# -*- coding: utf-8 -*-
"""
Created on Mon Mar 23 11:35:11 2026

@author: pjaub
"""

import numpy as np
import matplotlib.pyplot as plt

plt.close('all')

data = np.loadtxt("huron.csv", delimiter=";")

annees = data[:,0]
niveaux = data[:,1]

plt.plot(annees, niveaux, "o-", color = "k", markersize=3)
plt.xlabel("Années")
plt.ylabel("Niveau du lac (m)")
plt.title("Niveaux du lac Huron")

T = np.array([np.ones(len(annees)), annees, annees**2]).T

beta = np.linalg.inv(T.T @ T) @ (T.T @ niveaux)
ajustement = T @ beta
plt.plot(annees, ajustement, 'r')

plt.show()