我正在使用polyfit
将数据拟合到一行。该行的方程式为y = mx + b
形式。我正在尝试检索坡度上的误差和y截距上的误差。这是我的代码:
fit, res, _, _, _ = np.polyfit(X,Y,1, full = True)
此方法返回残差。但是我不想要残差。所以这是我使用的另一种方法:
slope, intercept, r_value, p_value, std_err = stats.linregress(X,Y)
我知道
std_err
返回坡度上的错误。我仍然需要获取y截距的标准偏差。我怎样才能做到这一点? 最佳答案
如果可以使用最小二乘拟合,则可以使用以下函数来计算斜率,y截距,相关系数,斜率的标准偏差和y截距的标准偏差:
import numpy as np
def lsqfity(X, Y):
"""
Calculate a "MODEL-1" least squares fit.
The line is fit by MINIMIZING the residuals in Y only.
The equation of the line is: Y = my * X + by.
Equations are from Bevington & Robinson (1992)
Data Reduction and Error Analysis for the Physical Sciences, 2nd Ed."
pp: 104, 108-109, 199.
Data are input and output as follows:
my, by, ry, smy, sby = lsqfity(X,Y)
X = x data (vector)
Y = y data (vector)
my = slope
by = y-intercept
ry = correlation coefficient
smy = standard deviation of the slope
sby = standard deviation of the y-intercept
"""
X, Y = map(np.asanyarray, (X, Y))
# Determine the size of the vector.
n = len(X)
# Calculate the sums.
Sx = np.sum(X)
Sy = np.sum(Y)
Sx2 = np.sum(X ** 2)
Sxy = np.sum(X * Y)
Sy2 = np.sum(Y ** 2)
# Calculate re-used expressions.
num = n * Sxy - Sx * Sy
den = n * Sx2 - Sx ** 2
# Calculate my, by, ry, s2, smy and sby.
my = num / den
by = (Sx2 * Sy - Sx * Sxy) / den
ry = num / (np.sqrt(den) * np.sqrt(n * Sy2 - Sy ** 2))
diff = Y - by - my * X
s2 = np.sum(diff * diff) / (n - 2)
smy = np.sqrt(n * s2 / den)
sby = np.sqrt(Sx2 * s2 / den)
return my, by, ry, smy, sby
print lsqfity([0,2,4,6,8],[0,3,6,9,12])
输出:
(1, 0, 1.0, 0.0, 2.4494897427831779)
该功能由Filipe P. A. Fernandes编写,最初发布为here。
关于python - 检索y截距的标准偏差,我们在Stack Overflow上找到一个类似的问题:https://stackoverflow.com/questions/27764220/