最小平方法求回归系数
最小平方法（least-squares solution）
- 最佳拟合线：目标是使误差最小，即这条线与所有的数据点最近。
- 回归线是给定X，a和b，用公式(线性方程)来预测Y的值。
- 最小平方法：先求出每一个Y的实际值与预测值之间的距离并求平方，然后计算误差的平方和来确定直线和真实数据的总误差，与实际数据点误差平方和最小的直线就是最佳拟合线。
- 最小二乘法(ordinary least squares, OLS)
- SP为离差的乘积和，SSx为X的误差平方和，Sy和Sx分别是Y和X的标准差
- 矩阵形式：b = (X’X)^-1 X’y
- Best fit line：The goal is to minimize the error, which means that this line is closest to all data points.
- The regression line is used to predict the value of Y using the formula (linear equation) given X, a, and b.
- Least squares method：First, calculate the distance between the actual and predicted values of each Y and square it. Then, calculate the sum of squared errors to determine the total error between the line and the actual data. The line with the smallest sum of squared errors with the actual data points is the best fit line.
- Ordinary least squares, OLS
- SP is the product sum of deviations, SSx is the sum of squared errors of X, Sy and Sx are the standard deviations of Y and X, respectively
- Matrix form：b = (X’X)^-1 X’y
最小平方法求回归系数.txt · 最后更改: 2024/04/12 04:44 由 2104龚文滕