Weighted Least Squares: mathematical introduction

[@SpartacanUsuals]

Hi, many thanks for your comment - much appreciated. Best, Ben

[@gausspro8937]

An extremely solid explanation of WLS! Even though 8 years later, +1 for you Ben!

[@natureshorts6657]

This video is awesome. You explained this well, and the math makes so much sense. My professor spent about 5 min on this total, which wasn't really enough to understand it all. Your videos help so much. Thank you!

[@jarrodvos2347]

Excellent explanation; thank you, Ben.

[@anasfrh]

Hehehehe, I remember in high school further math, there were people who used to just randomly think of some transformations like the division you did to solve some problem and that never came to my mind naturally. That's when I realized that down the line, if I ever wanted to do math at an advanced level, a lot of it is probably about somehow thinking of these creative transformations or assumptions that seem so obvious after the fact but are hard to think of intuitively (at least for me).

[@samarioantonio]

man you go OFF!!!! good work...can you do grad level bayesian analysis?

[@pawanacharya2915]

I am using the weighted regression for the new lab data. How can I define the weights for the respective data set ?

[@zenith_journey]

apparently im at a top university, but this explains it so much better. thanks a lot ben!

[@lastua8562]

which one?

[@monicadias1830]

Mr Ben Lambert, would you like my 9000 pounds per year tuition fees because my university doesn't deserve it. you do!

[@alhabfortnite5297]

make that£9250 :/ also we offering him 3% interest on top too? :/

[@lastua8562]

@@alhabfortnite5297 interest on what?

[@ambroseezzat2703]

How about you blame yourself, not your university? It's your job to go out and learn, and to supplement your material. Your professors have PhD's and lifelong experience in their fields. Don't insult them. They're not supposed to hold your hand.

[@xuanminglu1507]

You manage to teach what took my professor 3hours in less than 30 minuets and in a more clear way, love your work.

[@arnek1568]

Nice video Ben, clears things out! I do have a question about when we are dealing with categorical variables (with heteroskedasticity). In this case we can't use the weighted least squares method, I guess? From what I've read, you could use the White Huber consisten robust stand. error method. Have you got any idea how this works? Thanks already!

[@lastua8562]

with categorical variables you cannot use usual regression models as data points are not of quantitative structure and cannot be ranked. If they are categorical ordinal, perhaps you could but you'd need to be very careful about interpreting the models I suppose.

[@radeenmostafa6987]

@@lastua8562 i guess the person you replied already pass the university level lol

[@NhatLinhNguyen82]

What if Var is not a linear combination of sigma squared and xi squared, but let say, non linear, xi^2, or 0.5 * xi?

[@SpartacanUsuals]

+Nhat Linh Nguyen Thanks for your comment. Suppose that the variance is a linear combination of xi and xi^2 equal to f(xi). You could use this variance function to make weights. Those weights would be equal to the square root of f(xi), which would mean that var(ei/sqrt(f(xi))) = f(xi)/f(xi) = 1. Does that make sense? Sorry, it is difficult to write eqns. on these comments. Best, Ben

[@NhatLinhNguyen82]

Ben Lambert Thank you Ben. I think I got it. Also your next videos explaining about how to estimate the weights. I got 2 masters degree where they covered Econometric very briefly so you videos becomes essential for my professional growth.

[@SpartacanUsuals]

+Nhat Linh Nguyen Glad to hear it. Whereabouts are you? What sort of work are you doing with econometrics? Best, Ben

[@NhatLinhNguyen82]

Ben Lambert My career is in finance, but I was more a qualitative / fundamental analyst guy. I want to move to the asset management, where econometric is an important part of doing research on asset class performance and also evaluating quantitative strategies.

[@lizi9019]

The showing of the variance being a constant is pretty straightforward. But can you please show me why E(epsi/square root of x)conditional on x equals 0? You need an error term that has a constant variance and zero mean for OLS to work. I've not found people showing this and I cannot prove it myself. Thank you!

[@lizi9019]

What I was asking is how a remedy to hetroskedasticity can cure/less the potential problem of endogeneity. The answer is no. In practice, you need to address all of these issues respectively to ensure that the OLS is or close to being a blue estimator. Lecturers always teach ways to treat these issues in a way that gives you the impression that if a regression model has an issue with one thing, you go fix it and now the regression model is free of any other issues. When I raised the question, I just started to learn econometrics at PhD level. Now it's been a whole semester and I've somehow established a better understanding of stats in general. P.S. this guy's lectures are really good for an intuitive understanding of stats, but they're all at only master's level.

[@jinxianglai166]

nice work man!

[@SarfrazRazaOfficial]

which tool u r using for writing?

[@mualagathaaa666]

thank youu! you rock. God bless you!

[@dimuthu999]

very helpful. thanks a lot

[@ambroseezzat2703]

But why do you pronounce "Linear" the way you do? The real question that keeps me up at night.

[@bradley5210]

lin-ear

[@olofreichenberg6885]

Great!

[@naegahosh4746]

Istg you just took that 6 minutes and 33 seconds and my lecturer takes weeks just to explain this thing and nobody still know wtf is going on in class lol

[@Hamking1]

This video makes me cry :'(............... only because I wish you could be my professor and not my current professor: mr. kim jong un-able-to-speak-english