float Yi&＃61; (float)Integer.parseInt(listY.get(i).toString());
float Y &＃61; at(Integer.parseInt(listX.get(i).toString()));
float deltaY &＃61; Yi - Y;
float deltaY2 &＃61; deltaY*deltaY;
/*
System.out.println("Yi:" &＃43; Yi);
System.out.println("Y:" &＃43; Y);
System.out.println("deltaY:" &＃43; deltaY);
System.out.println("deltaY2:" &＃43; deltaY2);
*/
sumDeltaY2 &＃43;&＃61; deltaY2;
//System.out.println("sumDeltaY2:" &＃43; sumDeltaY2);
}
sst &＃61; sumYY - (sumY*sumY)/pn;
//System.out.println("sst:" &＃43; sst);
E &＃61;1- sumDeltaY2/sst;
return round(E,4) ;
}
//用于实现精确的四舍五入
public double round(double v,int scale){
if(scale<0){
throw new IllegalArgumentException(
"The scale must be a positive integer or zero");
}
BigDecimal b &＃61; new BigDecimal(Double.toString(v));
BigDecimal one &＃61; new BigDecimal("1");
return b.divide(one,scale,BigDecimal.ROUND_HALF_UP).doubleValue();
}
public float round(float v,int scale){
if(scale<0){
throw new IllegalArgumentException(
"The scale must be a positive integer or zero");
}
BigDecimal b &＃61; new BigDecimal(Double.toString(v));
BigDecimal one &＃61; new BigDecimal("1");
return b.divide(one,scale,BigDecimal.ROUND_HALF_UP).floatValue();
}
}
演示程序&＃xff1a;
LinearRegression.java
/**
*
Linear Regression
*
* Demonstrate linear regression by constructing the regression line for a set
* of data points.
*
*
require DataPoint.java,RegressionLine.java
*
*
为了计算对于给定数据点的最小方差回线&＃xff0c;需要计算SumX,SumY,SumXX,SumXY; (注&＃xff1a;SumXX &＃61; Sum (X^2))
*
回归直线方程如下&＃xff1a; f(x)&＃61;a1x&＃43;a0
*
斜率和截距的计算公式如下&＃xff1a;
*
n: 数据点个数
*
a1&＃61;(n(SumXY)-SumX*SumY)/(n*SumXX-(SumX)^2)
*
a0&＃61;(SumY - SumY * a1)/n
*
(也可表达为a0&＃61;averageY-a1*averageX)
*
*
画线的原理&＃xff1a;两点成一直线&＃xff0c;只要能确定两个点即可
* 第一点&＃xff1a;(0,a0) 再随意取一个x1值代入方程&＃xff0c;取得y1&＃xff0c;连结(0,a0)和(x1,y1)两点即可。
* 为了让线穿过整个图,x1可以取横坐标的最大值Xmax&＃xff0c;即两点为(0,a0),(Xmax,Y)。如果y&＃61;a1*Xmax&＃43;a0,y大于
* 纵坐标最大值Ymax&＃xff0c;则不用这个点。改用y取最大值Ymax&＃xff0c;算得此时x的值&＃xff0c;使用(X,Ymax)&＃xff0c; 即两点为(0,a0),(X,Ymax)
*
*
拟合度计算&＃xff1a;(即Excel中的R^2)
*
*R2 &＃61; 1 - E
*
误差E的计算&＃xff1a;E &＃61; SSE/SST
*
SSE&＃61;sum((Yi-Y)^2) SST&＃61;sumYY - (sumY*sumY)/n;
*
*/
public class LinearRegression
{
private static final int MAX_POINTS &＃61; 10;
private double E;
/**
* Main program.
*
* &＃64;param args
* the array of runtime arguments
*/
public static void main(String args[])
{
RegressionLine line &＃61; new RegressionLine();
line.addDataPoint(new DataPoint(20, 136));
line.addDataPoint(new DataPoint(40, 143));
line.addDataPoint(new DataPoint(60, 152));
line.addDataPoint(new DataPoint(80, 162));
line.addDataPoint(new DataPoint(100, 167));
printSums(line);
printLine(line);
}
/**
* Print the computed sums.
*
* &＃64;param line
* the regression line
*/
private static void printSums(RegressionLine line)
{
System.out.println("\n数据点个数 n &＃61; " &＃43; line.getDataPointCount());
System.out.println("\nSum x &＃61; " &＃43; line.getSumX());
System.out.println("Sum y &＃61; " &＃43; line.getSumY());
System.out.println("Sum xx &＃61; " &＃43; line.getSumXX());
System.out.println("Sum xy &＃61; " &＃43; line.getSumXY());
System.out.println("Sum yy &＃61; " &＃43; line.getSumYY());
}
/**
* Print the regression line function.
*
* &＃64;param line
* the regression line
*/
private static void printLine(RegressionLine line)
{
System.out.println("\n回归线公式: y &＃61; " &＃43;
line.getA1() &＃43;
"x &＃43; " &＃43; line.getA0());
System.out.println("拟合度&＃xff1a; R^2 &＃61; " &＃43; line.getR());
}
}
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