/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.math.regression;
import org.apache.commons.math.distribution.ContinuousDistribution;
import org.apache.commons.math.distribution.TDistributionImpl;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
import cern.colt.matrix.DoubleFactory1D;
import cern.colt.matrix.DoubleFactory2D;
import cern.colt.matrix.DoubleMatrix1D;
import cern.colt.matrix.DoubleMatrix2D;
import cern.colt.matrix.linalg.Algebra;
/**
*
*/
public class OrdinaryLeastSquaresRegression extends LeastSquaresRegression {
private static final Logger s_logger = LoggerFactory.getLogger(OrdinaryLeastSquaresRegression.class);
private final Algebra _algebra = new Algebra();
@Override
public LeastSquaresRegressionResult regress(final double[][] x, final double[][] weights, final double[] y, final boolean useIntercept) {
if (weights != null) {
s_logger.info("Weights were provided for OLS regression: they will be ignored");
}
return regress(x, y, useIntercept);
}
public LeastSquaresRegressionResult regress(final double[][] x, final double[] y, final boolean useIntercept) {
checkData(x, y);
final double[][] indep = addInterceptVariable(x, useIntercept);
final double[] dep = new double[y.length];
for (int i = 0; i < y.length; i++) {
dep[i] = y[i];
}
final DoubleMatrix2D matrix = DoubleFactory2D.dense.make(indep);
final DoubleMatrix1D vector = DoubleFactory1D.dense.make(dep);
final DoubleMatrix2D transpose = _algebra.transpose(matrix);
final DoubleMatrix1D betasVector = _algebra.mult(_algebra.mult(_algebra.inverse(_algebra.mult(transpose, matrix)), transpose), vector);
final double[] yModel = convertArray(_algebra.mult(matrix, betasVector).toArray());
final double[] betas = convertArray(betasVector.toArray());
return getResultWithStatistics(x, y, betas, yModel, transpose, matrix, useIntercept);
}
private LeastSquaresRegressionResult getResultWithStatistics(final double[][] x, final double[] y, final double[] betas, final double[] yModel, final DoubleMatrix2D transpose,
final DoubleMatrix2D matrix, final boolean useIntercept) {
double yMean = 0.;
for (final double y1 : y) {
yMean += y1;
}
yMean /= y.length;
double totalSumOfSquares = 0.;
double errorSumOfSquares = 0.;
final int n = x.length;
final int k = betas.length;
final double[] residuals = new double[n];
final double[] stdErrorBetas = new double[k];
final double[] tStats = new double[k];
final double[] pValues = new double[k];
for (int i = 0; i < n; i++) {
totalSumOfSquares += (y[i] - yMean) * (y[i] - yMean);
residuals[i] = y[i] - yModel[i];
errorSumOfSquares += residuals[i] * residuals[i];
}
final double regressionSumOfSquares = totalSumOfSquares - errorSumOfSquares;
final double[][] covarianceBetas = convertArray(_algebra.inverse(_algebra.mult(transpose, matrix)).toArray());
final double rSquared = regressionSumOfSquares / totalSumOfSquares;
final double adjustedRSquared = 1. - (1 - rSquared) * (n - 1.) / (n - k);
final double meanSquareError = errorSumOfSquares / (n - k);
final ContinuousDistribution studentT = new TDistributionImpl(n - k);
// final ProbabilityDistribution<Double> studentT = new
// StudentTDistribution(n - k);
for (int i = 0; i < k; i++) {
stdErrorBetas[i] = Math.sqrt(meanSquareError * covarianceBetas[i][i]);
tStats[i] = betas[i] / stdErrorBetas[i];
try {
pValues[i] = 1 - studentT.cumulativeProbability(Math.abs(tStats[i]));
} catch (final org.apache.commons.math.MathException e) {
throw new com.opengamma.analytics.math.MathException(e);
}
}
return new LeastSquaresRegressionResult(betas, residuals, meanSquareError, stdErrorBetas, rSquared, adjustedRSquared, tStats, pValues, useIntercept);
}
}