linear regression 



y = ax + b 
x 自变量
y 因变量
a 斜率
b 截距

a = sum( (x - x_ ) * (y - y_ ) ) /  sum( ( x - x_ )^2 )

b = y_ - a * x_

x_  x的均值
y_  y的均值 

误差评估
MSE 均方差 
MSE = sum((y - y_)^2) / n 




import numpy as np

# 注意 后面的 :
def simpleLrFit(array_x,array_y):
  x = np.array(array_x)
  x_ = x.mean()
  y = np.array(array_y)
  y_ = y.mean()
  v1 = (x - x_)*(y-y_)
  # v2 = (x - x_) * (x-x_)
  v2 = (x - x_) ** 2
  a = v1.sum() / v2.sum()
  b = y_ - a*x_
  return a,b 

list1 = [1,2,3]  
list2 = [1,2,5]

x = np.array(list1)
y = np.array(list2)


a,b = np.polyfit(x, y, deg=1)
# 2.0 -1.3333333333333315
print(a,b)

# 2.0 -1.3333333333333335
a1,b1 = simpleLrFit(list1,list2)
print(a1,b1)


import scipy.stats as stats
result = stats.linregress(x, y)
print(result)


LinregressResult(slope=2.0, intercept=-1.3333333333333335, rvalue=0.9607689228305228, pvalue=0.1789123750220667, stderr=0.5773502691896255, intercept_stderr=1.2472191289246466)