机器学习之最小二乘法完成一元线性回归【内附Python实现】

最小二乘法代码实现

import numpy as np
import matplotlib.pyplot as plt


# 利用最小二乘法定义损失函数,w与b是预测函数的未知参数,ponits是坐标信息
def compute_cost(w, b, points):
    # 实际值与估计值之差的平方和
    total_cost = 0
    M = len(points)
    for i in range(M):
        x = points[i, 0]  # x坐标值
        y = points[i, 1]  # y坐标值
        # 最小二乘法公式
        total_cost += (y - w * x - b) ** 2
        # 返回累加和的平均值
    return total_cost / M


# 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_avg = average(points[:, 0])
    sum_w_up = 0
    sum_x2 = 0
    sum_delta = 0

    for i in range(M):
        x = points[i, 0]
        y = points[i, 1]
        sum_w_up += y * (x - x_avg)
        sum_x2 += x ** 2
    # 根据公式计算w
    w = sum_w_up / (sum_x2 - M * (x_avg ** 2))
    for i in range(M):
        x = points[i, 0]
        y = points[i, 1]
        sum_delta += (y - w * x)
    # 根据公式计算b
    b = sum_delta / M

    return w, b

# 导入外部数据
points = np.genfromtxt('data.csv', delimiter=',')
w, b = fit(points)
cost = compute_cost(w, b, points)
x = points[:, 0]
y = points[:, 1]
# 将数据制作成散点图
plt.scatter(x, y)
pred_y = w * x + b		# 自动与x内的每一个元素都进行一次操作，并赋值给pred_y
plt.plot(x, pred_y, c='r')
# 展示画出来的图
plt.show()

数据文件百度云自取，此代码写法是将其与.py文件放置与同一目录下

链接：https://pan.baidu.com/s/1CanV_l_-968bukjz8VHr2w
提取码：lwoa