简单线性回归（最小二乘法）

1、概述

线性方程求解

线性回归模型

最小二乘法

求解线程回归

1、代码实现

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()

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)

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()

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