NMath User's Guide

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42.5 Significance of Parameters (.NET, C#, CSharp, VB, Visual Basic, F#)

Instances of class LinearRegressionParameter test statistical hypothesis about individual parameters in a LinearRegression.

Creating Linear Regression Parameter Objects

You can construct a LinearRegressionParameter from a LinearRegression object and the index of the parameter you wish to test. For instance, this code creates a test object for the third parameter:

Code Example – C# linear regression

var param = new LinearRegressionParameter( lr, 2 );

Code Example – VB linear regression

Dim Param As New LinearRegressionParameter(LR, 2)

Alternatively, you can get an array of test objects for all parameters in a linear regression using the ParameterEstimates property on LinearRegression:

Code Example – C# linear regression

LinearRegressionParameter[] params = lr.ParameterEstimates;

Code Example – VB linear regression

Dim Params() As LinearRegressionParameter = LR.ParameterEstimates

Properties Linear Regression Parameters

Class LinearRegressionParameter provides the following properties:

● Value gets the value of the parameter.

● StandardError gets the standard error of the parameter.

● ParameterIndex gets the index of the parameter in the linear regresssion.

Hypothesis Tests

Class LinearRegressionParameter provides the following methods for testing statistical hypotheses regarding parameter values:

● TStatisticPValue() returns the p-value for a two-sided t test with the null hypothesis that the parameter is equal to a given test value, versus the alternative hypothesis that it is not.

● TStatistic() returns the value of the t statistic for the null hypothesis that the parameter value is equal to a given test value.

● TStatisticCriticalValue() gets the critical value for the t-statistic for a given alpha level.

● ConfidenceInterval() returns a confidence interval for the parameter for a given alpha level.

For example, this code tests whether the fifth parameter in a model is significantly different than zero:

Code Example – C# linear regression

var param = new LinearRegressionParameter( lr, 4 );

double tstat = param.TStatistic( 0.0 );

double pValue = param.TStatisticPValue( 0.0 );

double criticalValue = param.TStatisticCriticalValue( 0.05 );

Interval confidenceInterval = param.ConfidenceInterval( 0.05 );

Code Example – VB linear regression

Dim Param As New LinearRegressionParameter(LR, 4)

Dim TStat As Double = Param.TStatistic(0.0)

Dim PValue As Double = Param.TStatisticPValue(0.0)

Dim CriticalValue As Double = Param.TStatisticCriticalValue(0.05)

Dim ConfidenceInterval As Interval = Param.ConfidenceInterval(0.05)

Updating Linear Regression Parameters

The SetRegression() method updates the regression and parameter index in a parameter test object:

Code Example – C# linear regression

param.SetRegression( lr, 6 );

Code Example – VB linear regression

Param.SetRegression(LR, 6)

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