Covariance and correlation

This video explains what is meant by the covariance and correlation between two random variables, providing some intuition for their respective mathematical formulations. Check out ben-lambert.com/econometrics-... for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: ben-lambert.com/bayesian/ Accompanying this series, there will be a book: www.amazon.co.uk/gp/product/1...

[@SpartacanUsuals]

Hi, thanks for your comment. Good question. Essentially what it means is that the maximum covariance between two random variables, X and Y, is given by when the two variables are the same. In this case the sqrt(var(x).var(x))=var(x). The proof of this depends on the Cauchy-Schwarz inequality, and was a little too involved for me to post here. However, I have added it to my list of videos to do in the future. Best, Ben

[@ARM26878]

Hi Ben, have u gotten around to making that video? if yes could you please post the link? Thanks

[@cgabt1109]

Good content lasts forever. This has been useful for me, old engineer dog in his mid 50's , relearning statistics. I couldn't get my head around the differences between these two measures - your video did the trick!

[@luckyprod9013]

Man i feel you, 45 years old here and relearning math for my trading after 20 years spent on excel in corporate finance lol

[@jospremji]

@@luckyprod9013 hey, im into trading as well. how are you using statistics for your trading?

[@meshreporting]

These videos have been nothing but helpful. Thank you so much!

[@SpartacanUsuals]

Hi, glad to hear they are useful! All the best, Ben

[@talkohavy]

Well done! I'm taking a course called Linear Regression and I learned a lot from your video. Thank you for the lesson.

[@darynaivaskevych1907]

Thank you for the brilliant explanation! I finally understand why these formulas are like this.

[@tjfirhfjejUTH24]

good video very clear. if anyone is having trouble make sure you really understand joint pdfs, and expected values.

[@imranmahmood6105]

Why doesn’t everyone explain these concepts like this? This was excellent. Thank you!

[@h-s7218]

this video was just a piece of art ! thank you so much! well explained and really clear and smooth !

[@kejeros]

Thank you so much. I am actually getting excited for this final now. haha!

[@tymothylim6550]

Thank you very much for this video, Ben. It really helped me understand the intuition behind the formulae, as well as the relation between Cov and Corr! The visuals helped a lot with explaining, too!

[@batuhantekmen6607]

Very intuitive and can be watched along with a formal explanation or numerical calculations! Thank you.

[@myvoice8167]

Hello Sir,You are such a good instructor.Great job!!!!!! May God Bless you and your loved ones..

[@alextessier5727]

So helpful to finally understand the difference and the why's! Thank you!

[@imzhaodong]

I would say these videos are just awesome. thank you so much for effort.

[@harunsuaidi7349]

Ah, so that's where it comes from. I'm an Art graduate learning Statistics for my master degree in Instructional Technology. I never quite got how one could figure out the mathematical expression of the relationship between two sets of data. Now that you explained it, it becomes much clearer. Damn, mathematicians are smart.

[@gabrielasantana3809]

This guy just has a video for every question, thank you

[@kamalgurnani924]

Thanks a lot for explaining the idea behind that intuition!!!

[@shashikalaraju5769]

Perfect. You are amazing teacher. You inspire me. Thank you

[@Stirner219]

It's really nice that you also explain the underlying logic of cov and cor. B/C doing without understanding is not much worth. Thanx :)

[@edentrainor776]

This is such a damn clear ad well explained explanation it hurts.

[@antibioticsOfWorld]

thank you !! i am doing masters in data science and it helped me to understand the basics properly

[@july-9319]

thank you for the intuition, ben!

[@owenlie]

Straight to the brain! Thank You!

[@user-zt8dj4nq9g]

Really appreciate for the perfect explanation.

[@Kike_Reloaded]

Great explanation, thanks for sharing!

[@palashmyaccount]

Great Explanation. Thank you!

[@nackyding]

Thank you for the concise definition.

[@Elsmeire]

Exam in two days, great videos

[@waihinlee3899]

Thank you, very clear explanation.

[@hondopirat2735]

Super Catalin, très utile !

[@Josh54152]

This is very good, thank you for your help.

[@aref6561]

Thank you very much. This was very helpful.

[@isabelchen3302]

This is wonderful, thank you!

[@saraw8951]

Thank you so much! it's really helpful for my paper

[@emanuelhuber4312]

Thank you! Awesome video

[@COSMOPOLITANWORLD]

You made it easy to understand! Thanks a lot!!

[@emilylawrence6051]

What kind of people disliked this video? this video is amazing! Thank you Ben!

[@husseinfarag7937]

Thanks man, this was really helpful

[@Skandawin78]

very good explanation. thanks. what is colinearity?

[@Banaan1985]

Cheers dude. Helpful video

[@JackTheOrangePumpkin]

Thanks, this was really enlightening

[@jfregnard]

Very helpful. Thanks !

[@sophievanbeek7768]

This is helping me so much, thank you!

[@TrangPham-cy5km]

Sophie Van Beek i dont know how to identity the (+) or (-)of Y. Can you help me

[@SachinModi9]

Ben Ji, Awesome video..

[@moliv8927]

Good video, explained well and on point

[@najlahs7311]

Thaaaaaank youuuuuu. So breif and clear.

[@amanuelnigatu4621]

this what I want intuition tnx man

[@Jdonovanford]

I've read that the formula for betas is beta=cov(x,y)/var(x). However, the formula given in many places for betas does not divide by n (or n-2): beta=sum[(x-x_m)*(y-ym)]/sum(x-x_m)^2. IN this formula, neither the numerator or denominator are divided by N or n-1… to be called covariance and variance.

[@nickpenacl_]

question not related with topic ... which instrument (system) did you use for write in the board, will appreciate your explain

[@katiegraham8484]

This is an awesome explanation. It would be even better if there was an example to accompany it

[@bharathbhimshetty8926]

Yep...

[@nicholaschen5821]

well, u said when P=1, it means X and Y are perfect positively related. Is that mean the gradian of the line is one or this just mean the points are in the same line and no matter the degree between the line and X-axis?

[@SpartacanUsuals]

+Nicholas Chen Thanks for your comment - good question. If two variables are perfectly correlated then it means we can draw a perfectly straight line through samples from both variables. It doesn't require however, that the relationship is 1:1 between them. Essentially perfect correlation just means that we if we had one variable we could perfectly (ie with no error) predict the other variable. Does that make sense? Best, Ben

[@nicholaschen5821]

Thank you, that is a very helpful answer!!!

[@GK-qv3xd]

Brilliant!

[@horizontaalschaalbaar9470]

Love the black background. For some unknown(?) reason, almost all programs use white backgrounds, which I hate because I don't want to be sitting in front of a big ball of light. Tip: there are great plugins to make webpages "dark".

[@horizontaalschaalbaar9470]

I readded this comment because it was deleted. Why??? Strange things happen here... It even had likes gd!!!

[@khazovaru9892]

Thank youuuuuuuuu 😘😘😘😘

[@SciFiFactory]

Ah, so it is basically the normalized slope of a linear function? y=m*x with the slope [m]=[y/x] Then times x on both sides: y*x=m*x^2 On the left side would be the covariance, if you were to substitute it with (y-mu) and (x-mu). And then to normalize the units on both sides they are divided by something that has the same units as y*x. So here we use the standard deviations sy=sqrt(var(y)) and sx=sqrt(var(x)) .... But I am confused why it never gets bigger than the standard deviation? I mean, aren't like 32% of the samples out side of the standard deviation? So that in 32% of the cases you have something like (y-mu)>=sy , or in 5% of the cases you have something like (y-mu)>=2*sy ?

[@andrescheepers3223]

really enjoys the word sort've...

[@henriquebenassi]

Excellent.

[@randomyoutubeaccount6906]

I needed an example. What id Mew? and the expectation, is that the mean? also do we use the total of x and y anywhere? Sorry i'm bad at math and got lost in this video at the same point every time I watched.

[@kunstkt]

Towards the end you say that var(x)*var(y) is "the greatest possible way in which x and y can covary". What does that mean?

[@diodin8587]

+1

[@kunstkt]

@@diodin8587 corr=cov/sd(x)*sd(y). The strongest possible correlations are 1 and -1, and they correspond to covariances of sd(x)*sd(y) and -sd(x)*sd(y). He must have meant the square root of var(x)*var(y).

[@trent_tsu]

thank u very much！

[@MochitoMaker]

I don't get why in one case we have X>Mx and we get +++ and then we have the same equation with X>Mx and we get +- - What's the logic? Thanks.

[@ugurgudelek]

X and Y dont have to be perfectly correlated. So, in some X>Mx cases, Y can be smaller than its mean.

[@sidekick3rida]

What does it mean to "plot a realization?"

[@priyankpatel4041]

can you give about jtc cross correlation detail

[@GEconomaster112]

Giga chad, thanks!!

[@EOCmodernRS]

I'm not looking for a formula, I'm looking for examples. I don't get the formula. In my head it says ''(E(x)-E(x))*(E(y)-E(y), which is 0. I don't get the formula....

[@ARM26878]

at 4:50 whats the intuition that the covariance of x,y can never exceed variance of x times variance of y" ? Thanks

[@ARM26878]

probably you meant - the covariance of x,y can never exceed std dev of x times std dev of y" ? I'm still not sure about its intuition.

[@christinating1340]

why use covariance when correlation can tell you the direction and strengh of a relationship in a standardized/comparable form? What does covariance give us that correlation does not?

[@DmitriNesteruk]

There are plenty of places where covariance is used _in lieu_ of correlation. For example, in Modern Portfolio Theory we calculate the covariance matrix in order to be able to calculate the efficient frontier.

[@hugovreugdenhil]

Thanks

[@sanathgunawardena832]

Nice!

[@utkarsh5667]

how did you prove that cov(X,Y)=0 implies there is no correlation between the random variables?

[@arunthashapiruthviraj2783]

Clear my doubt

[@deepak2012able]

Thankyou

[@shrijithr9345]

Can someone tell me or point to me someplace where it's explained "How we 'know' that the covariance of x,y can never exceed variance of x times variance of y" ?

[@ARM26878]

I have the exact same doubt. Did u find out the answer?

[@robertotosacanogalarza9021]

Good!

[@Darius1295]

Important to point out that Covariance and Correlation can be zero even if the two variables are dependent.

[@piersanna8866]

you say, if x is higher than its mean, then y tends to be also positive. But seconds later yous say if x is higher than its mean then the second parenthesis is likely to be negative. this doesn't make sense and is a contradiction.... could someone please explain????

[@mohammadrezakhedmati7777]

He's talking about two different scenarios. In the first one, he assumes X and Y are positively correlated ( just like the first graph he drew) and in the second one he assumes these variables are negatively correlated (second graph). That's why the sign of the second parenthesis varies. You've probably figured this out by now, but I tried to give my explanation just in case someone else has the same question. Cheers!

[@pomegranate8593]

cheers lad

[@magnusonx1]

British accent....NICE ! ! ! Wishing all Yankees could have British accents

[@hamzatarq7000]

100%

[@tastsolakis1519]

thanks for the explanation really good! Next time though please talk a little more clear!

[@pkavenger9990]

In future I think Universities will go obsolete. Any Government can pay experts to make a course and just upload it. Why burn your fuel and energy to get to a place and then spend so much energy coming back home to learn the same thing you can learn from just KZbin.

[@joannaqian7755]

save my life

[@zip9267]

help

[@krunkerdylan6146]

cut out the 'sort of' 🤣such a brit!

[@bebla8381]

i want the fucking explanation for the formula, the intuitive reason of why it is what it is. why is that so hard to find? the ACTUAL intuitive explanation for the formula, every fucking video about covariance they show you the formula and thats it.. it makes me wonder if anyone actually understands where the formula truly comes from

[@deedi9001]

The logic is fucking confusing

[@ilhamkseibi6157]

oh man, things with you sounds much more complicated, if you are trying to do something like khan academy, well you are not

[@GuglielmoRiva97]

try saying "sort of" less often