python - Python 中的 OLS : dimension of estimated coefficient matrix is not OK

Question

我编写了一个Python代码来估计(单变量)线性回归模型的参数，但是估计系数矩阵的维数不合适。向量“beta_estimated”(下面报告)的维度应该是 (1×1)，但实际上是 (n×n)。有什么想法吗？

# Linear regression in Python (univariate)
import numpy as np     
import scipy as sci     

x_original  =  np.random.normal(1,1, 100)    
x = np.array([x_original])    
#x_transpose  = x.T                 
beta = [5]  

y_original = (beta * x) + np.random.normal(0, 10, 100)    
y = np.array(y_original)    
#y_transpos = y.T     
product1 = np.dot(x.T, x)    
product2 = np.dot(x.T, y )    
Minv = np.linalg.inv(product1)    
beta_estimated =  np.dot(Minv, product2)

Answer 1

我不确定您想做什么，但如果我不得不猜测该产品是您没有所需尺寸的原因。对于您的情况:

x   # has a shape of (1, 100)
x.T # has a shape of (100, 1)

np.dot(x.T, x) # produces an array with shape (100, 100)
np.dot(x, x.T) # would produce an array with a shape of (1, 1) 

因此，如果我认为您应该反转两个点积中的参数np.dot()。你的代码应该变成:

product1 = np.dot(x, x.T)    
product2 = np.dot(y, x.T)