Calculatrice de Régression Linéaire

def linear_regression(x: list, y: list) -> dict:
    n = len(x)
    if n < 2:
        raise ValueError("Need at least 2 data points")
    sum_x = sum(x)
    sum_y = sum(y)
    sum_xy = sum(xi * yi for xi, yi in zip(x, y))
    sum_x2 = sum(xi ** 2 for xi in x)
    mean_x = sum_x / n
    mean_y = sum_y / n

    slope = (n * sum_xy - sum_x * sum_y) / (n * sum_x2 - sum_x ** 2)
    intercept = mean_y - slope * mean_x

    # R-squared
    ss_res = sum((yi - (slope * xi + intercept)) ** 2 for xi, yi in zip(x, y))
    ss_tot = sum((yi - mean_y) ** 2 for yi in y)
    r2 = 1 - ss_res / ss_tot if ss_tot != 0 else 1.0

    return {"slope": slope, "intercept": intercept, "r_squared": r2,
            "pearson_r": r2 ** 0.5 if r2 >= 0 else 0}

x = [1, 2, 3, 4, 5]
y = [2.1, 3.9, 6.2, 7.8, 10.1]
result = linear_regression(x, y)
print(f"y = {result['slope']:.4f}x + {result['intercept']:.4f}")
print(f"R² = {result['r_squared']:.4f}")

# Predict
x_new = 6
y_pred = result['slope'] * x_new + result['intercept']
print(f"Prediction at x=6: {y_pred:.2f}")