Curve Fitting with Python

import matplotlib.pyplot as plt
import numpy as np

file = open("data.txt","r")
X=[]
Y=[]
n=0
solve=[]
for line in file:
    n  = n+1
    line = line.rstrip().split()
    X.append(float(line[0]))
    Y.append(float(line[1]))
plt.scatter(X,Y,s=2,c="cyan")
plt.grid("true")

y_avg=sum(Y)/n
sum_x = sum(X)
sum_y = sum(Y)
sum_xx = sum([x*x for x in X])
sum_xxx = sum([x*x*x for x in X])
sum_xxxx = sum([x*x*x*x for x in X])
sum_xxxxx = sum([x*x*x*x*x for x in X])
sum_xxxxxx = sum([x*x*x*x*x*x for x in X])
sum_xy = sum([x*y for x,y in zip(X,Y)])
sum_xxy = sum([x*x*y for x,y in zip(X,Y)])
sum_xxxy = sum([x*x*x*y for x,y in zip(X,Y)])
sum_xxxxy = sum([x*x*x*x*y for x,y in zip(X,Y)])
st = sum([(y-y_avg)**2 for y in Y])


def FOC():
    A = [[n,sum_x],[sum_x,sum_xx]]
    B = [[sum_y],[sum_xy]]
    solve = np.linalg.solve(A,B)
    Y1 = [float(solve[0]+x*solve[1]) for x in X]
    sr1 = sum([(y-y1)**2 for y,y1 in zip(Y,Y1)])
    r1 = ((st-sr1)/st)**(1/2)
    print("First order curve:\na0=",solve[0],", a1=",solve[1])
    print("Correlation coefficient of first order curve = ",r1)
    print("St=",st)
    print("Sr=",sr1)
    plt.plot(X,Y1)
def SOC():
    A = [[n,sum_x,sum_xx],[sum_x,sum_xx,sum_xxx],[sum_xx,sum_xxx,sum_xxxx]]
    B = [[sum_y],[sum_xy],[sum_xxy]]
    solve = np.linalg.solve(A,B)
    Y2 = [float(solve[0]+x*solve[1]+x*x*solve[2]) for x in X]
    sr2 = sum([(y-y2)**2 for y,y2 in zip(Y,Y2)])
    r2 = ((st-sr2)/st)**(1/2)
    print("Second order curve:\na0=",solve[0],", a1=",solve[1],", a2=",solve[2])
    print("Correlation coefficient of second order curve = ",r2)
    print("St=",st)
    print("Sr=",sr2)
    plt.plot(X,Y2)
def TOC():
    A = [[n,sum_x,sum_xx,sum_xxx],[sum_x,sum_xx,sum_xxx,sum_xxxx],[sum_xx,sum_xxx,sum_xxxx,sum_xxxxx],[sum_xxx,sum_xxxx,sum_xxxxx,sum_xxxxxx]]
    B = [[sum_y],[sum_xy],[sum_xxy],[sum_xxxy]]
    solve = np.linalg.solve(A,B)
    Y3 = [float(solve[0]+x*solve[1]+x*x*solve[2]+x*x*x*solve[3]) for x in X]
    sr3 = sum([(y-y3)**2 for y,y3 in zip(Y,Y3)])
    r3 = ((st-sr3)/st)**(1/2)
    print((st-sr3)/st)
    print("Third order curve:\na0=",solve[0],", a1=",solve[1],", a2=",solve[2],", a3=",solve[3])
    print("Correlation coefficient of third order curve = ",r3)
    print("St=",st)
    print("Sr=",sr3)
    plt.plot(X,Y3)

FOC()
SOC()
TOC()
plt.show