import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

# Read data from CSV file
data = pd.read_csv('linear_regression_data.csv')
x = data['x'].values
y = data['y'].values

# Perform linear regression using explicit formula
# For linear regression y = mx + c, the formulas are:
# m = (n*Σ(xy) - Σ(x)*Σ(y)) / (n*Σ(x²) - (Σ(x))²)
# c = (Σ(y) - m*Σ(x)) / n

n = len(x)
sum_x = np.sum(x)
sum_y = np.sum(y)
sum_xy = np.sum(x * y)
sum_x_squared = np.sum(x * x)

# Calculate slope (m) and intercept (c) using explicit formulas
m = (n * sum_xy - sum_x * sum_y) / (n * sum_x_squared - sum_x * sum_x)
c = (sum_y - m * sum_x) / n

# Regression line
y_pred = m * x + c

# Plot data and fitted line
plt.figure(figsize=(10, 6))
plt.scatter(x, y, alpha=0.6, label='Data points')
plt.plot(x, y_pred, color='red', linewidth=2, label=f'Fit: y = {m:.2f}x + {c:.2f}')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Linear Regression Example (Using Explicit Formula)')
plt.legend()
plt.grid(True, alpha=0.3)
plt.show()

print(f"Slope (m): {m:.6f}")
print(f"Intercept (c): {c:.6f}")