最小二乘法求解线性回归模型

### 0.引入依赖
import numpy as np
import matplotlib.pyplot as plt
### 1.导入数据
points = np.genfromtxt('data.csv',delimiter=',')
# 提取points中的两列数据，分别作为x,y
x = points[:, 0]
y = points[:, 1]
# 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，另外还要传入数据的x，y
def compute_cost(w, b, points):
    total_cost = 0
    M = len(points)
    
    #逐点计算平方损失，然后计算平均值
    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.定义算法拟合函数
# 先定义一个求均值的函数
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 is: ", w)
print("b is: ", b)
cost = compute_cost(w, b, points)
print("cost is : ",cost)
### 5.画出拟合曲线
plt.scatter(x,y)
#针对每一个x，计算得出预测的y值
pred_y = w * x + b
plt.plot(x, pred_y, c='r')
plt.show()