（C#）直线的最小二乘法线性回归
（C#）直线的最小二乘法线性回归

（C#）直线的最小二乘法线性回归
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1.Point结构

``````/// <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

``````/// <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2
if (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a
double 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

``````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);

}``````

4.运行结果

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