[机器学习]简单线性回归—

[机器学习]简单线性回归——最小二乘法

一.线性回归及最小二乘法概念

2.代码实现

# 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=',')
# points[0,0]# 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：最小平方损失函数
# 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 = 0M = len(points)# 逐点计算平方损失误差，然后求平均数for i in range(M):x = points[i, 0]y = points[i, 1]total_cost += (y - w * x - b) ** 2return 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 = 0num = 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 = 0sum_x2 = 0sum_delta = 0for 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ww = 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 / Mreturn 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，计算出预测的y值
pred_y = w * x + b
plt.plot(x, pred_y, c='r')
plt.show()

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression # sklearn库实现# 1. 导入数据（data.csv）
points = np.genfromtxt('data.csv', delimiter=',')
points[0,0]# 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：最小平方损失函数
# 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 = 0M = len(points)# 逐点计算平方损失误差，然后求平均数for i in range(M):x = points[i, 0]y = points[i, 1]total_cost += (y - w * x - b) ** 2return total_cost / Mlr = LinearRegression()
x_new = x.reshape(-1, 1) # 将1行数据变为二维数组
y_new = y.reshape(-1, 1)
lr.fit(x_new, y_new)# 3. 从训练好的模型中提取系数和截距：使用的也是最小二乘法
w = lr.coef_[0][0]
b = lr.intercept_[0]print("w is: ", w)
print("b is: ", b)cost = compute_cost(w, b, points)print("cost is: ", cost)plt.scatter(x, y)
# 针对每一个x，计算出预测的y值
pred_y = w * x + bplt.plot(x, pred_y, c='r')
plt.show()