如何在python中运行非线性回归

我在 python中有以下信息(数据帧)

product baskets scaling_factor
12345   475     95.5
12345   108     57.7
12345   2       1.4
12345   38      21.9
12345   320     88.8

我想运行以下非线性回归并估计参数.

a,b和c

我想要适合的等式：

scaling_factor = a - (b*np.exp(c*baskets))

在sas中我们通常运行以下模型:(使用高斯牛顿法)

proc nlin data=scaling_factors;
 parms a=100 b=100 c=-0.09;
 model scaling_factor = a - (b * (exp(c*baskets)));
 output out=scaling_equation_parms 
parms=a b c;

有没有类似的方法来估计Python中的参数使用非线性回归,我怎么能看到python中的情节.

解决方法

###the top two lines are required on my linux machine
import matplotlib
matplotlib.use('Qt4Agg')
import matplotlib.pyplot as plt
from matplotlib.pyplot import cm
import numpy as np
from scipy.optimize import curve_fit #we could import more,but this is what we need
###defining your fitfunction
def func(x,a,b,c):
    return a - b* np.exp(c * x) 
###OP's data
baskets = np.array([475,108,2,38,320])
scaling_factor = np.array([95.5,57.7,1.4,21.9,88.8])
###let us guess some start values
initialGuess=[100,100,-.01]
guessedFactors=[func(x,*initialGuess ) for x in baskets]
###making the actual fit
popt,pcov = curve_fit(func,baskets,scaling_factor,initialGuess)
#one may want to
print popt
print pcov
###preparing data for showing the fit
basketCont=np.linspace(min(baskets),max(baskets),50)
fittedData=[func(x,*popt) for x in basketCont]
###preparing the figure
fig1 = plt.figure(1)
ax=fig1.add_subplot(1,1,1)
###the three sets of data to plot
ax.plot(baskets,linestyle='',marker='o',color='r',label="data")
ax.plot(baskets,guessedFactors,marker='^',color='b',label="initial guess")
ax.plot(basketCont,fittedData,linestyle='-',color='#900000',label="fit with ({0:0.2g},{1:0.2g},{2:0.2g})".format(*popt))
###beautification
ax.legend(loc=0,title="graphs",fontsize=12)
ax.set_ylabel("factor")
ax.set_xlabel("baskets")
ax.grid()
ax.set_title("$mathrm{curve}_mathrm{fit}$")
###putting the covariance matrix nicely
tab= [['{:.2g}'.format(j) for j in i] for i in pcov]
the_table = plt.table(cellText=tab,colWidths = [0.2]*3,loc='upper right',bbox=[0.483,0.35,0.5,0.25] )
plt.text(250,65,'covariance:',size=12)
###putting the plot
plt.show()
###done

最后,给你：

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