如果有两个或两个以上的自变量,这样的线性回归分析就称为多元线性回归
实际问题中,一个现象往往是受多个因素影响的,所以多元线性回归比一元线性回归的实际应用更广
相同点
不同点
# 简单线性回归(梯度下降法)
### 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
# 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) ** 2
return total_cost/M
### 3.定义模型的超参数
alpha = 0.0001
initial_w = 0
initial_b = 0
num_iter = 10
### 4.定义核心梯度下降算法的函数
def grad_desc(points, initial_w, initial_b, alpha, num_iter):
w = initial_w
b = initial_b
#定义一个list保存所有的损失函数值,用来显示下降的过程
cost_list = []
for i in range(num_iter):
cost_list.append(compute_cost(w, b, points))
w, b = step_grad_desc(w, b, alpha, points)
return [w, b, cost_list]
def step_grad_desc(current_w, current_b, alpha, points):
sum_grad_w = 0
sum_grad_b = 0
M = len(points)
# 对每个点,代入公式求和
for i in range(M):
x = points[i, 0]
y = points[i, 1]
sum_grad_w += (current_w * x + current_b - y) * x
sum_grad_b += (current_b * x + current_b - y)
# 用公式求当前梯度
grad_w = 2/M * sum_grad_w
grad_b = 2/M * sum_grad_b
# 梯度下降,更新当前的w和b
updated_w = current_w - alpha * grad_w
updated_b = current_b - alpha * grad_b
return updated_w, updated_b
### 5.测试:运行梯度下降算法计算最优的w和b
w, b, cost_list = grad_desc(points, initial_w, initial_b, alpha, num_iter)
print("w is: ", w)
print("b is: ", b)
cost = compute_cost(w, b, points)
print("cost is : ",cost)
plt.plot(cost_list)
plt.show()
### 6.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()