直线拟合相关系数公式 -凯发k8官网

开发语言：c#

在实际项目中，经常需要用到直线拟合，比如已有一些数值，需要插值出一些离散点，本文利用常见的一元线性回归算法和最小二乘法拟合直线。

调用方法：

linefitmethod.linearfit(pionts, out a, out b);

double y1 = linefitmethod.linearval(x, a, b);

dcorr1 = linefitmethod.corrcoef(dy.toarray(), listy.toarray());

（0<|corr(x,y)|<1 表示具有一定线性相关性，越接近1表示越线性相关）

using system;using system.collections.generic;using system.linq;using system.text;using system.threading.tasks;using system.drawing; namespace method.yosao{ /*=================================================== * 类名称: linefitmethod * 类描述:直线拟合及相关系数计算 * 创建人: yosao * 创建时间: 2020/6/6/星期六 11:49:28 * 修改人: * 修改时间: * 版本： @version 1.0 =====================================================*/ class linefitmethod { /// 
 /// 一元线性回归 最小平方算法 /// 将离散点拟合为 y = a x   b 型直线 /// 
 ///  ///  ///  ///  public static bool linearfit(double[] x, double[] y, out double a, out double b) { double xsum = 0; double ysum = 0; double xysum = 0; double x2sum = 0; int size = x.length; if (size < 2) { a = 0; b = 0; return false; } for (int i = 0; i < size; i  ) { xsum = xsum   x[i]; ysum = ysum   y[i]; xysum = xysum   x[i] * y[i]; x2sum = x2sum   x[i] * x[i]; } a = (size * xysum - xsum * ysum) / (size * x2sum - xsum * xsum   1e-10); b = (ysum - a * xsum) / size; return true; } /// 
 /// 计算拟合后的值 /// 
 ///  ///  ///  ///  public static void linearval(double[] x, double a, double b, double[] y) { for (int i = 0; i < x.length; i  ) { y[i] = a * x[i]   b; } } /// 
 /// 计算拟合后的值 /// 
 ///  ///  ///  /// y public static double linearval(double x, double a, double b) { return a * x   b; } /// 
 /// 计算相关系数，线性相关性 /// l=线性相关 0<| corr(x,y)|<1的时候，说明两个随机变量具有一定程度的线性关系。越大线性相关性越强 /// 
 ///  ///  ///  public static double corrcoef(double[] y1, double[] y2) { double xy = 0, x = 0, y = 0, xsum = 0, ysum = 0; double corrc = 0; int m = y1.length; for (int i = 0; i < m; i  ) { xsum  = y1[i]; ysum  = y2[i]; } for (int i = 0; i < m; i  ) { x = x   (m * y1[i] - xsum) * (m * y1[i] - xsum); y = y   (m * y2[i] - ysum) * (m * y2[i] - ysum); xy = xy   (m * y1[i] - xsum) * (m * y2[i] - ysum); } corrc = math.abs(xy) / (math.sqrt(x) * math.sqrt(y)); return corrc; } /// 
 /// * 最小二乘法直线拟合（不是常见的一元线性回归算法） /// * 将离散点拟合为 a x   b y   c = 0 型直线 /// * 假设每个点的 x y 坐标的误差都是符合 0 均值的正态分布的。 /// * 与一元线性回归算法的区别：一元线性回归算法假定 x 是无误差的，只有 y 有误差。 /// * 最后将直线改写为 y = a x   b 形式 /// 
 ///  ///  ///  ///  ///  public static bool linearfit(list points, out double a, out double b) { double c = 0; int size = points.count; if (size < 2) { a = 0; b = 0; c = 0; return false; } double x_mean = 0; double y_mean = 0; for (int i = 0; i < size; i  ) { x_mean  = points[i].x; y_mean  = points[i].y; } x_mean /= size; y_mean /= size; //至此，计算出了 x y 的均值 double dxx = 0, dxy = 0, dyy = 0; for (int i = 0; i < size; i  ) { dxx  = (points[i].x - x_mean) * (points[i].x - x_mean); dxy  = (points[i].x - x_mean) * (points[i].y - y_mean); dyy  = (points[i].y - y_mean) * (points[i].y - y_mean); } double lambda = ((dxx   dyy) - math.sqrt((dxx - dyy) * (dxx - dyy)   4 * dxy * dxy)) / 2.0; double den = math.sqrt(dxy * dxy   (lambda - dxx) * (lambda - dxx)); a = dxy / den; b = (lambda - dxx) / den; c = -a * x_mean - b * y_mean; //将参数由 a x   b y   c = 0转换为y = a x   b if (b != 0) { a = - a / b; b = - c / b; } else { //直线方程则为x=c/a; return false; } return true; } }}

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