Covariance Clearly Explained!

Covariance is closely related to Correlation. But what it really says? This video explains covariance with visualizations.
#machinelearning #datascience
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[@BrianAmedee]

The fact that I (a math teacher) learnt something new from this, means my students need to see it. Thumbs up my friend

[@NormalizedNerd]

You just made my day! ❤

[@GMoDiLLa]

I’m a statistics student in my final year of undergrad. I just felt like checking out a video on covariationnas we begin PCA. This is by far the most clear it has ever been explained, and so succinctly! Well done, I feel I can think about it more clearly now.

[@pewpewhuang4162]

Could you explain why eigenvectors corresponding to largest eigenvalues maximize projected variance intuitively? really asking

[@oskarvavtar4990]

Some extra things that would be worth mentioning: 1) in the absence of linearity, the correlation itself may give you very little information. In some cases, data set with Corr = 0.9 might be closer to the one with Corr = 0, than to the other with Corr = 1. In other words, very weak trends (maybe not even worth mentioning) may give you high Corr value. 2) In random generated sets, certain degree of correlation may appear randomly, without a good reason. 3) Not only does correlation not imply causation, causation doesn't imply correlation as well. Take for example y = |x| for x \in [-1, 1]. Clearly y=f(x), yet Corr = 0.

[@NormalizedNerd]

Great comment! May be I will make a dedicated video on Correlation in the future :D

[@YourNerdGal]

This is literally the greatest explanation that I've ever heard. Beautifully animated and very straight to the point. The best video ever on this topic! You saved my life!😊

[@veronicatellnes6424]

Actually such a good video, the visual representations helped me finally get the inuition i was missing for covariance. Thank you!

[@thecheckplease2357]

KZbin can't be serious that this video doesn't top their search result! Kudos to the channel. This video seriously deserves every compliment this world can offer. Keep up the great work thanks!

[@thisukainol]

6:34 6:34 For example, let's say we observe a correlation between the number of ice cream cones sold at a beach and the number of drownings. There might indeed be a correlation, as both tend to increase during hot summer days. However, it would be incorrect to conclude that eating ice cream causes drownings or vice versa. Instead, there could be a third variable, such as temperature, that influences both variables independently.

[@jepp1572]

Instantly subscribed. Please keep up the work! Amazing visualization.

[@luvshell1]

I agree; this video was amazing! And you are so right- the video, in the end, was so good to see what the values look like at different plot points.

[@ReubenSilveira6]

Excellent video. Very intuitive and well explained! As someone who's both a student and a teacher of maths, I'm impressed from both angles!

[@hariind86]

The animations helped me get an idea of what I was calculating for this long :) Maths is beautiful✨

[@7ezem345]

great video ! i really appreciate the effort you put into this

[@wenwenbai]

Great video. You really did explain the concept in a very elegant way.

[@EpicGamer-ux1tu]

It's crazy learning correlation without telling you about covariance

[@robertturley2974]

Fantastic explanation, but one of the things that really sets this apart from some of the others I have seen is that you take time at the end to show the different values for different points. Really a great way to both help people visualize and check if they understood correctly.

[@tomhaswell6283]

Incredible explanation and visualization! Thank you!

[@dimitrismylonas4159]

Thanks for this video, you really helped me understand covariance visually.

[@kadidiasaboudoumbia4797]

This is so well explained. Thank you so much

[@nicolesamuel1838]

great video! you really helped me to understand in 7 minutes what my proffesor could not in 1 hour! thanks!

[@dineshkumare1750]

this is the kind of explanation we need . 🙂

[@zakaboudich2972]

what a beautiful animation, amazing video friend!

[@SENSE.WORLDWIDE]

First time I comment a video of a math explanation in years, wow very good!

[@rishabhnarula1999]

thank you sir, great teaching and visualizations. 👍😊

[@montanalee3560]

Great video, thank you! I finally understand covariance. Very helpful and beautiful visualizations as I study for my statistics final :)

[@akashpratapsingh9298]

The video looks more like an animation exercise rather than an educational video. The formulas are explained but the intuition behind them is as opaque as before. A few videos from 3Blue1Brown could be a good reference for this channel.

[@michelleelizabeth9956]

Good animation, well explained, thanks for sharing 👍

[@luataina5253]

Very intuitive, thanks!

[@komudamatata5492]

amazing video, so happy I came across it

[@Copley417]

Excellent explanations!

[@MOHDIMRAN-zc4ev]

thanku so much man

[@mainakmukherjee3444]

Can you tell me why we perform eigen decomposition to the covariance matrix in PCA ?

[@Muneh14]

that is exactly what i've been looking for for along time ,,, very clear and a big thumb for everything but espessially for the last visualization .....

[@christosm.2407]

Amazing intuition and excellent animation! Interestingly, the sign of correlation follows the monotony of sine function in each of the 4 quarters of the unit circle. In the top right quarter [0, 90deg] the sine function is monotonically increasing and correlation is positive, in the top left quarter [90, 180deg] the sine function is monotonically decreasing and correlation is negative and so on.

[@NormalizedNerd]

Thanks mate! Is this observation true for bottom two quadrants?

[@christosm.2407]

@@NormalizedNerd Ah! Actually not. In the bottom two the behavior is reversed! The sign of tangent in each quadrant would have been a better example. :)

[@nourredinekebaili]

thank you it is clear!

[@GarrisonBush]

Very helpful thank you!

[@melodylin5058]

the visual is sick!! amazing

[@bello3137]

well explained !

[@ggxue]

thank you clearly explained.

[@OmarAmil]

Thank you

[@ryanpereira9238]

Well explained.

[@steven_king]

Wow this is fantastic

[@neethinnandakumar4303]

Can't wait for your channel to get discovered

[@FariaManalRahman]

thanks!!!

[@yts9363]

well explained

[@S.G.2]

tyvm

[@MeargNgusseSahle]

thankyou

[@michaelcoleman7762]

great video!

[@enzeru97]

Perfect!

[@raghavbhatia5548]

amazing and satisfying

[@pavlonatalenko1828]

Brilliant animations, thanks

[@NormalizedNerd]

Thanks mate!!

[@ishitaswaroop8779]

very good video!

[@ayaelayyan8826]

amazing video

[@Dubai_life_]

Thsnk you much. Please more statistics.

[@jmb9040]

eloquently explained

[@PritishMishra]

1:37 Hello sir can I know how you drew that type of Graph with Manim? I just want the name or line of the code about how you drew that kind of grid please sir!

[@NormalizedNerd]

For creating the grid you need to use NumberPlane object.

[@PritishMishra]

@@NormalizedNerd Thanks man

[@MrJeepiez]

super good animaitions and music

[@abuhelal2073]

super video

[@sathiyanarayanan7245]

Thank you..

[@lucasluzzi]

This is art

[@KristalBox]

Damm next level teaching

[@EthericImpulse]

That is beautiful 😢

[@malikjavadov366]

this is the best thin ever!

[@user-gh6xx7mx1x]

Nice animation

[@sauravmishra2010]

It’s truly intuitive … is there a way I can connect with you?

[@prajakta4359]

Best explanation..👍..sir, please make videos on regression line.....🙏

[@NormalizedNerd]

Thanks!!

[@govamurali2309]

Please do degrees of freedom

[@thienphan1541]

This video is well explained than my teacher

[@felicemorgigi1764]

I recognise a lot of 3Blue1Brown's animation and audio style here ^^ nevertheless, thanks for the helpful video

[@NormalizedNerd]

Yeah, I'm using his python library!

[@lliw4934]

Lovely animations, 3B1B style c:

[@NormalizedNerd]

Thanks a lot! Yup using his library.

[@TheoriesofEverything]

Limpid. Great job.

[@NormalizedNerd]

Thanks a lot :D

[@Aziiz_Bejaoui_7]

wow