一元线性回归模型控制方程求解

梅国平，袁捷敏，毛小兵，李杰编著《概率论与数理统计》，科学出版社，2007年版P.268给出一个一元线性回归模型控制问题求解方程组：书中解得p1=2.51 p2=2.48上述控制方程组的解可以表示成两条曲线中间夹一条直线与直线y=2、直线y=3相交的四个交点所对应的横坐标x值。

用mathematica软件做出的示意图如下，mathematic软件中相应的隐函数作图命令为：用Java语言编写出求解类似控制方程组求解程序。

程序求解过程的难点在于上述方程组中的根号开方部分，这个程序把解上述复杂方程组的根号开方问题转化为求一个一元二次方程的两个根。

借鉴其他参考书中有关论述，用被控区间两个端点的中心对应的回归直线上投影点横坐标x值，代替控制方程中根号下的未知数，近似讨论了一下控制区间的长度是否满足可控条件，不是很准确。

精确讨论上述控制方程组的可控问题比较复杂，这个程序没有实现。

程序运行启动界面截图：点击“求解”按钮后程序运行界面截图：源程序清单如下：主程序：一元线性回归模型控制方程求解.java/***根据给定的因变量被控区间，求出自变量的施控区间。

**作者：Adam**/public class 一元线性回归模型控制方程求解{public static void main(String args []){界面求解实例= new 界面(6.45,-1.58,2.0,3.0,4.78,2.306,0.2,10.0,2.5); }}输入输出界面类：界面.javaimport javax.swing.JFrame;import javax.swing.JLabel;import javax.swing.JTextField;import javax.swing.JButton;import javax.swing.JPanel;import java.awt.BorderLayout;import java.awt.GridLayout;import java.awt.event.ActionListener; import java.awt.event.ActionEvent; public class 界面{private JFrame 主窗口;private JLabel a标签;private JTextField a;private JLabel b标签;private JTextField b;private JLabel Tn_2标签;private JTextField Tn_2;private JLabel Se标签;private JTextField Se;private JLabel n标签;private JTextField n;private JLabel averageOfX标签;private JTextField averageOfX;private JLabel lxx标签;private JTextField lxx;private JLabel 左端点标签;private JTextField 左端点;private JLabel 右端点标签;private JTextField 右端点;private JLabel 可控否标签;private JLabel 左端点dY原始值;private JLabel 左端点根1标签;private JTextField 左端点根1值;private JLabel 左端点根1dY检验值;private JLabel 左端点根2标签;private JTextField 左端点根2值;private JLabel 左端点根2dY检验值;private JLabel 右端点dY原始值;private JLabel 右端点根1标签;private JTextField 右端点根1值;private JLabel 右端点根1dY检验值;private JLabel 右端点根2标签;private JTextField 右端点根2值;private JLabel 右端点根2dY检验值;private JButton 求解;private 求解按钮动作实际求解;private JButton 重置;private JButton 退出;界面(){初始化界面();实际求解= new 求解按钮动作(this);求解.addActionListener(实际求解);}界面(double originalA,double originalB,double original左端点,double original右端点,double originalLxx,double originalTn_2,double originalSe,double originalN,double originalAverageOfX){初始化界面();a.setText(Double.toString(originalA));b.setText(Double.toString(originalB));左端点.setText(Double.toString(original左端点));右端点.setText(Double.toString(original右端点));lxx.setText(Double.toString(originalLxx));Tn_2.setText(Double.toString(originalTn_2));Se.setText(Double.toString(originalSe));n.setText(Double.toString(originalN));averageOfX.setText(Double.toString(originalAverageOfX));实际求解= new 求解按钮动作(this);求解.addActionListener(实际求解);}private void 初始化界面(){主窗口= new JFrame("一元线性回归模型控制方程求解");主窗口.setSize(900,400);主窗口.setLocation(120,120);a标签= new JLabel("a：");a = new JTextField(20);输入文本框数字检查check = new 输入文本框数字检查(主窗口);a.getDocument().addDocumentListener(check);b标签= new JLabel("b：");b = new JTextField("",20);b.getDocument().addDocumentListener(check);Tn_2标签= new JLabel("Tn_2：");Tn_2 = new JTextField("",20);Tn_2.getDocument().addDocumentListener(check);Se标签= new JLabel("Se：");Se = new JTextField("",20);Se.getDocument().addDocumentListener(check);n标签= new JLabel("n：");n = new JTextField("",20);n.getDocument().addDocumentListener(check);averageOfX标签= new JLabel("average of x：");averageOfX = new JTextField("",20);averageOfX.getDocument().addDocumentListener(check);lxx标签= new JLabel("lxx：");lxx = new JTextField("",20);lxx.getDocument().addDocumentListener(check);左端点标签= new JLabel("左端点：");左端点= new JTextField("",20);左端点.getDocument().addDocumentListener(check);右端点标签= new JLabel("右端点：");右端点= new JTextField("",20);右端点.getDocument().addDocumentListener(check);JPanel 输入第一行= new JPanel();JPanel 输入第二行= new JPanel();JPanel 输入第三行= new JPanel();输入第一行.add(a标签);输入第一行.add(a);输入第一行.add(b标签);输入第一行.add(b);输入第一行.add(Tn_2标签);输入第一行.add(Tn_2);输入第二行.add(Se标签);输入第二行.add(Se);输入第二行.add(n标签);输入第二行.add(n);输入第二行.add(averageOfX标签);输入第二行.add(averageOfX);输入第三行.add(lxx标签);输入第三行.add(lxx);输入第三行.add(左端点标签);输入第三行.add(左端点);输入第三行.add(右端点标签);输入第三行.add(右端点);左端点dY原始值= new JLabel("左端点dy原始值：",JLabel.CENTER); 左端点根1标签= new JLabel("由根1：",JLabel.CENTER);左端点根1值= new JTextField(20);左端点根1dY检验值= new JLabel("dy检验值：",JLabel.CENTER);左端点根2标签= new JLabel("由根2：",JLabel.CENTER);左端点根2值= new JTextField(20);左端点根2dY检验值= new JLabel("dy检验值：",JLabel.CENTER);右端点dY原始值= new JLabel("右端点dy原始值：",JLabel.CENTER); 右端点根1标签= new JLabel("由根1：",JLabel.CENTER);右端点根1值= new JTextField(20);右端点根1dY检验值= new JLabel("dy检验值：",JLabel.CENTER);右端点根2标签= new JLabel("由根2：",JLabel.CENTER);右端点根2值= new JTextField(20);右端点根2dY检验值= new JLabel("dy检验值：",JLabel.CENTER); JPanel rightPoint1 = new JPanel();JPanel rightPoint2 = new JPanel();JPanel rightPoint3 = new JPanel();JPanel leftPoint1 = new JPanel();JPanel leftPoint2 = new JPanel();JPanel leftPoint3 = new JPanel();leftPoint1.add(左端点dY原始值);leftPoint2.add(左端点根1标签);leftPoint2.add(左端点根1值);leftPoint2.add(左端点根1dY检验值);leftPoint3.add(左端点根2标签);leftPoint3.add(左端点根2值);leftPoint3.add(左端点根2dY检验值);rightPoint1.add(右端点dY原始值);rightPoint2.add(右端点根1标签);rightPoint2.add(右端点根1值);rightPoint2.add(右端点根1dY检验值);rightPoint3.add(右端点根2标签);rightPoint3.add(右端点根2值);rightPoint3.add(右端点根2dY检验值);求解= new JButton("求解");重置= new JButton("重置");重置.addActionListener(new 重置按钮动作(this));退出= new JButton("退出");退出.addActionListener(new 退出按钮动作(this));JPanel 按钮行= new JPanel();按钮行.add(求解);按钮行.add(重置);按钮行.add(退出);可控否标签= new JLabel("",JLabel.CENTER);JPanel pointPanel = new JPanel(new GridLayout(11,1)); pointPanel.add(输入第一行);pointPanel.add(输入第二行);pointPanel.add(输入第三行);pointPanel.add(可控否标签);pointPanel.add(leftPoint1);pointPanel.add(leftPoint2);pointPanel.add(leftPoint3);pointPanel.add(rightPoint1);pointPanel.add(rightPoint2);pointPanel.add(rightPoint3);pointPanel.add(按钮行);主窗口.setLayout(new BorderLayout());主窗口.add(pointPanel,BorderLayout.CENTER);主窗口.setVisible(true);主窗口.validate();主窗口.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); }public void set主窗口(JFrame 主窗口){this.主窗口= 主窗口;}public JFrame get主窗口(){return 主窗口;}public void setA标签(JLabel a标签){this.a标签= a标签;}public JLabel getA标签(){return a标签;}public void setA(JTextField a){this.a = a;主窗口.validate();}public JTextField getA(){return a;}public void setB标签(JLabel b标签)this.a标签= a标签;主窗口.validate();}public JLabel getB标签(){return b标签;}public void setB(JTextField b){this.b = b;主窗口.validate();}public JTextField getB(){return b;}public void setTn_2标签(JLabel Tn_2标签) {this.Tn_2标签= Tn_2标签;主窗口.validate();}public JLabel getTn_2标签(){return Tn_2标签;}public void setTn_2(JTextField Tn_2){this.Tn_2 = Tn_2;主窗口.validate();}public JTextField getTn_2(){return Tn_2;}public void setSe标签(JLabel Se标签)this.Se标签= Se标签;主窗口.validate();}public JLabel getSe标签(){return Se标签;}public void setSe(JTextField Se){this.Se = Se;主窗口.validate();}public JTextField getSe(){return Se;}public void setN标签(JLabel n标签){this.n标签= n标签;主窗口.validate();}public JLabel getN标签(){return n标签;}public void setN(JTextField n){this.n = n;主窗口.validate();}public JTextField getN(){return n;}public void setAverageOfX标签(JLabel averageOfX标签)this.averageOfX标签= averageOfX标签;主窗口.validate();}public JLabel getAverageOfX标签(){return averageOfX标签;}public void setAverageOfX(JTextField averageOfX) {this.averageOfX = averageOfX;主窗口.validate();}public JTextField getAverageOfX(){return averageOfX;}public void setLxx标签(JLabel lxx标签){this.lxx标签= lxx标签;主窗口.validate();}public JLabel getLxx标签(){return lxx标签;}public void setLxx(JTextField lxx){this.lxx = lxx;主窗口.validate();}public JTextField getLxx(){return lxx;}public void set左端点标签(JLabel 左端点标签)this.左端点标签= 左端点标签;主窗口.validate();}public JLabel get左端点标签(){return 左端点标签;}public void set左端点(JTextField 左端点){this.左端点= 左端点;主窗口.validate();}public JTextField get左端点(){return 左端点;}public void set右端点标签(JLabel 右端点标签) {this.右端点标签= 右端点标签;主窗口.validate();}public JLabel get右端点标签(){return 右端点标签;}public void set右端点(JTextField 右端点){this.右端点= 右端点;主窗口.validate();}public JTextField get右端点(){return 右端点;}public void set可控否标签(JLabel 可控否标签)this.可控否标签= 可控否标签;主窗口.validate();}public JLabel get可控否标签(){return 可控否标签;}public void set左端点dY原始值(JLabel 左端点dY原始值){this.左端点dY原始值= 左端点dY原始值;主窗口.validate();}public JLabel get左端点dY原始值(){return 左端点dY原始值;}public void set左端点根1标签(JLabel 左端点根1标签){this.左端点根1标签= 左端点根1标签;主窗口.validate();}public JLabel get左端点根1标签(){return 左端点根1标签;}public void set左端点根1值(JTextField 左端点根1值){this.左端点根1值= 左端点根1值;主窗口.validate();}public JTextField get左端点根1值(){return 左端点根1值;}public void set左端点根1dY检验值(JLabel 左端点根1dY检验值)this.左端点根1dY检验值= 左端点根1dY检验值;主窗口.validate();}public JLabel get左端点根1dY检验值(){return 左端点根1dY检验值;}public void set左端点根2标签(JLabel 左端点根2标签){this.左端点根2标签= 左端点根2标签;主窗口.validate();}public JLabel get左端点根2标签(){return 左端点根2标签;}public void set左端点根2值(JTextField 左端点根2值){this.左端点根2值= 左端点根2值;主窗口.validate();}public JTextField get左端点根2值(){return 左端点根2值;}public void set左端点根2dY检验值(JLabel 左端点根2dY检验值) {this.左端点根2dY检验值= 左端点根2dY检验值;主窗口.validate();}public JLabel get左端点根2dY检验值(){return 左端点根2dY检验值;}public void set右端点dY原始值(JLabel 右端点dY原始值)this.右端点dY原始值= 右端点dY原始值;主窗口.validate();}public JLabel get右端点dY原始值(){return 右端点dY原始值;}public void set右端点根1标签(JLabel 右端点根1标签){this.右端点根1标签= 右端点根1标签;主窗口.validate();}public JLabel get右端点根1标签(){return 右端点根1标签;}public void set右端点根1值(JTextField 右端点根1值){this.右端点根1值= 右端点根1值;主窗口.validate();}public JTextField get右端点根1值(){return 右端点根1值;}public void set右端点根1dY检验值(JLabel 右端点根1dY检验值) {this.右端点根1dY检验值= 右端点根1dY检验值;主窗口.validate();}public JLabel get右端点根1dY检验值(){return 右端点根1dY检验值;}public void set右端点根2标签(JLabel 右端点根2标签)this.右端点根2标签= 右端点根2标签;主窗口.validate();}public JLabel get右端点根2标签(){return 右端点根2标签;}public void set右端点根2值(JTextField 右端点根2值){this.右端点根2值= 右端点根2值;主窗口.validate();}public JTextField get右端点根2值(){return 右端点根2值;}public void set右端点根2dY检验值(JLabel 右端点根2dY检验值) {this.右端点根2dY检验值= 右端点根2dY检验值;主窗口.validate();}public JLabel get右端点根2dY检验值(){return 右端点根2dY检验值;}public void set求解(JButton 求解){this.求解= 求解;主窗口.validate();}public JButton get求解(){return 求解;}public void set实际求解(求解按钮动作实际求解)this.实际求解= 实际求解;主窗口.validate();}public 求解按钮动作get实际求解(){return 实际求解;}public void set重置(JButton 重置){this.重置= 重置;主窗口.validate();}public JButton get重置(){return 重置;}public void set退出(JButton 退出){this.退出= 退出;主窗口.validate();}public JButton get退出(){return 退出;}}输入参数是否为数字格式检查类：输入文本框数字检查.java import javax.swing.event.DocumentListener;import javax.swing.event.DocumentEvent;import javax.swing.text.Document;import javax.swing.text.BadLocationException;import javax.swing.JOptionPane;import javax.swing.JFrame;public class 输入文本框数字检查implements DocumentListener {private JFrame 主窗口;输入文本框数字检查()主窗口= null;}输入文本框数字检查(JFrame 主窗口){this.主窗口= 主窗口;}public void set主窗口(JFrame 主窗口){this.主窗口= 主窗口;}public JFrame get主窗口(){return 主窗口;}public void insertUpdate(DocumentEvent e){数字检查(e.getDocument());}public void removeUpdate(DocumentEvent e){数字检查(e.getDocument());}public void changedUpdate(DocumentEvent e){数字检查(e.getDocument());}private void 数字检查(Document doc){double t = 0;try{t = Double.parseDouble(doc.getText(0,doc.getLength())); }catch(BadLocationException e){//System.out.println("文本框字符位置越界！");错误提示("读取文本框字符位置越界！","内部错误");catch(NumberFormatException e){//System.out.println("您输入了非数字字符，请输入数字！");错误提示("您输入了非数字字符，请输入数字！","输入错误");}}private void 错误提示(Object 提示信息,String 标题){JOptionPane.showMessageDialog(主窗口,提示信息,标题,JOptionPane.ERROR_MESSAGE); }}根据输入参数计算施控区间端点值的求解按钮动作类：求解按钮动作.javaimport java.awt.event.ActionListener;import java.awt.event.ActionEvent;import javax.swing.JOptionPane;public class 求解按钮动作implements ActionListener{private 界面源对象;private double a;private double b;private double Tn_2;private double Se;private double n;private double averageOfX;private double lxx;private double 左端点;private double 右端点;private boolean 输入异常;private boolean 可控否;求解按钮动作(){源对象= null;a = 0;b = 0;Tn_2 = 0;Se = 0;n = 0;averageOfX = 0;lxx = 0;左端点= 0;右端点= 0;输入异常= true;可控否= false;}求解按钮动作(界面源对象){this.源对象= 源对象;try{a = Double.parseDouble(源对象.getA().getText());b = Double.parseDouble(源对象.getB().getText());Tn_2 = Double.parseDouble(源对象.getTn_2().getText());Se = Double.parseDouble(源对象.getSe().getText());n = Double.parseDouble(源对象.getN().getText());averageOfX = Double.parseDouble(源对象.getAverageOfX().getText());lxx = Double.parseDouble(源对象.getLxx().getText());左端点= Double.parseDouble(源对象.get左端点().getText());右端点= Double.parseDouble(源对象.get右端点().getText());输入异常= false;}catch(NullPointerException 空文本框){输入异常= true;错误提示("文本框为空，请输入数值！","输入错误");}catch(NumberFormatException 数字格式异常){输入异常= true;错误提示("输入数字格式错误","内部错误");}可控否= false;}public void set源对象(界面源对象){this.源对象= 源对象;}public 界面get源对象(){return 源对象;}public void setA(double a){this.a = a;}public double getA(){return a;}public void setB(double b){this.b = b;}public double getB(){return b;}public void setTn_2(double Tn_2) {this.Tn_2 = Tn_2;}public double getTn_2(){return Tn_2;}public void setSe(double Se) {this.Se = Se;}public double getSe(){return Se;}public void setN(double n){this.n = n;}public double getN(){return n;}public void setAverageOfX(double averageOfX) {this.averageOfX = averageOfX;}public double getAverageOfX(){return averageOfX;}public void setLxx(double lxx){this.lxx = lxx;}public double getLxx(){return lxx;}public void set左端点(double 左端点){this.左端点= 左端点;}public double get左端点(){return 左端点;}public void set右端点(double 右端点){this.右端点= 右端点;}public double get右端点(){return 右端点;}public void set输入异常(boolean 输入异常){this.输入异常= 输入异常;}public boolean get输入异常(){return 输入异常;}public void set可控否(boolean 可控否){this.可控否= 可控否;}public boolean get可控否(){return 可控否;}public void actionPerformed(ActionEvent e){try{a = Double.parseDouble(源对象.getA().getText());b = Double.parseDouble(源对象.getB().getText());Tn_2 = Double.parseDouble(源对象.getTn_2().getText());Se = Double.parseDouble(源对象.getSe().getText());n = Double.parseDouble(源对象.getN().getText());averageOfX = Double.parseDouble(源对象.getAverageOfX().getText());lxx = Double.parseDouble(源对象.getLxx().getText());左端点= Double.parseDouble(源对象.get左端点().getText());右端点= Double.parseDouble(源对象.get右端点().getText());输入异常= false;}catch(NullPointerException 空文本框){输入异常= true;错误提示("文本框为空，请输入数值！","输入错误");}catch(NumberFormatException 数字格式异常){输入异常= true;错误提示("输入数字格式错误","内部错误");}if(输入异常== false){求解端点(左端点,new 左端点());求解端点(右端点,new 右端点());确定是否可控();if(可控否== true){修改可控否标签("被控区间满足可控条件，可以实现控制。