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.math4.legacy.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 * @since 2.0
31 */
32 public interface MultipleLinearRegression {
33
34 /**
35 * Estimates the regression parameters b.
36 *
37 * @return The [k,1] array representing b
38 */
39 double[] estimateRegressionParameters();
40
41 /**
42 * Estimates the variance of the regression parameters, ie Var(b).
43 *
44 * @return The [k,k] array representing the variance of b
45 */
46 double[][] estimateRegressionParametersVariance();
47
48 /**
49 * Estimates the residuals, ie u = y - X*b.
50 *
51 * @return The [n,1] array representing the residuals
52 */
53 double[] estimateResiduals();
54
55 /**
56 * Returns the variance of the regressand, ie Var(y).
57 *
58 * @return The double representing the variance of y
59 */
60 double estimateRegressandVariance();
61
62 /**
63 * Returns the standard errors of the regression parameters.
64 *
65 * @return standard errors of estimated regression parameters
66 */
67 double[] estimateRegressionParametersStandardErrors();
68 }