摘要：
最小二乘法的原理非常简单，这里不再赘述。对于预测公式y’=a*x+b，最优解如下：双a=Sxy/Sxx；doubleb=yAvg-a*xAvg；doubler=Sxy/数学。sqrt；式中，r为相关系数。绝对值越大，线性相关性越大。通过计算f（a，b）=^2的极值，可以获得上述解。
最小二乘法原理十分简单，这里不再赘述。对于预测公式y' = a * x + b，最优解如下
double a = Sxy / Sxx;
double b = yAvg - a * xAvg;
double r = Sxy / Math.sqrt(Sxx * Syy);
其中，r为相关系数，绝对值越大，线性相关性越大。对f(a, b) = (y - y')^2求极值，即可得到上述解。
package coshaho.learn; import java.util.HashMap; import java.util.Map; import java.util.Random; /** * 最小二乘法 * @author coshaho * */ public class MyLineRegression { /** * 最小二乘法 * @param X * @param Y * @return y = ax + b, r */ public Map<String, Double> lineRegression(double[] X, double[] Y) { if(null == X || null == Y || 0 == X.length || 0 == Y.length || X.length != Y.length) { throw new RuntimeException(); } // x平方差和 double Sxx = varianceSum(X); // y平方差和 double Syy = varianceSum(Y); // xy协方差和 double Sxy = covarianceSum(X, Y); double xAvg = arraySum(X) / X.length; double yAvg = arraySum(Y) / Y.length; double a = Sxy / Sxx; double b = yAvg - a * xAvg; // 相关系数 double r = Sxy / Math.sqrt(Sxx * Syy); Map<String, Double> result = new HashMap<String, Double>(); result.put("a", a); result.put("b", b); result.put("r", r); return result; } /** * 计算方差和 * @param X * @return */ private double varianceSum(double[] X) { double xAvg = arraySum(X) / X.length; return arraySqSum(arrayMinus(X, xAvg)); } /** * 计算协方差和 * @param X * @param Y * @return */ private double covarianceSum(double[] X, double[] Y) { double xAvg = arraySum(X) / X.length; double yAvg = arraySum(Y) / Y.length; return arrayMulSum(arrayMinus(X, xAvg), arrayMinus(Y, yAvg)); } /** * 数组减常数 * @param X * @param x * @return */ private double[] arrayMinus(double[] X, double x) { int n = X.length; double[] result = new double[n]; for(int i = 0; i < n; i++) { result[i] = X[i] - x; } return result; } /** * 数组求和 * @param X * @return */ private double arraySum(double[] X) { double s = 0 ; for( double x : X ) { s = s + x ; } return s ; } /** * 数组平方求和 * @param X * @return */ private double arraySqSum(double[] X) { double s = 0 ; for( double x : X ) { s = s + Math.pow(x, 2) ; ; } return s ; } /** * 数组对应元素相乘求和 * @param X * @return */ private double arrayMulSum(double[] X, double[] Y) { double s = 0 ; for( int i = 0 ; i < X.length ; i++ ) { s = s + X[i] * Y[i] ; } return s ; } public static void main(String[] args) { Random random = new Random(); double[] X = new double[20]; double[] Y = new double[20]; for(int i = 0; i < 20; i++) { X[i] = Double.valueOf(Math.floor(random.nextDouble() * 97)); Y[i] = Double.valueOf(Math.floor(random.nextDouble() * 997)); } System.out.println(new MyLineRegression().lineRegression(X, Y)); } }