Covariance and correlation 

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!

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

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

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!

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

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

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

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.

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

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

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

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

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

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

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

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 :)

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

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

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

very good explanation. thanks. what is colinearity?

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

thank you for the intuition, ben!

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

Really appreciate for the perfect explanation.

Straight to the brain! Thank You!

Great explanation, thanks for sharing!

This is very good, thank you for your help.

Thank you, very clear explanation.

Great Explanation. Thank you!

Thank you very much. This was very helpful.

Thank you for the concise definition.

Ben Ji, Awesome video..

This is wonderful, thank you!

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

Super Catalin, très utile !

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

Thank you! Awesome video

Thanks man, this was really helpful

Very helpful. Thanks !

Cheers dude. Helpful video

Thaaaaaank youuuuuu. So breif and clear.

Thanks, this was really enlightening

Good video, explained well and on point

Exam in two days, great videos

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.

This is helping me so much, thank you!

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

this what I want intuition tnx man

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

thank u very much！

Brilliant!

can you give about jtc cross correlation detail

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".

Thank youuuuuuuuu 😘😘😘😘

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?

Excellent.

Giga chad, thanks!!

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.

Nice!

What does it mean to "plot a realization?"

really enjoys the word sort've...

Thanks

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 ?

Thankyou

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

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.

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?

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?

Good!

Clear my doubt

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" ?

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

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....

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

cheers lad

100%

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

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????

save my life

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 RU-vid.

help

cut out the 'sort of' 🤣such a brit!

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

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

The logic is fucking confusing

try saying "sort of" less often

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