使用python实现线性回归算法

以下是使用Python实现线性回归算法的步骤和代码：

1.导入必要的库和数据集

import numpy as np
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split

2.生成数据集

X, y = make_regression(n_samples=500, n_features=1, noise=20, random_state=4)

3.将数据集分为训练集和测试集

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)

4.定义线性回归模型

class LinearRegression:
    def __init__(self, lr=0.01, n_iters=1000):
        self.lr = lr
        self.n_iters = n_iters
        self.weights = None
        self.bias = None

    def fit(self, X, y):
        # 初始化参数
        n_samples, n_features = X.shape
        self.weights = np.zeros(n_features)
        self.bias = 0
        # 梯度下降
        for _ in range(self.n_iters):
            y_predicted = np.dot(X, self.weights) + self.bias
            dw = (1 / n_samples) * np.dot(X.T, (y_predicted - y))
            db = (1 / n_samples) * np.sum(y_predicted - y)
            self.weights -= self.lr * dw
            self.bias -= self.lr * db

    def predict(self, X):
        y_predicted = np.dot(X, self.weights) + self.bias
        return y_predicted

5.训练模型并预测结果

regressor = LinearRegression(lr=0.01, n_iters=1000)
regressor.fit(X_train, y_train)
predictions = regressor.predict(X_test)

6.评估模型

def mse(y_true, y_pred):
    return np.mean((y_true - y_pred) ** 2)

print("Mean Squared Error:", mse(y_test, predictions))