用python手动编写均方误差，均方根误差，平均绝对误差，R方各自函数的代码

在Python中，我们可以手动编写计算统计指标如均方误差(Mean Squared Error, MSE)，均方根误差(Root Mean Squared Error, RMSE)，平均绝对误差(Average Absolute Error, MAE)以及R方(R-squared)的函数。以下是简单的示例：

import numpy as np

def mean_squared_error(y_true, y_pred):
    """
    计算均方误差
    :param y_true: 真实值数组
    :param y_pred: 预测值数组
    :return: MSE
    """
    mse = np.mean((y_true - y_pred)**2)
    return mse

def root_mean_squared_error(y_true, y_pred):
    """
    计算均方根误差
    :param y_true: 真实值数组
    :param y_pred: 预测值数组
    :return: RMSE
    """
    rmse = np.sqrt(mean_squared_error(y_true, y_pred))
    return rmse

def average_absolute_error(y_true, y_pred):
    """
    计算平均绝对误差
    :param y_true: 真实值数组
    :param y_pred: 预测值数组
    :return: MAE
    """
    mae = np.mean(np.abs(y_true - y_pred))
    return mae

def r_squared(y_true, y_pred):
    """
    计算R方 (只适用于回归模型)
    :param y_true: 真实值数组
    :param y_pred: 预测值数组
    :return: R^2
    """
    ss_total = np.sum((y_true - np.mean(y_true))**2)
    ss_residual = np.sum((y_true - y_pred)**2)
    r_squared = 1 - (ss_residual / ss_total)
    return r_squared

# 使用示例
y_true = [1, 2, 3, 4, 5]
y_pred = [1.5, 2.5, 3.5, 4.5, 5.5]

mse = mean_squared_error(y_true, y_pred)
rmse = root_mean_squared_error(y_true, y_pred)
mae = average_absolute_error(y_true, y_pred)
r_squared_value = r_squared(y_true, y_pred)

print(f"MSE: {mse}, RMSE: {rmse}, MAE: {mae}, R^2: {r_squared_value}")