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package com.util;
/**
* 作者:杜航 功能:最小二乘法 线性回归(Least squares)
*
* y = a x + b b = sum( y ) / n - a * sum( x ) / n a = ( n * sum( xy ) - sum( x
* ) * sum( y ) ) / ( n * sum( x^2 ) - sum(x) ^ 2 )
*
*/
public class LeastSquares
{
/*
* 杜航 功能:返回估计的y值
*/
public static float estimate(float[] x, float[] y, float input)
{
float a = getA(x, y);
float b = getB(x, y);
System.out.println("线性回归系数a值:\t" + a + "\n" + "线性回归系数b值:\t" + b);
return (a * input + b);
}
/*
* 杜航 功能:返回x的系数a 公式:a = ( n sum( xy ) - sum( x ) sum( y ) ) / ( n sum( x^2 )
* - sum(x) ^ 2 )
*/
public static float getA(float[] x, float[] y)
{
int n = x.length;
return (float) ((n * pSum(x, y) - sum(x) * sum(y)) / (n * sqSum(x) - Math
.pow(sum(x), 2)));
}
/*
* 杜航 功能:返回常量系数系数b 公式:b = sum( y ) / n - a sum( x ) / n
*/
public static float getB(float[] x, float[] y)
{
int n = x.length;
float a = getA(x, y);
return sum(y) / n - a * sum(x) / n;
}
/*
* 杜航 功能:求和
*/
private static float sum(float[] ds)
{
float s = 0;
for (float d : ds)
{
s = s + d;
}
return s;
}
/*
* 杜航 功能:求平方和
*/
private static float sqSum(float[] ds)
{
float s = 0;
for (float d : ds)
{
s = (float) (s + Math.pow(d, 2));
}
return s;
}
/*
* 杜航 功能:返回对应项相乘后的和
*/
private static float pSum(float[] x, float[] y)
{
float s = 0;
for (int i = 0; i < x.length; i++)
{
s = s + x[i] * y[i];
}
return s;
}
/*
* 杜航 功能:main()测试线性回归的最小二乘法java实现函数
*/
public static void main(String[] args)
{
float[] x =
// { 540, 360, 240, 480, 420 };
{ 205, 325, 445, 505, 625 };
float[] y =
// { 520, 475, 430, 386, 500 };
{ 100, 123, 148, 407, 319, 301 };
System.out.println("经线性回归后的y值:\t" + estimate(x, y,240));
}
}