问题描述
我一直在寻找一种在Javascript中执行线性曲线拟合的方法。我发现了几个库，但它们没有传播错误。我的意思是，我有数据和相关的测量误差，如：
I was looking for a way to perform a linear curve fit in Javascript. I found several libraries, but they don't propagate errors. What I mean is, I have data and associated measurement errors, like:
x = [ 1.0 +/- 0.1, 2.0 +/- 0.1, 3.1 +/- 0.2, 4.0 +/- 0.2 ]
y = [ 2.1 +/- 0.2, 4.0 +/- 0.1, 5.8 +/- 0.4, 8.0 +/- 0.1 ]
我的符号 a +/- b 表示 {值：a，错误：b} 。
我想将其纳入 y = mx + b ，找到 m 和 b 及其传播错误。我知道我可以实现的最小二乘法算法，但它只对y变量产生错误，并且我在两者中都有明显的错误。
I want to fit this into y = mx + b, and find m and b with their propagated errors. I know the Least Square Method algorithm, that I could implement, but it only take errors on the y variable, and I have distinct errors in both.
我也找不到Javascript中的库来做到这一点;但如果有一个其他语言的开源库，我可以检查它以了解如何在JS中实现它。
I also could not find a library in Javascript to do that; but if there is an open source lib in other language, I can inspect it to find out how and implement it in JS.
像Origin或plotly这样的程序能够实现这个，但我不知道怎么做。此示例数据集的结果是：
Programs like Origin or plotly are able to implement this, but I don't know how. The result for this example dataset is:
m = 1.93 +/- 0.11
b = 0.11 +/- 0.30
推荐答案
非常有用的书提供了一种将数据拟合到直线上的方法，X和Y坐标都存在不确定性。在这两个版本中可以找到：
The very useful book Numerical Recipes provides a method to fit data to a straight line, with uncertainties in both X and Y coordinates. It can be found online in these two versions:
- ，第15节-3
- ，在
- Numerical Recipes in C, in section 15-3
- Numerical Recipes in Fortran 77, in section 15-3
该方法基于最小化χ （卡方），它与最小二乘法相似，但考虑了每个数据点的个体不确定性。当不确定性σ 仅在Y轴上时，与1 /σ 成比例的权重被分配给计算。当数据在X和Y坐标中存在不确定性时，分别由σ 和σ 给出，适合直线
The method is based on minimizing the χ (chi-square) which is similar to the least-square but takes into account the individual uncertainty of each data point. When the uncertainty σ is on the Y axis only, a weight proportional to 1/σ is assigned to the point in the calculations. When the data has uncertainties in the X and Y coordinates, given by σ and σ respectively, the fit to a straight line
使用χ ，其中每个点的权重与
uses a χ where each point has a weight proportional to
详细方法和代码（在C或Fortran中）可以在书中找到。由于，我无法在此处重现。
The detailed method and the code (in C or Fortran) can be found in the book. Due to copyright, I cannot reproduce them here.
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