Curve Fitting y = ax^b Python Program

This Python program implements least square method to fit curve of type y = axb.

We first read n data points from user and then we implement curve fitting for y = axb using least square approach in Python programming language as follow:

Python Source Code: Fitting y = axb


# This is naive approach, there are shortcut methods for doing it!
# Least square method
# Fitting y = ax^b to given n data points
import numpy as np

# Reading value of n
n = int(input("How many data points? "))

# Creating numpy array x & y to store n data points
x = np.zeros(n)
y = np.zeros(n)

# Reading data
print("Enter data:")
for i in range(n):
    x[i] = float(input("x["+str(i)+"]= "))
    y[i] = float(input("y["+str(i)+"]= "))
    
# Finding required sum for least square methods
sumX,sumX2,sumY,sumXY = 0,0,0,0
for i in range(n):
    sumX = sumX + np.log(x[i])
    sumX2 = sumX2 +np.log(x[i])*np.log(x[i])
    sumY = sumY + np.log(y[i])
    sumXY = sumXY + np.log(x[i])*np.log(y[i])

# Finding coefficients A and B
B = (n*sumXY-sumX*sumY)/(n*sumX2-sumX*sumX)
A = (sumY - B*sumX)/n

# Obtaining a and b
a = np.exp(A)
b = np.exp(B)

# Displaying coefficients a, b & equation
print("\nCoefficients are:")
print("a: ", a)
print("b: ", b)

Output

How many data points? 4
Enter data:
x[0]= 61
y[0]= 350
x[1]= 26
y[1]= 400
x[2]= 7
y[2]= 500
x[3]= 2.6
y[3]= 600

Coefficients are:
a:  701.9919475945616
b:  0.8429434259442341