手写线性回归代码，并做实验评估算法性能

好的，我可以帮你手写线性回归代码并进行实验评估。以下是代码实现：

import numpy as np
import matplotlib.pyplot as plt

class LinearRegression:
    def __init__(self, learning_rate=0.01, num_iterations=1000):
        self.learning_rate = learning_rate
        self.num_iterations = num_iterations
        self.weights = None
        self.bias = None
        
    def fit(self, X, y):
        # Initialize weights and bias
        n_samples, n_features = X.shape
        self.weights = np.zeros(n_features)
        self.bias = 0
        
        # Gradient descent
        for i in range(self.num_iterations):
            y_pred = np.dot(X, self.weights) + self.bias
            dw = (1 / n_samples) * np.dot(X.T, (y_pred - y))
            db = (1 / n_samples) * np.sum(y_pred - y)
            self.weights -= self.learning_rate * dw
            self.bias -= self.learning_rate * db
            
    def predict(self, X):
        y_pred = np.dot(X, self.weights) + self.bias
        return y_pred
    
    def mse(self, y_pred, y_true):
        return np.mean((y_pred - y_true) ** 2)

这里我们使用梯度下降法来学习线性回归模型的参数。在训练过程中，我们计算预测值与真实值之间的误差，并通过计算梯度来更新权重和偏置。

下面我们来用一个简单的实例来测试我们的代码：

# Generate some random data
np.random.seed(0)
X = np.random.rand(100, 1)
y = 2 + 3 * X + np.random.randn(100, 1)

# Split data into training and test sets
X_train, X_test = X[:80], X[80:]
y_train, y_test = y[:80], y[80:]

# Train the model
model = LinearRegression()
model.fit(X_train, y_train)

# Make predictions on test set
y_pred = model.predict(X_test)

# Evaluate the model
mse = model.mse(y_pred, y_test)
print("Mean Squared Error:", mse)

# Plot the results
plt.scatter(X_test, y_test, color='blue')
plt.plot(X_test, y_pred, color='red')
plt.show()

这里我们生成了一些随机数据，并将其分为训练集和测试集。然后我们训练模型并在测试集上进行预测。最后，我们计算模型的均方误差并绘制真实值和预测值之间的关系图。

你可以根据自己的需要更改参数，并使用不同的数据集来测试模型的性能。