Calculate Linear Regression Equation from Data Points in Python

Program Overview

This Python program first reads a value x, then reads n data points as decimal pairs (xᵢ, yᵢ).
It calculates the slope m and intercept b using linear regression formulas, and displays the final equation y = mx + b.

Formulas Used:

• x̄ = (∑xᵢ) / n → Mean of x values
• ȳ = (∑yᵢ) / n → Mean of y values
• ∑xᵢyᵢ = x₁y₁ + x₂y₂ + ... + xₙyₙ
• ∑xᵢ² = x₁² + x₂² + ... + xₙ²
• m = (∑xᵢyᵢ - ȳ ∑xᵢ) / (∑xᵢ² - x̄ ∑xᵢ)
• b = ȳ - m x̄

Python Code:

n = int(input("Enter number of points: "))

x_vals = []
y_vals = []

for i in range(n):
    x_i = float(input(f"x[{i+1}] = "))
    y_i = float(input(f"y[{i+1}] = "))
    x_vals.append(x_i)
    y_vals.append(y_i)

sum_x = sum(x_vals)
sum_y = sum(y_vals)
sum_xy = sum(x * y for x, y in zip(x_vals, y_vals))
sum_x2 = sum(x ** 2 for x in x_vals)

x_mean = sum_x / n
y_mean = sum_y / n

m = (sum_xy - y_mean * sum_x) / (sum_x2 - x_mean * sum_x)
b = y_mean - m * x_mean

print(f"Linear equation: y = {round(m, 4)}x + {round(b, 4)}")

Sample Output:

Enter number of points: 3  
x[1] = 1  
y[1] = 2  
x[2] = 2  
y[2] = 3  
x[3] = 3  
y[3] = 5  

Linear equation: y = 1.5x + 0.0

Step-by-Step Explanation:

- The program collects x and y values into lists
- It computes the required sums and means
- Then it applies the regression formulas to calculate m and b
- Finally, it prints the linear equation rounded to 4 decimal places