Deriving OLS Slope and Intercept Formulas for Simple Regression

* New Version: Here is a re-do of one of my oldest videos, on the mathematical derivation behind the ols slope and intercept formulas. The old one was rushed and cruddy. This one is much slower, and hopefully clearer. I was pretty tired when I made it though, so please let me know if I did anything wrong/confusing!

Note: At 16:05 when I add the Sigma, I accidentally write down a "-" in front of it. This should be a +, but this error does not carry through to the rest of the video.

[andotech]

This is pure gold. Thank you for not skipping any steps or combining too many steps! There are a ton of videos and documents online describing how to derive and solve these equations, and the vast majority skip steps and then I'm lost. In order to understand every detail, I need to understand every step. I do, now! Thank you!

[kevinberlanga]

This is the best video explaining the derivation ever. Please teach my class

[TubularOfficial]

THANK YOU!!!! IM ACTUALLY GONNA CRY CAUSE I GET IT

[lennyste]

Outstanding explanation! I just had 2 homework problems that used this "trick" of equating the sum of Xi with the sum of Xbar - I would have been lost without this video! Thanks

[Jamus]

Thank you so much for this video, you derived the OLS and explained every step you made in a much better and understandable way than my lecturer!

[kyliekent]

This is such a great explanation way better then my professor!!

[zm]

Really enjoyed your video. Learnt this today and I have exam tomorrow.

[jas-hysy]

For the two star equations at 19:33 .. can you show how to get from the first one to the second one?

[colinhendricks]

Can you watch 15:30-16:10 again please? I believe you may have accidentally switched the + E(B1*x-bar*Xi) to - E(B1*x-bar*Xi) when you are putting the summation signs (which I have represented with "E") into the equation. Would this change anything that follows?

[kalubakamanga]

Your videos are extremely helpful.Thank you so much

[JacobLocke]

Hey, thanks, I spent a lot of time looking for an explanation for this (19:07), not even the most recognized econometrics books explain it (they take it for granted) =D

[juanbravo]

can someone explain me how to get at min 17:26 sumatory of (xi - x_bar)? woudn't It be sum(x_i + x_bar)?

[deborahsakazhila]

Hey! How would you derive the OLS estimates for multiple regression?

[arnoldsalami]

This has been helpful, Pls can you do a video explaining the derivation of OLS estimators in Multiple linear regression WITHOUT using matrix algebra

[TheJohnlennon]

At 17:41 I think you may have got them the wrong way around (shouldn't it be *sum of beta 1 multiplied by x bar minus xi (in brackets) multiplied by xi*? multiplying out gives the *sum of xixi minus the sum of x bar xi*...whereas in the previous expression it's the *sum of x bar xi minus the sum of xixi*? Or does this order not matter? Thanks - videos are v.helpful btw.

[Esraberry]

Well explained , perfectly helpful 🙏🏻

[cecileboulanger]

Thank you so much i finally get it can't thank you enough

[jonathanlogrono]

is this true if we know that the intercept is equal to 0?

[shielamaetaotao]

thanks for this video. it unloaded some of my burden

[mastaniec]

I have assignments to complete. I want to get answers from you for that assignment. Can you help me and how can I send you that assignment to get answers☺️