1、demo
package com.math.demo; import java.math.BigDecimal; import com.math.regression.RegressionEquation; import com.math.regression.RegressionModel; /*** * * @author miaoyibo * */ public class RegressionDemo { public static void main(String[] args) { double[] dependentValues= {58,105,88,118,117,137,157,169,149,202}; double[] independentValues= {2,6,8,8,12,16,20,20,22,26}; RegressionEquation re=new RegressionEquation(dependentValues, independentValues); RegressionModel regressionModel = re.getRegressionModel(); System.out.println("b0=="+regressionModel.getB0()); System.out.println("b1=="+regressionModel.getB1()); System.out.println("coefficient of determination=="+regressionModel.getR()); System.out.println("T test=="+new BigDecimal(+regressionModel.getP())); } }2、实现
package com.math.regression; import org.apache.commons.math3.stat.descriptive.moment.Mean; import JSci.maths.statistics.TDistribution; /*** * least squares method * @author miaoyibo * */ public class RegressionEquation { //因变量y private double[] dependentValues; //自变量x private double[] independentValues; Mean meanUtil = new Mean(); double xmean; double ymean; double sse; double sst; public RegressionEquation(double[] dependentValues, double[] independentValues) { this.dependentValues = dependentValues; this.independentValues = independentValues; xmean=meanUtil.evaluate(independentValues); ymean=meanUtil.evaluate(dependentValues); } public RegressionModel getRegressionModel() { RegressionModel model=new RegressionModel(); double[] regression = calRegression(); double sse=0; double sst=0; for(int i=0;i<dependentValues.length;i++) { double yi=independentValues[i]*regression[1]+regression[0]; double y=dependentValues[i]; sse=sse+(y-yi)*(y-yi); sst=sst+(y-ymean)*(y-ymean); } double coefficientOfDetermination = (sst-sse)/sst; model.setB0(regression[0]); model.setB1(regression[1]); model.setR(coefficientOfDetermination); Ttest(sse,model); return model; } /*** * 计算回归方程 * @return */ public double[] calRegression() { if(dependentValues.length!=independentValues.length) { return null; } double numerator=0d; double denominator=0d; for(int i=0;i<dependentValues.length;i++) { double x=independentValues[i]; double y=dependentValues[i]; numerator=numerator+(x-xmean)*(y-ymean); denominator=denominator+(x-xmean)*(x-xmean); } double b1=numerator/denominator; double b0=ymean-b1*xmean; double[] model= {b0,b1}; return model; } /*** * 利用T检验检验两个变量之间是否存在一个显著的回归关系。 * @return */ private void Ttest(double sse,RegressionModel model) { //计算标准误差 //自由度为2，因为涉及两个变量。 double s=Math.sqrt(sse/(dependentValues.length-2)); //计算标准差 double xx=0; for(int i=0;i<independentValues.length;i++) { double xi=independentValues[i]; xx=xx+((xi-xmean)*(xi-xmean)); } double sb=s/Math.sqrt(xx); //计算t值 double t=model.getB1()/sb; //计算p值 TDistribution td=new TDistribution(dependentValues.length-2); double cumulative = td.cumulative(t); double p; if(t>0) { p=(1-cumulative)*2; }else { p=cumulative*2; } model.setP(p); } } package com.math.regression; public class RegressionModel { //y轴截距 private double b0; //斜率 private double b1; //判定系数 private double r; private double p; public double getB0() { return b0; } public void setB0(double b0) { this.b0 = b0; } public double getB1() { return b1; } public void setB1(double b1) { this.b1 = b1; } public double getR() { return r; } public void setR(double r) { this.r = r; } public double getP() { return p; } public void setP(double p) { this.p = p; } }