# I Trying to understand least squares estimates

Tags:
1. Feb 25, 2017

### Nastya

Hi, I'm trying to understand which mathematical actions I need to perform to be able to arrive at the solution shown in the uploaded picture. Thank you.

#### Attached Files:

• ###### Screenshot at Feb 26 00-11-44.png
File size:
12.2 KB
Views:
36
2. Feb 25, 2017

### Staff: Mentor

3. Feb 25, 2017

### WWGD

As a general statement, least squares allows you to obtain " best possible solutions " to systems like :

Ax=b , where b is not in the column space of A. This statement leads to a system like the one you attached to your post. You find the values of x that minimize the
$L^2$ distance $||Ax -b ||_2$, and this is the orthogonal projection of b onto Ax.

4. Feb 25, 2017

### Nastya

Yes, thank you. I will review the matrix multiplication.