[Python 2.X] Regression linéaire décalée

Bonjour,

je souhaite faire une régression linéaire de mes données.
https://github.com/Suntoryy/Help/blob/master/data.xlsx

Code:

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import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from math import log10
from numpy import polyfit
import numpy.polynomial.polynomial as poly
import scipy
from scipy import stats
 
data=pd.read_excel('data.xlsx',sheet_name='Sheet2',index=False,dtype={'Ra': float})
print(data)
 
x=np.log10(data['Ra'].values)
y1=np.log10(data['Nu_top'].values)
y2=np.log10(data['Nu_bottom'].values)
x2=np.log10(data['Ra'].head(11).values)
y4=np.log10(data['Nu_top'].head(11).values)
x3=np.log10(data['Ra'].tail(4).values)
y5=np.log10(data['Nu_top'].tail(4).values)
 
plt.xscale('log')
plt.yscale('log')
plt.scatter(x, y1, label='Nu_top')
plt.scatter(x, y2, label='Nu_bottom')
 
plt.errorbar(x, y1 , yerr=data['Ecart type top'].values, linestyle="None") 
plt.errorbar(x, y2 , yerr=data['Ecart type bot'].values, linestyle="None")
 
 
"""a=np.ones(10, dtype=np.float)
weights = np.insert(a,0,1E10)"""
 
lr = scipy.stats.linregress(x2, y4)
print(lr)
plt.plot(lr[0]*x2+lr[1],y4)
"""
coefs = poly.polyfit(x2, y4, 1)
print(coefs)
ffit = poly.polyval(x2, coefs)
plt.plot(x2, ffit, label='fit: b=%5.3f, a=%5.3f' % tuple(coefs))
 
absError = ffit - x2
 
SE = np.square(absError) # squared errors
MSE = np.mean(SE) # mean squared errors
RMSE = np.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (np.var(absError) / np.var(x2))
print('RMSE:', RMSE)
print('R-squared:', Rsquared)
print()
print('Predicted value at x=0:', ffit[0])
print()
 
 
coefs = poly.polyfit(x3, y5, 1)
ffit = poly.polyval(x3, coefs)
plt.plot(x3, ffit, label='fit: b=%5.3f, a=%5.3f' % tuple(coefs))
 """
plt.grid
plt.title("Nusselt en fonction de Ra")
plt.xlabel('log10(Ra)')
plt.ylabel('log10(Nu)')
plt.legend()
plt.show()

la régression linéaire avec scipy.stats.linregress() ne fonctionne pas ... ma courbe est décalée et je sais pas pourquoi ...
Par contre avec polyfit j'ai réussi a faire un fit de mes données mais j'ai pas le coeff de regression R.
Mon problème physique est décrit par: log10(Nu)=coeff*log10(Na). Donc x=log10(Na) et y=log10(Nu)
Pièce jointe 481186

import pandas as pd import numpy as np import matplotlib.pyplot as plt from math import log10 from numpy import polyfit import numpy.polynomial.polynomial as poly import scipy from scipy import stats data=pd.read_excel('data.xlsx',sheet_name='Sheet2',index=False,dtype={'Ra': float}) print(data) x=np.log10(data['Ra'].values) y1=np.log10(data['Nu_top'].values) y2=np.log10(data['Nu_bottom'].values) x2=np.log10(data['Ra'].head(11).values) y4=np.log10(data['Nu_top'].head(11).values) x3=np.log10(data['Ra'].tail(4).values) y5=np.log10(data['Nu_top'].tail(4).values) fig = plt.figure(figsize=(12, 8)) plt.xscale('log') plt.yscale('log') plt.scatter(x, y1, label='Nu_top') plt.scatter(x, y2, label='Nu_bottom') plt.errorbar(x, y1 , yerr=data['Ecart type top'].values, linestyle="None") plt.errorbar(x, y2 , yerr=data['Ecart type bot'].values, linestyle="None") """a=np.ones(10, dtype=np.float) weights = np.insert(a,0,1E10)""" lr = scipy.stats.linregress(x2, y4) plt.plot(x2,lr[0]*x2+lr[1], label='fit: b=%5.3f, a=%5.3f, R=%5.3f' % lr[0:3]) lr = scipy.stats.linregress(x3, y5) plt.plot(x3,lr[0]*x3+lr[1], label='fit: b=%5.3f, a=%5.3f, R=%5.3f' % lr[0:3]) """ coefs = poly.polyfit(x2, y4, 1) print(coefs) ffit = poly.polyval(x2, coefs) plt.plot(x2, ffit, label='fit: b=%5.3f, a=%5.3f' % tuple(coefs)) absError = ffit - x2 SE = np.square(absError) # squared errors MSE = np.mean(SE) # mean squared errors RMSE = np.sqrt(MSE) # Root Mean Squared Error, RMSE Rsquared = 1.0 - (np.var(absError) / np.var(x2)) print('RMSE:', RMSE) print('R-squared:', Rsquared) print() print('Predicted value at x=0:', ffit[0]) print() coefs = poly.polyfit(x3, y5, 1) ffit = poly.polyval(x3, coefs) plt.plot(x3, ffit, label='fit: b=%5.3f, a=%5.3f' % tuple(coefs)) """ plt.grid plt.title("Nusselt en fonction de Ra") plt.xlabel('log10(Ra)') plt.ylabel('log10(Nu)') plt.legend() plt.show() fig.savefig('a.png')