Starfruit Python Advanced Lecture 12-Array array (5) Use vector to derive linear regression least square method formula (the most detailed in the whole network so far)

My CSDN blog column: https://blog.csdn.net/yty_7

Github address: https://github.com/yot777/

Reference document 1: https://blog.csdn.net/c406495762/article/details/78760239
Reference document 2: https://blog.csdn.net/nomadlx53/article/details/50849941
Reference document 3: http: // blog.sina.com.cn/s/blog_8eac0b290101fsqb.html

 

Prediction error of linear regression

Vectorization derivation process

The first formula decomposed by the sum

The second formula decomposed by the sum

The third formula decomposed by the sum

The fourth formula decomposed by the sum

Derivation of vectorization

Differentiate w

Derivate the first formula decomposed

Derivation of the second formula

The third formula derived by differentiation

Derivation of the fourth formula

Derivative derivation result

Let w = 0 find the minimum

to sum up

The general formula for the prediction error of linear regression:

Matrix formula of prediction error of linear regression:

The estimated minimum formula of w:

 

My CSDN blog column: https://blog.csdn.net/yty_7

Github address: https://github.com/yot777/

If you think this chapter is helpful to you, welcome to follow, comment and like! Github welcomes your Follow and Star!