/*
 * 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;

The multiple linear regression can be represented in matrix-notation.
 y=X*b+u

where y is an n-vector regressand, X is a [n,k] matrix whose k columns are called
regressors, b is k-vector of regression parameters and u is an n-vector
of error terms or residuals.
The notation is quite standard in literature,
cf eg Davidson and MacKinnon, Econometrics Theory and Methods, 2004.
Since:
2.0/**
 * The multiple linear regression can be represented in matrix-notation.
 * <pre>
 *  y=X*b+u
 * </pre>
 * 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
 * <b>regressors</b>, b is <code>k-vector</code> of <b>regression parameters</b> and <code>u</code> is an <code>n-vector</code>
 * of <b>error terms</b> or <b>residuals</b>.
 *
 * The notation is quite standard in literature,
 * cf eg <a href="http://www.econ.queensu.ca/ETM">Davidson and MacKinnon, Econometrics Theory and Methods, 2004</a>.
 * @since 2.0
 */
public interface MultipleLinearRegression {

    
Estimates the regression parameters b.
Returns:
The [k,1] array representing b/**
     * Estimates the regression parameters b.
     *
     * @return The [k,1] array representing b
     */
    double[] estimateRegressionParameters();

    
Estimates the variance of the regression parameters, ie Var(b).
Returns:
The [k,k] array representing the variance of b/**
     * Estimates the variance of the regression parameters, ie Var(b).
     *
     * @return The [k,k] array representing the variance of b
     */
    double[][] estimateRegressionParametersVariance();

    
Estimates the residuals, ie u = y - X*b.
Returns:
The [n,1] array representing the residuals/**
     * Estimates the residuals, ie u = y - X*b.
     *
     * @return The [n,1] array representing the residuals
     */
    double[] estimateResiduals();

    
Returns the variance of the regressand, ie Var(y).
Returns:
The double representing the variance of y/**
     * Returns the variance of the regressand, ie Var(y).
     *
     * @return The double representing the variance of y
     */
    double estimateRegressandVariance();

    
Returns the standard errors of the regression parameters.
Returns:
standard errors of estimated regression parameters/**
     * Returns the standard errors of the regression parameters.
     *
     * @return standard errors of estimated regression parameters
     */
     double[] estimateRegressionParametersStandardErrors();

}