The tutor shows a nice trick to obtain a least squares line using matrix algebra.

In my Nov 25 post I mentioned how, with Excel or LibreOffice Calc, to get a best-fit line for

The same line can be gotten by hand, with the following ideas:

1. Imagining the best fit line to be of form y=mx+b, the table above can be related as the matrix equation
   
2. We multiply each side by the transpose matrix:
   
3. Performing the multiplication on each side yields
   

which means



Solving, we get m=1.15, b=2.9: our best-fit line is y=1.15x + 2.9, same with the result from November 25 using a spreadsheet.

Neat, eh?

Source:

Johnson/Riess/Arnold. Introduction to Linear Algebra, Second Ed. Don Mills: Addison-Wesley, 1989.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.