Explaining linear regression

Explaining basic interpretations to linear regression and how to do a hypothesis test with it
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[@berjonah110]

The name "Least Squares Regression" comes from the fact that the OLS estimators are the solution to a minimization problem. The objective for this minimization is the sum of the squared error. So minimizing this sum gives the smallest (least) squared error.
In fact most of the more advanced ML models are based on an extension of linear regression. Most of these don't have an analytic solution like ordinary least squares, but we can solve for the parameters using gradient descent (or variations).

[@Unaimend]

💙. Thanks again for your nice videos :) Will you also make one about multiple linear regression? I am particular interested in the necessary preconditions for those models, like, for example homorscedacity.
EDIT: I should probably wait with those questions until I finish the video

[@memelord4639]

you are in luck, i found the video it’s the one you clicked on!

[@Unaimend]

@@memelord4639 Indeeds, a lucky day 😅

[@Mystic2122]

GOAT yt channel

[@AtticusRex-t6g]

This is a great teaching aid for linear regression. One thing though: in your formulation of the normal equations the X is transposed; it should be (X X^T)^{-1} X Y if you're solving X^T \beta = Y.

[@johannbauer2863]

7:24 every other relation, that's monotonically increasing: am I a joke to you?

[@KinomaroMakhosini]

Very fun stuff, next Extra sum of squares and coefficients of partial determination?

[@andrej5027]

Thanks so much !!!!

[@Eloss69]

Reading about the bases of least squares lately, trying to understand what motivates some researchers to modeling the noise with Gaussian Processes (context of Bayesian Regression). Does anyone has any insight?
Nice video coming at the right time !

[@briskioO]

Nice lil intro to regression. Got hit with hat matrices in my linear regression class last week and I nearly perished.

[@Matthew-eb3di]

MY FAVORITE STATS CHANNEL RELEASED A VIDEO ON MY FAVORITE TECHNIQUE

[@culturemanoftheages]

10:31 I think you missed a subscript "i" on the X

[@tangyzhangy]

Cool video

[@drdca8263]

7:24 : that something is strictly monotonic doesn’t imply that it is linear though…
Edit: oh, someone else already commented this

[@very-normal]

ngl monotonic was not what I had in mind when I said that line, but I can see why people would think that, my b

[@kventinho]

can you explain? does this mean the word "linear" doesn't refer to that at all?

[@very-normal]

I didn’t realize that “the more the merrier” could technically also imply other monotonic increasing relationships. To be more correct, I should have said something along the lines of “another step produces the same change in the outcome”

[@victorh2056]

​@@kventinho
Monotonic functions are those which only ever go one direction (up or down in 2D) or go parallel to the horizontal axis.
So, you can imagine a regular constant function is monotonic, a linear function as well, but other functions also display such properties like e^x, log(x), x^2 (0;+ inf), sqrt(x) and so on.
They were just pointing that out as these functions could better describe a monotonic increase depending on the data at hand.

[@EkShunya]

what tools u use to make these videos , they are really pretty?

[@very-normal]

Thanks! Final Cut Pro for editing, Figma for design, manim for math notation and plots. These cover pretty much 95% of my workflow

[@vinicius_martinelli]

❤