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?
This video saved my life
That's amazing video, Beautiful explanation of linear regression in terms of linear algebra.
Great content! This was the missing link between my linear algebra and econometrics courses :D
Amazing! cleared lots of confusions
This is just way too good. Thanks a lot!
Thank you so much, you made algebra and linear regression click for me
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?
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?