The routine fits equations to data by minimizing the sum of squared residuals: 

SS = Sum [y(k) - ycalc(k)]^2 , 

where y(k) and ycalc(k) are respectively the observed and calculated value of the dependent variable for observation k. ycalc(k) is a function of the regression parameters b(0) and b(1). In case constant term is used, the observed values obey the following equation: 

y(k) = b(0) + b(1) * x 

i.e 

Y = b(0) + b(1)*X. 

or if constant term is NOT used: 

y(k) = b(0) * x 

To calculate additional regression statistical parameters, use RegressTest routine.

MulLinRegress, RegressTest

The following example loads data for simple linear regression (line equation) and then extracts line parameters b(0)=n and b(1)=k:

using Dew.Math;
using Dew.Stats;
using Dew.Stats.Units;
using Steema.TeeChart;
namespace Dew.Examples
{
  private void Example(Styles.Line series1, Styles.Line series2)
  {
    Vector x = new Vector(0);
    Vector y = new Vector(0);
    Vector b = new Vector(0);
    Vector yhat = new Vector(0);
    x.SetIt(false,new double[] {1.0, 1.5, 2.3, 3.8, 4.2, 5.0, 5.3, 5.9});
    y.SetIt(false,new double[] {11, 12, 12.5, 14, 14.3, 15.2, 15.3, 17});
    LinRegress(x,y,b,null,yhat,null);
    MtxVecTee.DrawValues(x,y,series1,false); // draw original data
    MtxVecTee.DrawValues(x,yhat,series2,false); // draw fitted data
  }
}