Curve Fitting y = ab^x Python Program

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

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

Python Source Code: Fitting y = abx

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

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)

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 + x[i]
sumX2 = sumX2 +x[i]*x[i]
sumY = sumY + np.log(y[i])
sumXY = sumXY + 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? 5
Enter data:
x[0]= 0
y[0]= 2
x[1]= 1
y[1]= 7
x[2]= 2
y[2]= 11
x[3]= 3
y[3]= 26
x[4]= 4
y[4]= 50

Coefficients are:
a:  2.4386066263877857
b:  2.170578677954671
```