001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    package org.apache.commons.math3.stat.regression;
018    
019    /**
020     * The multiple linear regression can be represented in matrix-notation.
021     * <pre>
022     *  y=X*b+u
023     * </pre>
024     * where y is an <code>n-vector</code> <b>regressand</b>, X is a <code>[n,k]</code> matrix whose <code>k</code> columns are called
025     * <b>regressors</b>, b is <code>k-vector</code> of <b>regression parameters</b> and <code>u</code> is an <code>n-vector</code>
026     * of <b>error terms</b> or <b>residuals</b>.
027     *
028     * The notation is quite standard in literature,
029     * cf eg <a href="http://www.econ.queensu.ca/ETM">Davidson and MacKinnon, Econometrics Theory and Methods, 2004</a>.
030     * @version $Id: MultipleLinearRegression.java 1416643 2012-12-03 19:37:14Z tn $
031     * @since 2.0
032     */
033    public interface MultipleLinearRegression {
034    
035        /**
036         * Estimates the regression parameters b.
037         *
038         * @return The [k,1] array representing b
039         */
040        double[] estimateRegressionParameters();
041    
042        /**
043         * Estimates the variance of the regression parameters, ie Var(b).
044         *
045         * @return The [k,k] array representing the variance of b
046         */
047        double[][] estimateRegressionParametersVariance();
048    
049        /**
050         * Estimates the residuals, ie u = y - X*b.
051         *
052         * @return The [n,1] array representing the residuals
053         */
054        double[] estimateResiduals();
055    
056        /**
057         * Returns the variance of the regressand, ie Var(y).
058         *
059         * @return The double representing the variance of y
060         */
061        double estimateRegressandVariance();
062    
063        /**
064         * Returns the standard errors of the regression parameters.
065         *
066         * @return standard errors of estimated regression parameters
067         */
068         double[] estimateRegressionParametersStandardErrors();
069    
070    }