Predicting intercept and coefficient for linear regression model for multiple variable

Question

I have the following equation: P = B0 + B1*Var1 + B2*Var2 I have the values of P, Var1 and Var2 with me. I tried to model this and then calculate the coefficients and intercept. Below is the code and the output I am getting: P = [1035.89, 1060.4, 1064, 1075.89, 1078.69, 1074.93, 1090.71, 1080.95, 1086.19,1080.46] # Total power l = [51.275510204081634, 102.89115646258503, 160.7142857142857, 205.78231292517006, 256.80272108843536, 307.82312925170066, 360.5442176870748, 409.0136054421768, 460.03401360544217, 492.3469387755102] t = [6.110918671507064, 12.262374116954474, 19.153625686813186, 24.524748233908948, 30.60526432496075, 36.685780416012555, 42.96898037676609, 48.7454706632653, 54.82598675431711, 58.67698027864992] X = [] for index in range(0,len(P)): row = [] row.append(t[index]) row.append(l[index]) X.append(row) print "Using statsmodels" import statsmodels.api as sm X = sm.add_constant(X) est = sm.OLS(P, X).fit() print est.params[0] print est.params[1] print est.params[2] I am getting the results as: Using statsmodels 1048.32518503 0.0102496334198 0.0860026475829 Is this correct? Does est.params[0] refers to B0 of the equation? I get B0 in the range of 600-650 when I run experiments? Can this data mismatch because of wrong data ?

Answer 1

我不熟悉statsmodels，但这是使用curve_fit的实现（请参阅下面的代码）。模型预测与您观察到的实验结果不匹配的原因在于我认为您的模型（B0 + B1*Var1 + B2*Var2）没有很好地描述数据（指数/ log / sqrt可能会更好）。在接下来的图中，我显示了原始数据，curve_fit（下面的代码）获得的拟合以及使用参数的拟合。

正如您所看到的，两个拟合函数都给出了相同的结果，但是，在我看来，您的数据应该由另一个函数建模。如果我找时间，我会寻找更适合您数据的功能。

from scipy.optimize import curve_fit
import numpy as np 
import matplotlib.pyplot as plt

P = [1035.89, 1060.4, 1064, 1075.89, 1078.69, 1074.93, 1090.71, 1080.95, 1086.19,1080.46] # Total power
l = [51.275510204081634, 102.89115646258503, 160.7142857142857, 205.78231292517006, 256.80272108843536, 307.82312925170066, 360.5442176870748, 409.0136054421768, 460.03401360544217, 492.3469387755102]
t = [6.110918671507064, 12.262374116954474, 19.153625686813186, 24.524748233908948, 30.60526432496075, 36.685780416012555, 42.96898037676609, 48.7454706632653, 54.82598675431711, 58.67698027864992]

# your model
def func(x, b0, b1, b2):

    var1, var2 = x

    return b0 + np.dot(b1, var1) + np.dot(b2, var2)

# Curve fit
coeff, _ = curve_fit(func, (l, t), P)
b0, b1, b2 = coeff[0], coeff[1], coeff[2]
print b0, b1, b2

# plot the data
xval = range(1 ,len(P)+1)
plt.scatter(xval, P, s=30, marker = "v", label='P')
plt.scatter(xval, func((l,t), *coeff), s=30, marker = "v", color="red", label='curvefit')
plt.legend(loc='upper left')
plt.figure()
plt.scatter(xval, P, s=30, marker = "v", label='P')
plt.scatter(xval, func((l, t), 1048.32518503, 0.0860026475829, 0.0102496334198 ), s=30, marker = "v",color="black",label='your parameter')
plt.legend(loc='upper left')
plt.show()
print "residuals curve_fit:",((P - func((l,t), *coeff))**2).sum()
print "residuals stats:",((P - func((l,t), 1048.32518503,0.086002647582,0.0102496334198))**2).sum()