How to find the parameter b such that the following sum of quadratic expressions is minimized? S

dreangannaa

dreangannaa

Answered question

2022-04-23

How to find the parameter b such that the following sum of quadratic expressions is minimized?
Suppose you have x1,,xn. My task is to find bR such that the sum i=1n(xib)2 is minimal.
Now, I think we can view it as a multivariate function and differentiate...
So how specifically should I proceed?
EDIT:
the xi were squared by mistake. Anyway, in accordance with JCAA and sven I differentiated and calculated such as the following:
2b2x1+2b2x2++2b2xn=0
b=i=1nxin

Answer & Explanation

Patricia Duffy

Patricia Duffy

Beginner2022-04-24Added 16 answers

So you want to find a point on the line through 0 parallel to vector v=(1,..,1) which is the projection of the point X=(x1,,xn) onto that line. This is a standard linear algebra problem. The vector connecting X with point (b,..,b) must be perpendicular to the vector v. Which implies (take the dot product) xi=nb or b=xin.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?