java实现简单线性回归—显著性检验

Bertha 。 2023-02-22 14:00 60阅读 0赞

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;
    	}
    	
    	
    
    }