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.
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)