简单线性回归（最小二乘法）

桃扇骨 2023-02-09 13:21 10阅读 0赞

![format_png][]

### 0.引入依赖 ###

import numpy as np
    import matplotlib.pyplot as plt

### 1.导入数据（data.csv） ###

points = np.genfromtxt('data.csv',delimiter=',')
    
    # 提取points中的两列数据，分别作为x,y
    x=points[:,0] #取所有的第一列
    y=points[:,1] #取所有的第二列
    
    # 用plt画出散点图
    
    plt.scatter(x,y)
    plt.show()

![format_png 1][]

### 2. 定义损失函数 ###

# 损失函数是系数的函数，还要传入数据的x，y
    def computer_cost(w,b,points):
        total_cost = 0
        M = len(points)
        
        # 逐点计算平方损失误差，然后求平均值
        for i in range(M):
            x=points[i,0]
            y=points[i,1]
            total_cost += (y - w * x - b) ** 2
            
        return total_cost/M

### 3. 定义核心算法拟合函数 ###

# 先定义一个球均值的函数
    def average(data):
        sum = 0
        num = len(data)
        for i in range(num):
            sum += data[i]
        return sum/num
    
    # 定义核心拟合函数
    def  fit(points):
        M = len(points)
        x_bar= average(points[:,0])
        
        sum_yx = 0
        sum_x2 = 0
        sum_delta = 0 
        for i in range(M):
            x=points[i,0]
            y=points[i,1]
            sum_yx += y * (x - x_bar)
            sum_x2 += x ** 2
            
        # 根据公式计算w
        w = sum_yx / (sum_x2 - M * (x_bar ** 2))
        
        
        for i in range(M):
            x=points[i,0]
            y=points[i,1] 
            sum_delta += (y - w * x)
        b = sum_delta / M
        
        return w,b

### 4. 测试 ###

w,b = fit(points)
    
    print("w = " ,w)
    print("b = " , b)
    
    cost = computer_cost(w,b,points)
    print("cost = ", cost)

![format_png 2][]

### 5. 画出拟合曲线 ###

plt.scatter(x,y)
    # 针对每一个x，计算出预测的y值
    pred_y = w * x + b
    
    plt.plot(x,pred_y,c='r')
    plt.show()

![format_png 3][]

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