Least Squares as a Maximum Likelihood estimator

This video explains how Ordinary Least Squares regression can be regarded as an example of Maximum Likelihood estimation.

[lhansa]

Great Video, Ben! For all of those who are still wondering what ML actually does and why we observe an identical result for the Least-Squares estimator, I would like to give a short intuition: For every unknown parameter (i.e. the mean of a distribution or the least-squares estimator), ML literally "maximizes" the likelihood of observing your actual data with respect to your unknown parameter, given an assumed distribution. In the context of Least-Square estimation, we assume the errors (not the residuals) to follow a normal distrubution with zero-mean. Hence, ML finds the least-squares estimator (recall that the errors are just a function the least-square estimator) which maximizes the likelihood of observing an error distribution which mean is 0.
Note : Errors are never observed, solely the residuals . Hence, for any inferential calculations, errors must be estimated in a second step.

[linhphan]

Thanks so much for all the videos. They really help to build the intuition before reading the technical textbook

[programacaosimples]

Thank you, Ben! You are the best teacher I`ve ever had. Because of you I am teaching econometrics in R for portuguese speakers

[robertzimny]

Hi, why is the (x-mi)^2 part of the pdf replaced with (y_i - beta * x_i)^2?
I mean the formula around ~ 2:25 in the video.

[tighthead]

Hi Ben, thanks for the great videos they're a great help. Could you point me to some material where I can find a similar derivation for the linear regression model which includes B0 (intercept)? I guess your video should be the exact same derivation until the derivative part (chain rule)? Many thanks again.

[mariodamianorusso]

Hello ben, love your videos, graduating without them would probably be much harder. Just two things that I think might be wrong (hopefully this will save some confusion for the other viewers):
1) at 3:28 you say "to the power N" but you write a 2 instead.
2) what you write at 2:06 is the distribution of y_i~N(x_i*B, sigma), not x_i

[deepaknandwani]

Awesome and great teaching skill you have, Thank you so much.

[bluejimmy]

At 3:19, why the product of the probability not equals zero? The probability of exactly one value in a pdf is zero. The product of many zeros is zero? The likelihood function will always give you zero? I think it makes sense for discrete probability. How does the likelihood formula make sense for continuous random variable?

[mehradghazanfaryan]

how can you manage to simplify all the crucial stats material this much where professors who teach the graduate degrees are absolute unable to do so

[developandplay]

Thank you this was exactly what I was wondering about. This link is not that commonly explained. If you just want that confirmation and know all of the math already just watch 7:15

[crossvalidation]

Awesome video, very helpful!!! THANK YOU!!!

[mosessiphegaba]

Hi Ben thank you so much for the video...

[muhammadseyab]

Sir have u uploaded related to Baysian Estimator Your videos are just awesom

[manojnagendiran]

Hi thanks for the video.. I have an clarification'
shouldn't be the likelihood function L=f(yi | beta, sigma)=gassian distribution ( instead of Xi)

[goncausta]

very good explanation thank you so much

[stefandindayal]

Hi Ben, first off love your videos. Just wanted to know how did you get the likelihood function in the beginning.