?? linear_least_squares_fitting_procedure.cpp
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//原理部分請參考有關(guān)資料,這里只給出c++程序。
//point.h
class Point //Point類的聲明
{
public: //外部接口
Point(float xx=0, float yy=0) {X=xx;Y=yy;}
float GetX() {return X;}
float GetY() {return Y;}
friend float linefit(Point l_point[], int n_point); //友元函數(shù)
//int型變量為點數(shù)
private: //私有數(shù)據(jù)成員
float X,Y;
};
//End of point.h
//main.cpp
#include<iostream>
#include<cmath>
#include "point.h"
using namespace std;
float linefit(Point l_point[], int n_point) //友元函數(shù)體
{
float av_x,av_y; //聲明變量
float L_xx,L_yy,L_xy;
//變量初始化
av_x=0; //X的平均值
av_y=0; //Y的平均值
L_xx=0; //Lxx
L_yy=0; //Lyy
L_xy=0; //Lxy
for(int i=0;i<n_point;i++) //計算X、Y的平均值
{
av_x+=l_point[i].X/n_point;
av_y+=l_point[i].Y/n_point;
}
for(i=0;i<n_point;i++) //計算Lxx、Lyy和Lxy
{
L_xx+=(l_point[i].X-av_x)*(l_point[i].X-av_x);
L_yy+=(l_point[i].Y-av_y)*(l_point[i].Y-av_y);
L_xy+=(l_point[i].X-av_x)*(l_point[i].Y-av_y);
}
cout<<"This line can be fitted by y=ax+b."<<endl;
cout<<"a="<<L_xy/L_xx; //輸出回歸系數(shù)a
cout<<" b="<<av_y-L_xy*av_x/L_xx<<endl; //輸出回歸系數(shù)b
return float(L_xy/sqrt(L_xx*L_yy)); //返回相關(guān)系數(shù)r
}
int main()
{
Point l_p[10]={Point(6,10),Point(14,20),Point(26,30),
Point(33,40),Point(46,50),Point(54,60),Point(67,70),
Point(75,80),Point(84,90),Point(100,100)}; //初始化數(shù)據(jù)點
float r=linefit(l_p,10); //進(jìn)行線性回歸計算
cout<<"Line coefficient r="<<r<<endl; //輸出相關(guān)系數(shù)
}
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