In the least squares problem we find that
\[ A^T Ax = A^T b \]
I'm assuming this linear equation represents some kind of fitted line for the data. However, a previous step in the quiz involved setting all the coordinates to to simplify finding and .
So I went ahead and tried this method on a simple set I made up of 20 pieces of data of coordinates :
A little spread out but I expect basically a positive linear relationship with y as a function of x.
Now I find with my calculator stat functions that , so I set all to :
My calculations from here:
I wind up with a line equation that looks like
If I try and plot this, the line sits way outside any of my data.
Did I miss some crucial step? Do the two constants change in subtracting the mean of X to begin with? Or am I misunderstanding the meaning of and ? As far as I can tell the quiz doesn't seem to suggest one way or another.