diff --git a/src/site/xdoc/userguide/stat.xml b/src/site/xdoc/userguide/stat.xml index e63b56fe8..6ad146af4 100644 --- a/src/site/xdoc/userguide/stat.xml +++ b/src/site/xdoc/userguide/stat.xml @@ -473,37 +473,47 @@ System.out.println(regression.getSlopeStdErr());

- - MultipleLinearRegression provides ordinary least squares regression - with a generic multiple variable linear model, which in matrix notation - can be expressed as: + + OLSMultipleLinearRegression and + + GLSMultipleLinearRegression provide least squares regression to fit the linear model:

- y=X*b+u + 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. + 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.

- Two implementations are provided: - OLSMultipleLinearRegression and + + OLSMultipleLinearRegression provides Ordinary Least Squares Regression, and - GLSMultipleLinearRegression + GLSMultipleLinearRegression implements Generalized Least Squares. See the javadoc for these + classes for details on the algorithms and forumlas used.

- Observations (x,y and covariance data matrices) can be added to the model via the addData(double[] y, double[][] x, double[][] covariance) method. - The observations are stored in memory until the next time the addData method is invoked. + Data for OLS models can be loaded in a single double[] array, consisting of concatenated rows of data, each containing + the regressand (Y) value, followed by regressor values; or using a double[][] array with rows corresponding to + observations. GLS models also require a double[][] array representing the covariance matrix of the error terms. See + + AbstractMultipleLinearRegression#newSampleData(double[],int,int), + + OLSMultipleLinearRegression#newSampleData(double[], double[][]) and + + GLSMultipleLinearRegression#newSampleData(double[],double[][],double[][]) for details.

Usage Notes:

@@ -511,44 +521,48 @@ System.out.println(regression.getSlopeStdErr());

OLS regression


-
Instantiate an OLS regression object and load dataset +
Instantiate an OLS regression object and load a dataset: -MultipleLinearRegression regression = new OLSMultipleLinearRegression(); +OLSMultipleLinearRegression regression = new OLSMultipleLinearRegression(); double[] y = new double[]{11.0, 12.0, 13.0, 14.0, 15.0, 16.0}; double[] x = new double[6][]; -x[0] = new double[]{1.0, 0, 0, 0, 0, 0}; -x[1] = new double[]{1.0, 2.0, 0, 0, 0, 0}; -x[2] = new double[]{1.0, 0, 3.0, 0, 0, 0}; -x[3] = new double[]{1.0, 0, 0, 4.0, 0, 0}; -x[4] = new double[]{1.0, 0, 0, 0, 5.0, 0}; -x[5] = new double[]{1.0, 0, 0, 0, 0, 6.0}; -regression.addData(y, x, null); // we don't need covariance +x[0] = new double[]{0, 0, 0, 0, 0}; +x[1] = new double[]{2.0, 0, 0, 0, 0}; +x[2] = new double[]{0, 3.0, 0, 0, 0}; +x[3] = new double[]{0, 0, 4.0, 0, 0}; +x[4] = new double[]{0, 0, 0, 5.0, 0}; +x[5] = new double[]{0, 0, 0, 0, 6.0}; +regression.newSample(y, x);
-
Estimate of regression values honours the MultipleLinearRegression interface: +
Get regression parameters and diagnostics: -double[] beta = regression.estimateRegressionParameters(); +double[] beta = regression.estimateRegressionParameters(); double[] residuals = regression.estimateResiduals(); double[][] parametersVariance = regression.estimateRegressionParametersVariance(); double regressandVariance = regression.estimateRegressandVariance(); + +double rSquared = regression.caclulateRSquared(); + +double sigma = regression.estimateRegressionStandardError();
GLS regression


-
Instantiate an GLS regression object and load dataset +
Instantiate a GLS regression object and load a dataset: -MultipleLinearRegression regression = new GLSMultipleLinearRegression(); +GLSMultipleLinearRegression regression = new GLSMultipleLinearRegression(); double[] y = new double[]{11.0, 12.0, 13.0, 14.0, 15.0, 16.0}; double[] x = new double[6][]; -x[0] = new double[]{1.0, 0, 0, 0, 0, 0}; -x[1] = new double[]{1.0, 2.0, 0, 0, 0, 0}; -x[2] = new double[]{1.0, 0, 3.0, 0, 0, 0}; -x[3] = new double[]{1.0, 0, 0, 4.0, 0, 0}; -x[4] = new double[]{1.0, 0, 0, 0, 5.0, 0}; -x[5] = new double[]{1.0, 0, 0, 0, 0, 6.0}; +x[0] = new double[]{0, 0, 0, 0, 0}; +x[1] = new double[]{2.0, 0, 0, 0, 0}; +x[2] = new double[]{0, 3.0, 0, 0, 0}; +x[3] = new double[]{0, 0, 4.0, 0, 0}; +x[4] = new double[]{0, 0, 0, 5.0, 0}; +x[5] = new double[]{0, 0, 0, 0, 6.0}; double[][] omega = new double[6][]; omega[0] = new double[]{1.1, 0, 0, 0, 0, 0}; omega[1] = new double[]{0, 2.2, 0, 0, 0, 0}; @@ -556,12 +570,9 @@ omega[2] = new double[]{0, 0, 3.3, 0, 0, 0}; omega[3] = new double[]{0, 0, 0, 4.4, 0, 0}; omega[4] = new double[]{0, 0, 0, 0, 5.5, 0}; omega[5] = new double[]{0, 0, 0, 0, 0, 6.6}; -regression.addData(y, x, omega); // we do need covariance +regression.newSampleData(y, x, omega);
-
Estimate of regression values honours the same MultipleLinearRegression interface as - the OLS regression. -