Example of least square method in simple linearity (C # source code)

If the given experimental data point is (XI, Yi), where I =,... n, then the sum of squared deviation between a straight line and a data point is

To make

To obtain the minimum value, the following requirements are required:

,

These two formulas are necessary to obtain the minimum value. The specific operation process is as follows:

The formula is obtained as follows:

Here is what I do with C #Source code:

Public   Class Leastsquare
{
///   <Summary>
/// To draw Linear Least Square Fitting Curve
///   </Summary>
///   <Param name = "G"> The device on which to draw the curve </Param>
///   <Param name = "LP"> A list of point used to do the approximation </Param>
Public   Static   Void Leastsquare2 (Graphics g, list < Pointf > LP)
{
// Clear the client window with the white color
G. Clear (color. White );

//Move the drawing origin to the point (200,200)
G. translatetransform (200,200);

// Use fillellipse method to draw each point as an ellipse
Foreach (Pointf P In LP)
{
G. fillellipse (brushes. Red, New Rectanglef (p. x -   5.0f , P. Y -   5.0f , 10.0f , 10.0f ));
}

Int I;
Float A, B, sumx, sumy2, Sumy, sumxy;
Sumx =   0.0f ;
Sumy2 =   0.0f ;
Sumy =   0.0f ;
Sumxy =   0.0f ;

// To calculate as per the description of the mathematical Formular
For (I =   0 ; I < LP. Count; I ++ )
{
Sumy + = Lp [I]. Y;
Sumy2 + = Lp [I]. Y * Lp [I]. Y;
Sumx + = Lp [I]. X;
Sumxy + = Lp [I]. x * Lp [I]. Y;
}

// Deduct the coefficients required to do the approximation using the mathematical Formular
A = (LP. Count * Sumxy - Sumx * Sumy) / (LP. Count * Sumy2 - Sumy * Sumy );
B = (Sumy2 * Sumx - Sumy * Sumxy) / (LP. Count * Sumy2 - Sumy * Sumy );

Pen newpen =   New Pen (color. Blue, 3.0f );
G. drawline (newpen, New Pointf ( 0 , - B / A ), New Pointf ( 360 ,( 360   - B) / A ));
}
}

The following is the call of the above Code Of Program : Private   Void Lineartoolstripmenuitem_click ( Object Sender, eventargs E)
{
// Declare a list of points
List < Pointf > Lp =   New List < Pointf > ();

// Pointf Array
Pointf [] pf =   New Pointf [] {
New Pointf ( 0.0f , 68366f ),
New Pointf ( 10.0f , 73.1f ), New Pointf ( 20366f , 66.4f ),
New Pointf ( 30366f , 70.6f ), New Pointf ( 40f , 64.6f ),
New Pointf ( 50366f , 68.8f ), New Pointf ( 60366f , 61.0f ),
New Pointf ( 70.0f , 65.8f ), New Pointf ( 80366f , 60.4f ),
New Pointf ( 90.0f , 61.0f )
};

// using addrange method of the List to add the pointf array to the end of the list
LP. addrange (PF);

//Call the static metod leastsquare2 of leastsquare class to proceed
Leastsquare. leastsquare2 (This. Creategraphics (), LP );
}

The following is the screen shot of the program running result ):

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