//6_4.cpp
#include<iostream>
#include<cmath>
#include "point.h"
using namespace std;
float linefit(Point l_point[], int n_point)	//友元函數體
{
	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a
	cout<<" b="<<av_y-L_xy*av_x/L_xx<<endl;	//輸出回歸系數b
	return float(L_xy/sqrt(L_xx*L_yy));	//返回相關系數r
}

void 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)};	//初始化數據點
	float r=linefit(l_p,10);	//進行線性回歸計算
	cout<<"Line coefficient r="<<r<<endl;	//輸出相關系數
}