**6.2****
****Regression Results** (.NET, C#, CSharp, VB, Visual Basic, F#)

Class **LinearRegression**
provides the following properties for accessing the regression results:

● IsGood gets a boolean value indicating whether or not the model parameters were successfully computed.

● ParameterCalculationErrorMessage gets any error message produced by the regression calculation object.

● Parameters gets the vector of computed model parameters.

● ParameterEstimates gets an array of **LinearRegressionParameter** objects suitable
for performing hypothesis testing on individual parameters (see Section 6.5).

● Residuals gets the vector of residuals. This is the difference between the vector of observed values and the values predicted by the model.

● Variance gets an estimate of the variance. This is the residual sum of squares divided by the degrees of freedom for the model. The degrees of freedom for the model is equal to the difference between the number of observations and the number of parameters.

● CovarianceMatrix gets the covariance matrix (sometimes
called the *dispersion matrix* or *variance-covariance matrix*).

GetStandardizedResiduals() gets the standardized residuals (also known as the internally studentized residuals). The residuals are renormalized to have unit variance using an overall measure of error variance.

GetStudentizedResiduals()
gets the (externally) studentized residuals, which renormalizes
the residuals to have unit variance using a leave-one-out measure of
error variance—that is, a vector of estimates of the residual variance
obtained when the *i*-th case is dropped
from the regression.

For more information about a linear regression fit, you can perform hypothesis tests on individual parameters (Section 6.5) or the overall model (Section 6.6).

You can also modify the model and recalculate the parameters, as described in Section 6.4.

**Variance Inflation Factor**

The variance inflation factor (VIF) quantifies
the severity of multicollinearity in a least squares regression analysis—that
is, how much the variance of a coefficient is increased because of collinearity.
Class **LinearRegression** provides
methods VarianceInflationFactor() and VarianceInflationFactors() for this purpose. For
instance:

Code Example – C# linear regression

DoubleVector vif = lr.VarianceInflationFactors();