist.gov/div898/strd/lls/data/Wampler4.shtml
     */
    @Test
    public void testWampler4() {
        double[] data = new double[]{
            75901, 0,
            -204794, 1,
            204863, 2,
            -204436, 3,
            253665, 4,
            -200894, 5,
            214131, 6,
            -185192, 7,
            221249, 8,
            -138370, 9,
            315911, 10,
            -27644, 11,
            455253, 12,
            197434, 13,
            783995, 14,
            608816, 15,
            1370781, 16,
            1303798, 17,
            2205519, 18,
            2408860, 19,
            3444321, 20};

        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        final int nvars = 5;
        final int nobs = 21;
        double[] tmp = new double[(nvars + 1) * nobs];
        int off = 0;
        int off2 = 0;
        for (int i = 0; i < nobs; i++) {
            tmp[off2] = data[off];
            tmp[off2 + 1] = data[off + 1];
            tmp[off2 + 2] = tmp[off2 + 1] * tmp[off2 + 1];
            tmp[off2 + 3] = tmp[off2 + 1] * tmp[off2 + 2];
            tmp[off2 + 4] = tmp[off2 + 1] * tmp[off2 + 3];
            tmp[off2 + 5] = tmp[off2 + 1] * tmp[off2 + 4];
            off2 += (nvars + 1);
            off += 2;
        }
        model.newSampleData(tmp, nobs, nvars);
        double[] betaHat = model.estimateRegressionParameters();
        TestUtils.assertEquals(betaHat,
                new double[]{
                    1.0,
                    1.0,
                    1.0,
                    1.0,
                    1.0,
                    1.0}, 1E-6);

        double[] se = model.estimateRegressionParametersStandardErrors();
        TestUtils.assertEquals(se,
                new double[]{215232.624678170,
                    236355.173469681, 77934.3524331583,
                    10147.5507550350, 564.566512170752,
                    11.2324854679312}, 1E-8);

        TestUtils.assertEquals(.957478440825662, model.calculateRSquared(), 1.0e-10);
        TestUtils.assertEquals(55702845333.3333, model.estimateErrorVariance(), 1.0e-4);
        TestUtils.assertEquals(835542680000.000, model.calculateResidualSumOfSquares(), 1.0e-3);
        return;
    }

    /**
     * Anything requiring beta calculation should advertise SME.
     */
    @Test(expected=org.apache.commons.math3.linear.SingularMatrixException.class)
    public void testSingularCalculateBeta() {
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        model.newSampleData(new double[] {1,  2,  3, 1, 2, 3, 1, 2, 3}, 3, 2);
        model.calculateBeta();
    }

    @Test
    public void testNoSSTOCalculateRsquare() {
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        model.newSampleData(new double[] {1,  2,  3, 1, 7, 8, 1, 10, 12}, 3, 2);
        Assert.assertTrue(Double.isNaN(model.calculateRSquared()));
    }

    @Test(expected=NullPointerException.class)
    public void testNoDataNPECalculateBeta() {
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        model.calculateBeta();
    }

    @Test(expected=NullPointerException.class)
    public void testNoDataNPECalculateHat() {
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        model.calculateHat();
    }

    @Test(expected=NullPointerException.class)
    public void testNoDataNPESSTO() {
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        model.calculateTotalSumOfSquares();
    }
}

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