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 * https://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
18 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22 package org.hipparchus.stat.regression;
23
24 /**
25 * The multiple linear regression can be represented in matrix-notation.
26 * <pre>
27 * y=X*b+u
28 * </pre>
29 * 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
30 * <b>regressors</b>, b is <code>k-vector</code> of <b>regression parameters</b> and <code>u</code> is an <code>n-vector</code>
31 * of <b>error terms</b> or <b>residuals</b>.
32 *
33 * The notation is quite standard in literature,
34 * cf eg <a href="http://www.econ.queensu.ca/ETM">Davidson and MacKinnon, Econometrics Theory and Methods, 2004</a>.
35 */
36 public interface MultipleLinearRegression {
37
38 /**
39 * Estimates the regression parameters b.
40 *
41 * @return The [k,1] array representing b
42 */
43 double[] estimateRegressionParameters();
44
45 /**
46 * Estimates the variance of the regression parameters, ie Var(b).
47 *
48 * @return The [k,k] array representing the variance of b
49 */
50 double[][] estimateRegressionParametersVariance();
51
52 /**
53 * Estimates the residuals, ie u = y - X*b.
54 *
55 * @return The [n,1] array representing the residuals
56 */
57 double[] estimateResiduals();
58
59 /**
60 * Returns the variance of the regressand, ie Var(y).
61 *
62 * @return The double representing the variance of y
63 */
64 double estimateRegressandVariance();
65
66 /**
67 * Returns the standard errors of the regression parameters.
68 *
69 * @return standard errors of estimated regression parameters
70 */
71 double[] estimateRegressionParametersStandardErrors();
72
73 }