utils.py

# stats functions

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy import stats


def z_score(data):
    """Return the z-score of each element in data"""
    mean_val = np.mean(data)
    std_val = np.std(data)
    return [(x - mean_val) / std_val for x in data]

def mse(y, y_hat):
    """Return the mean squared error of y and y_hat"""
    return np.mean((y - y_hat) ** 2)


def mape(y, y_hat):
    """Return the mean absolute percentage error of y and y_hat"""
    return np.mean(np.abs((y - y_hat) / y))


def check_normality(data):
    """check if data is normally distributed using visualizations and shapiro-wilk test."""
    # ensure data is a numpy array for consistency
    data = np.array(data)
    
    # visualizations: histogram and q-q plot
    fig, axs = plt.subplots(1, 2, figsize=(12, 5))

    # histogram
    axs[0].hist(data, bins=20, color='skyblue', edgecolor='black')
    axs[0].set_title('histogram')
    axs[0].set_xlabel('value')
    axs[0].set_ylabel('frequency')

    # q-q plot
    stats.probplot(data, dist="norm", plot=axs[1])
    axs[1].set_title('q-q plot')

    plt.tight_layout()
    plt.show()

    # shapiro-wilk test
    shapiro_stat, p_value = stats.shapiro(data)

    print(f"shapiro-wilk test: statistic = {shapiro_stat:.4f}, p-value = {p_value:.4f}")
    
    if p_value > 0.05:
        print("result: data is likely normally distributed (p > 0.05).")
    else:
        print("result: data is likely not normally distributed (p ≤ 0.05).")