Summer of Math Exposition

I like how you motivated the problem with a real world example. I think you could better justify why we square each distance instead of taking the absolute value. I also think you should discuss how your data set being small might affect the validity of the conclusion.

This felt like a 3B1B video verbatim, even down to the music! You struck a nice balance between moving fast enough to prevent me from being bored, and moving slow enough that I could follow your reasoning easily.

Thanks for the video, but there are some things in this explanation I find just slightly lacking, imagining it from the perspective of someone who’s encountering the topic for the first time. I don’t think it’s particularly clear, to new students, exactly why the line should be a better estimator for the first dataset than the curve in the way you claim, and I think you could clarify that a lot by showing that there’s another complicated curve running through those points where the patterns of increase and decrease based on increasing input is totally different, and make it more clear what it means for the line to fit the values if it’s not running through the points.

I also think that your introduction of the least-squares concept sort of brushes off a common intuition for what we could do other than squaring, which is just taking absolute values: you indicate that the residuals have to have different signs for each side of the line, but it’s not clear why if you don’t explain what residuals are. And the real answer to why we don’t do sum of absolute residuals, which a lot of people don’t know, is the Gauss-Markov theorem, which is obviously too complicated to delve fully into in this video, but I think indicating its existence could be an improvement.

Also, I understand that calculus is absolutely the right tool for proving the values of a and b, but you really jump into it with both feet, when a lot of your core audience (high schoolers, for instance) don’t know calculus, and even those who do might not be anticipating that sort of connection - where I live at least, there’s an expectation amongst people learning these subjects for the first time that you have a choice of “statistics or calculus,” not understanding how calculus informs the foundations of statistics.

I think what you have is an alright explanation for someone who already sort of knows what’s going on, but I don’t think you’re really putting yourself in the shoes of your target audience - which in fairness, is really hard to do, because I can tell you’re knowledgeable about this! So it’s hard to temporarily “forget” all the advanced things you know. And I don’t think you did a bad job actually making the video itself. I’m just trying to let you know where I see an area for improvement. I hope you have a nice rest of your day

This video does not offer much novelty since the basics of Simple Linear Regression have already been widely covered in previous works, but overall it is well made. The animations were great, despite some minor mistakes.

Pretty good. Some weird animation issues with the S vs F axes, but the explanation of ideas was very solid.

First of all there was a clear story line to the video. A nice presentation of a problem and then the detailed explanation of how to solve it mathematically. The visualization style was nice, however there are still some minor things left. e.g. the axis description flipping weirdly at the beginning of the video. The topic itself was not quite complex and easy to follow. Though I am bit confused on why the effects of “a” and “b” of an affine function have been explained and the general process of derivations have been assumed as general knowledge. Nevertheless, nice work.

Maybe give a quick review of correlation vs causation. Also, a deeper explanation of the properties of linear functions and why they are important for modeling data for the purposes you mentioned (what is the motivation for using linear vs nonlinear functions, and in what scenarios are they especially useful?) might help viewers get more comfortable with linear regression before they fully jump in. I also liked the challenge that you asked the reader to try and figure out at the end of the video, pushing them to dive deeper into the topics you covered.