C#直线的最小二乘法线性回归运算例子代码，本实例讲述了C#直线的最小二乘法线性回归运算方法。
1.Point结构
在编写C#窗体应用程序的时候，由于引用了System.Drawing命名空间，其中自带了Point结构，本文中的例子是一个控制台应用程序，因此自己制作了一个Point结构
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/// <summary>/// 二维笛卡尔坐标系坐标/// </summary>public
struct
Point{public
double
X;public
double
Y;public
Point(double
x = 0, double
y = 0){X = x;Y = y;}} |
2.线性回归
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/// <summary>/// 对一组点通过最小二乘法进行线性回归/// </summary>/// <param name="parray"></param>public
static
void
LinearRegression(Point[] parray){//点数不能小于2if
(parray.Length < 2){Console.WriteLine("点的数量小于2，无法进行线性回归");return;}//求出横纵坐标的平均值double
averagex = 0, averagey = 0;foreach
(Point p in
parray){averagex += p.X;averagey += p.Y;}averagex /= parray.Length;averagey /= parray.Length;//经验回归系数的分子与分母double
numerator = 0;double
denominator = 0;foreach
(Point p in
parray){numerator += (p.X - averagex) * (p.Y - averagey);denominator += (p.X - averagex) * (p.X - averagex);}//回归系数b（Regression Coefficient）double
RCB = numerator / denominator;//回归系数adouble
RCA = averagey - RCB * averagex;Console.WriteLine("回归系数A： "
+ RCA.ToString("0.0000"));Console.WriteLine("回归系数B： "
+ RCB.ToString("0.0000"));Console.WriteLine(string.Format("方程为： y = {0} + {1} * x",RCA.ToString("0.0000"), RCB.ToString("0.0000")));//剩余平方和与回归平方和double
residualSS = 0; //（Residual Sum of Squares）double
regressionSS = 0; //（Regression Sum of Squares）foreach
(Point p in
parray){residualSS +=(p.Y - RCA - RCB * p.X) *(p.Y - RCA - RCB * p.X);regressionSS +=(RCA + RCB * p.X - averagey) *(RCA + RCB * p.X - averagey);}Console.WriteLine("剩余平方和： "
+ residualSS.ToString("0.0000"));Console.WriteLine("回归平方和： "
+ regressionSS.ToString("0.0000"));} |
3.Main函数调用
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static
void
Main(string[] args){//设置一个包含9个点的数组Point[] array = new
Point[9];array[0] = new
Point(0, 66.7);array[1] = new
Point(4, 71.0);array[2] = new
Point(10, 76.3);array[3] = new
Point(15, 80.6);array[4] = new
Point(21, 85.7);array[5] = new
Point(29, 92.9);array[6] = new
Point(36, 99.4);array[7] = new
Point(51, 113.6);array[8] = new
Point(68, 125.1);LinearRegression(array);Console.Read();} |
4.运行结果
