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/*
* 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.
* <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.
*
* @return The [k,1] array representing b
*/
double[] estimateRegressionParameters();
/**
* 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.
*
* @return The [n,1] array representing the residuals
*/
double[] estimateResiduals();
/**
* 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.
*
* @return standard errors of estimated regression parameters
*/
double[] estimateRegressionParametersStandardErrors();
}
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