变换与线性回归

Question

我有一个要绘制的方程：

C（T）=γ T +α T ^ 3

我意识到，如果我分解出“ T”，则它变为C（T）= T（γ+α* T ^ 2），类似于y = x（b + ax ^ 2）。

我已经为另一个数据集编写了大部分代码，但到现在为止，但是我得到的图形似乎不正确。有什么建议吗？

import numpy as np
import matplotlib.pyplot as plt

a=np.loadtxt("CvsT.txt", skiprows=1)

T=a[:,0]
C=a[:,1]

size=a.shape
rows=size[0]
xsum=0
x2sum=0
ysum=0
y2sum=0
xysum=0
for n in range(rows):
    xsum=xsum+T[n]
    x2sum=x2sum+pow(T[n],2)
    ysum=ysum+C[n]
    y2sum=y2sum+pow(C[n],2)
    xysum=xysum+T[n]*C[n]

xsum=xsum/rows
print(xsum)
x2sum=x2sum/rows
print(x2sum)
ysum=ysum/rows
print(ysum)
y2sum=y2sum/rows
print(y2sum)
xysum=xysum/rows
print(xysum)

a=(xysum-xsum*ysum)/(x2sum-xsum**2)
b=(x2sum*ysum-xsum*xysum)/(x2sum-xsum**2)
print("\nThe regression parameters are: a = ",a, "and b = ", b)

TModel=np.linspace(0.20,0.6,100)
CModel=TModel*(a*TModel+b)

plt.plot(TModel, CModel, color="red", linestyle="dashed")
plt.plot(T,C,markersize=10, color="green", marker="o", linestyle="-")
plt.xlabel("T (K)", fontweight="bold", fontsize="large")
plt.ylabel("C (mJ/mol K)", fontweight="bold", fontsize="large", 
color="green")

================================================ ==========================

T[K]    C[mJ/(mol K)
0.244948974 0.538887743
0.264575131 0.595294045
0.316227766 0.727323862
0.331662479 0.769456951
0.360555128 0.865332306
0.374165739 0.927931032
0.424264069 1.107329219
0.447213595 1.185116028
0.479583152 1.294874511
0.509901951 1.417527425
0.547722558 1.588395417

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