线性回归

线性回归知识(参考链接)

 

 正规方程推导过程

代码实现

　　matlab

x(1:10,1) = [-0.5,-0.45,-0.35,-0.35,-0.1,0,0.2,0.25,0.3,0.5];
x(1:10,2) = 1;
y = [-0.2,0.1,-1.25,-1.2,0,0.5,-0.1,0.2,0.5,1.2];
y = transpose(y);
figure;
hold on
scatter(x(:,1),y,'r','filled');
axis([-1.0,1.0,-3.0,3.0])
%求权重
x_T = transpose(x);
w = inv(x_T*x)*x_T*y;
hat_y = x*w;
disp('权重'); disp(w);
x1 = linspace(-1,1,50);
hat_y = x1*w(1)+w(2);
plot(x1,hat_y,'g');
axis([-1.0,1.0,-3,3]);
title('线性回归')
xlabel('x')
ylabel('y')

　

　Python

import numpy as np
import math
import matplotlib.pyplot as plt
 X = np.hstack((np.array([[-0.5,-0.45,-0.35,-0.35,-0.1,0,0.2,0.25,0.3,0.5]]).reshape(-1, 1), np.ones((10,1))*1))
y = np.array([-0.2,0.1,-1.25,-1.2,0,0.5,-0.1,0.2,0.5,1.2]).reshape(-1,1)
# 用公式求权重
w = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)
hat_y = X.dot(w)
print("Weight:{}".format{list(w)})
x = np.linspace(-1, 1, 50)
hat_y = x * w[0] + w[1]
plt.figure(figsize=(4,4))
plt.xlim(-1.0, 1.0)
plt.xticks(np.linspace(-1.0, 1.0, 5))
plt.ylim(-3, 3)
plt.plot(x, hat_y, color='red')
plt.scatter(X[:,0], y[:,0], color='black')
plt.xlabel('$x_1$')
plt.ylabel('$y$')
plt.title('$Linear Regression$')
plt.show()