9 Regression as an Orthogonal Projection

[@AlphansoEric]

That's amazing video, Beautiful explanation of linear regression in terms of linear algebra.

[@MrOndra31]

Great content! This was the missing link between my linear algebra and econometrics courses :D

[@antonlinares2866]

Thank you so much, you made algebra and linear regression click for me

[@asifzahir7512]

Amazing! cleared lots of confusions

[@chiarasacchetti8284]

This video saved my life

[@breathemath4757]

This is just way too good. Thanks a lot!

[@sum1sw]

I'm not sure this is what I am looking for, if it is, then I missed it. I have an implicit function f(x,y,z)=0 (it is actually a model with adjustable parameters). I have an experimental data point (Xexp, Yexp, Zexp). You can probably see where I am heading with this. I want to know where a line, orthogonal/perpendicular to the surface, will intersect the surface. I'm calling this point of intersection Xcalc, Ycalc, Zcalc. How do I proceed? Based on other videos I watched, it looks like the first step is to linearize the surface using Taylor series. So, now I have a plane (in terms of partial derivatives and (Xcalc, Ycalc, Zcalc) which is still unknown. I want to know the point of intersection (Xcalc, Ycalc, Zcalc) of the orthogonal line from Xexp, Yexp, Zexp. At first, I thought is it a trial an error iterative procedure (I have to guess Xcalc, Ycalc, Zcalc) so I programmed that, but the answers I am getting do not seem to be correct. I'm also beginning to suspect that the solution can be direct, not iterative. Any thoughts?

[@GregorianWater]

why do we begin at y sub zero and not y sub 1?

[@teklehaimanotaman3150]

Very amazing lecture! thank you very much for your efforts. Is the line from the origin to the point y_hat the regression line please?