Thank you for posting these AWESOME VODEOS!! I took an Econometrics course 12 years ago and I've been looking EVERYWHERE for a channel that covered everything we studied so I can "freshen up" on the material. These videos are the exact same material but much more direct and much more entertaining!!! 👍
💙. 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
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.
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).
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 !
How would one convey the results of this linear regression in R? You did a great job explaining it in the hypothesis testing video but I cannot seem to bridge the gap.
Here’s what I’d write for exercise based on the model summary in this video: “An additional hour of exercise is associated with an average reduction of 3.3 (then place p-value and confidence interval here) in systolic blood pressure, adjusted for sex.” You could also write something similar for the sex variable as well, but adjusted for exercise time
I'd be curious to know your take on assumption verification practices. Tests like the Shapiro-Wilk always felt like too simplistic (and backwards since you usually don't want it to be significant, so you're essentially trying to "prove" the Null hypothesis, which is impossible). I understand why they are important, but once you get to more complicated analyses (e.g. multivariate models), assumptions begin to multiply to the point where you're almost garanteed to not meet all of them. So, as a non-statistician, you're left with either not doing the analysis at all, or doing it anyway with the asterisk that you're conclusion *might* be completely wrong. Anyway, long comment just to say that there might be a video there. Love the content! Take care
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”
@@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.
GOAT yt channel
I discovered this Channel today and I am seriously loving it.. awesome job, great effort and nicely explained..
Thank you for posting these AWESOME VODEOS!!
I took an Econometrics course 12 years ago and I've been looking EVERYWHERE for a channel that covered everything we studied so I can "freshen up" on the material.
These videos are the exact same material but much more direct and much more entertaining!!! 👍
Really enjoyed this video. Great refresher to watch even if you are already familiar with linear regression
💙. 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
you are in luck, i found the video it’s the one you clicked on!
@@memelord4639 Indeeds, a lucky day 😅
You explain things so well, wish I had you for my Biostatistics Theory course
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.
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).
What exactly is a ML model?
7:24 every other relation, that's monotonically increasing: am I a joke to you?
Very good, now do it for auto correlated daya
Thanks so much !!!!
Absolutely beautiful 🤩
Excellent videos. Can you do a summary/introduction to Survival Analysis and Mixed/Marginal Linear model?
Yeah! I have a smaller bits for these in my “biggest prize in statistics” video already for while you wait too
woops: 6:18 slight typo in treatment (treamtent in the slide)
also, love your channel keep up the good work 👏🏼👊🏼
Cool video
How do you measure the hours of sex, versus the hours of exercise?
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 !
Very fun stuff, next Extra sum of squares and coefficients of partial determination?
How would one convey the results of this linear regression in R? You did a great job explaining it in the hypothesis testing video but I cannot seem to bridge the gap.
Here’s what I’d write for exercise based on the model summary in this video:
“An additional hour of exercise is associated with an average reduction of 3.3 (then place p-value and confidence interval here) in systolic blood pressure, adjusted for sex.”
You could also write something similar for the sex variable as well, but adjusted for exercise time
I'd be curious to know your take on assumption verification practices. Tests like the Shapiro-Wilk always felt like too simplistic (and backwards since you usually don't want it to be significant, so you're essentially trying to "prove" the Null hypothesis, which is impossible). I understand why they are important, but once you get to more complicated analyses (e.g. multivariate models), assumptions begin to multiply to the point where you're almost garanteed to not meet all of them. So, as a non-statistician, you're left with either not doing the analysis at all, or doing it anyway with the asterisk that you're conclusion *might* be completely wrong. Anyway, long comment just to say that there might be a video there.
Love the content! Take care
7:24 : that something is strictly monotonic doesn’t imply that it is linear though…
Edit: oh, someone else already commented this
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
can you explain? does this mean the word "linear" doesn't refer to that at all?
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”
@@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.
10:31 I think you missed a subscript "i" on the X
Nice lil intro to regression. Got hit with hat matrices in my linear regression class last week and I nearly perished.
MY FAVORITE STATS CHANNEL RELEASED A VIDEO ON MY FAVORITE TECHNIQUE
it's kinda sweet that your favourite technique is linear regression. I rarely meet anybody who has a favourite statistical technique.
@@shrub4248 Haha that’s true, I’ve also never met anyone with a favorite technique but I have this odd love for linear regression haha
what tools u use to make these videos , they are really pretty?
Thanks! Final Cut Pro for editing, Figma for design, manim for math notation and plots. These cover pretty much 95% of my workflow
❤
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