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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  package org.apache.commons.math.stat.regression;
18  
19  /**
20   * The multiple linear regression can be represented in matrix-notation.
21   * <pre>
22   *  y=X*b+u
23   * </pre>
24   * 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
25   * <b>regressors</b>, b is <code>k-vector</code> of <b>regression parameters</b> and <code>u</code> is an <code>n-vector</code>
26   * of <b>error terms</b> or <b>residuals</b>.
27   * 
28   * The notation is quite standard in literature, 
29   * cf eg <a href="http://www.econ.queensu.ca/ETM">Davidson and MacKinnon, Econometrics Theory and Methods, 2004</a>.
30   * @version $Revision: 731356 $ $Date: 2009-01-04 15:39:45 -0500 (Sun, 04 Jan 2009) $
31   * @since 2.0
32   */
33  public interface MultipleLinearRegression {
34  
35      /**
36       * Estimates the regression parameters b.
37       * 
38       * @return The [k,1] array representing b
39       */
40      double[] estimateRegressionParameters();
41  
42      /**
43       * Estimates the variance of the regression parameters, ie Var(b).
44       * 
45       * @return The [k,k] array representing the variance of b
46       */
47      double[][] estimateRegressionParametersVariance();
48      
49      /**
50       * Estimates the residuals, ie u = y - X*b.
51       * 
52       * @return The [n,1] array representing the residuals
53       */
54      double[] estimateResiduals();
55  
56      /**
57       * Returns the variance of the regressand, ie Var(y).
58       * 
59       * @return The double representing the variance of y
60       */
61      double estimateRegressandVariance();
62      
63      /**
64       * Returns the standard errors of the regression parameters.
65       * 
66       * @return standard errors of estimated regression parameters
67       */
68       double[] estimateRegressionParametersStandardErrors();
69  
70  }