如何使用numpy.polyfit查找坡度上的错误并进行拦截 [英] How to find error on slope and intercept using numpy.polyfit

问题描述

我用numpy.polyfit将一条直线拟合到一些数据.数据本身不带有任何错误栏.这是我的代码的简化版本:

I'm fitting a straight line to some data with numpy.polyfit. The data themselves do not come with any error bars. Here's a simplified version of my code:

from numpy import polyfit

data = loadtxt("data.txt")
x,y = data[:,0],data[:,1]
fit = polyfit(x,y,1)

这当然给了我斜率和截距的值，但是如何找到最佳拟合值的不确定性呢?

Of course that gives me the values for the slope and intercept, but how to I find the uncertainty on the best-fit values?

推荐答案

我回答这个问题有点晚了，但是我认为这个问题仍然没有得到解答，对我来说，这是Google上的热门话题.因此，我认为以下是正确的方法

I'm a bit late to answer this, but I think that this question remains unanswered and was the top hit on Google for me. Therefore, I think the following is the correct method

x = np.linspace(0, 1, 100)
y = 10 * x + 2 + np.random.normal(0, 1, 100)

p, V = np.polyfit(x, y, 1, cov=True)

print "x_1: {} +/- {}".format(p[0], np.sqrt(V[0][0]))
print "x_2: {} +/- {}".format(p[1], np.sqrt(V[1][1]))

输出

x_1: 10.2069326441 +/- 0.368862837662
x_2: 1.82929420943 +/- 0.213500166807

因此，您需要返回协方差矩阵V，对于该矩阵，对角线的平方根是每个拟合系数的估计标准偏差.当然，这可以推广到更高的维度.

So you need to return the covariance matrix, V, for which the square root of the diagonals are the estimated standard-deviation for each of the fitted coefficients. This of course generalised to higher dimensions.

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