Covariance, Clearly Explained!!!

Covariance is one of those statistical terms that you might have heard before but didn't quite understand. It sounds fancy, but it's really quite simple and it is a computational stepping stone to many other interesting concepts like correlation. This video describes covariance, what it does and doesn't do, how it's computed, and why it is more useful as a computational stepping stone rather than an end in itself.
NOTE: This StatQuest assumes you already know about "variance". If not check out the quest: • Calculating the Mean, ...
And if you are interested in Part 2, which explains Correlation, here's the link: • Pearson's Correlation,...
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0:00 Awesome song and introduction
0:24 Review of variance
1:07 Motivation for Covariance
5:59 Types of Covariance relationships
7:32 How to calculate covariance
17:00 Why covariance is hard to interpret
20:31 Motivation for Correlation
21:20 Summary
Correction:
16:45 We should be dividing by 4-1, not 5-1. Oops! :)
#statquest #covariance

[@statquest]

Correction: 16:45 We should be dividing by 4-1, not 5-1. Oops! :) Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

[@statquest]

@武逸仙 The minus one provides an unbiased estimate. For an explanation of why there is a bias, see: kzbin.info/www/bejne/qXm1c5psd81-oKs

[@raj-nz4bj]

Great content for learners like us. Subscribed your channel. Even watched ads on video.

[@ankitaace5]

Shouldn't it be 5-1?

[@statquest]

@@ankitaace5 Since n=4 (there are 4 points in the graph), we have 4-1 in the denominator.

[@ankitaace5]

@@statquest Bam!! The whole video I was counting five dots , and then at 16:45 it was four dots. My bad!

[@Sandeep-zu6we]

I don't know why, but I feel like there should be "Superlike" button on these types of youtube videos

[@statquest]

BAM! :)

[@TheNettforce]

Thanks Sandeep, the KZbin gods listened to you and now there is a super thanks button 😉

[@kirstitties]

This is great. I failed year 10 and year 11 maths. As soon as you started talking about genes, my brain did that zoning out thing (monkey cymbals) but then you said "and if that's not your thing.... APPLES" ... I was like OK, I'm back, I'm here for it.... and then the doo doo doo doo to calculate gave me a smile. Top work. Subbed.

[@statquest]

Hooray!! I'm glad the video was helpful. :)

[@dannyisrael]

hahaha, same. and I'm in year 4 computer science... The apples saved me.

[@clovemao329]

same here, my brain brought itself to a picture of gene (like sequence of gene) and try to figure out what that axis mean to the genes. I guess it is flaw of human brain. Brain cell likes to connect itself to other cells, connecting the dots, yet such connection has never happened. Like this: 'statistic' cell -> 'biology' cell, error occurred, need to resolve first before continue, this cause me zoning out haha

[@MrJsganguli]

Damn..this guy us good. Too good.

[@thej1091]

Thank you for repeating in the same video. It's so underrated.

[@statquest]

Thanks! :)

[@rahulv7700]

Bam! The clarity of concepts, simple yet effective graphics and your amazing voiceover just made this nasty concept so damn interesting! You got a new subscriber):

[@statquest]

Thank you very much!

[@moart87]

The quality of the presentation keeps increasing Josh! Both from an entertainment and an educational point of view.

[@statquest]

Hooray!!!! Thank you! :)

[@_Chafia]

it deserves a book !

[@SantiagoMolano04]

Our stats for engineerin prof really really makes us feel deserted, you have no idea how much hope finding your channel has injected into us. Bless.

[@statquest]

Thank you!

[@think2086]

My cat thanks you. She learned a lot and is now doing my finances for me.

[@statquest]

BAM! :)

[@newgnewgg5447]

You are a legend.

[@statquest]

Thank you! :)

[@preetkamalhundal347]

@@statquest not a legand..... you are hilarious sir,,,,,,,, no words to explain your intelligency and way of explaining

[@michaelblostein]

I watched numerous videos teaching statistics and although there are many good videos describing these subjects and showing the formulas, this is the only video series that actually shows the logic behind the formulas, and as I always tell my kids, when you understand something you don't need to remember it, and these videos finally help me really understand these terms. They are clear and presented very well. Couldn't think of a better way to reach this subject.

[@statquest]

Thank you very much! I'm really happy that you appreciate my videos. :)

[@irtesamnasrat9866]

Josh, I’m really glad for being able to share the same planet with guys like you. I’ve watched your SVD/PCA videos and now this has saved me hours of internet research and the headache that comes with it. This is the most lucid explanation of covariance in existence. Can’t thank you enough (not just for this video but for each and every content you delivered and will deliver) for all the effort you put down for us. You’re truly what I call a lifesaver. May God bless you! :)))

[@statquest]

Thank you very much! :)

[@lugaresyplantas7819]

It's incredible, repeat, INCREDIBLE how you manage to turn difficult things into simple, easy to understand things. Thank you so much josh ! Greetings from Colombia 🐸

[@statquest]

Muchas gracias!!! :)

[@jasonq4816]

Not specifically on this video, but I hope you know your channel in general is a blessing to a lot of us out there. I took stats in undergrad and grad school and I can say with certainty you're the best stats teacher I have ever encountered. I don't use the word "enlightened" lightly but I sometimes feel that way after watching some of your videos on stats/machine learning. A lot of concepts I struggled with in undergrad/grad school and with CFA, somehow you're just able to explain them so effortlessly in a way I can understand. I really really wish you all the best with this channel!

[@statquest]

Wow! Thank you very much! :)

[@mirmubashir3128]

Sir how large covariance means strong relationship. ... although covariance means differences in two data set plzzz explain this

[@iandanforth]

This is hugely useful! I very much appreciate that you don't skip steps no matter how small as part of the explanation.

[@statquest]

Thank you so much! :)

[@petercourt]

Fantastic video, thank you! Your videos are the best explained on youtube, I'm so appreciative that you put the effort in to make these!

[@statquest]

Thank you very much! :)

[@bhanushreeprasad]

Though am new to Stats and have been away from learning for 15+ yrs, you make it so easy and kind of fluidy to learn stats now! I love your videos. Thanks a ton! Please continue your videos until eternity..

[@statquest]

Thank you very much!!! I'll keep making the videos as long as I can. :)

[@caspase888]

Have always been waiting for a video from you ... thanks 👍👍👍

[@ritubhatt3092]

It is the best video there is on Co variance. Made life absolutely easy. Thanks a lot from India🇮🇳 🥰!! DOUBLE BAMMM!

[@statquest]

Glad you liked it! :)

[@vikranttyagiRN]

Man you are phenomenal at explaining concepts in a way that's easier to understand. You are freaking awesome

[@statquest]

Thank you very much! :)

[@regexPattern]

One of the best videos I've seen. Your channel helps me undestand math better than many channels that speak in my native language.

[@statquest]

Wow, thanks!

[@prolixescalation1932]

Dude, you are the best. The form of the video, the explanations, the execution. The part that answered my main question was step by step calculation of an example, so thank you very much for this video - so much time saved!

[@statquest]

Thank you very much! I'm glad my video was helpful.

[@12tacco]

This is ridiculous, it's so easy to follow and understand! Better than watching Netflix 😅. These videos are amazing man!

[@statquest]

Thank you! :)

[@paulqin4613]

The best channel I have ever found on KZbin to get extra help in my statistics and data science study.

[@statquest]

Thank you! :)

[@rishabhkaul5556]

You are a legend. Your way of teaching is mindblowing. You make understanding concepts , a walk in the parkfield ! Thank you

[@statquest]

Wow, thanks!

[@chrisliu251]

Thank you for the amazing work. It's so much fun and very clear. After 7 pages of reading Covariance and Correlation, I felt confused. Your presentation makes it all clear for me! Thanks a lot !!

[@statquest]

Hooray! :)

[@fernandogutierrezcabrera4757]

I love your work. I didn´t understand covarice until i saw your explanation, I didn´t undertand it for 1 year! Awesome channel

[@statquest]

bam! :)

[@gurguer]

These videos in this channel are all great. They help me to clarify all basic concepts, which are very useful in the machine learning era.

[@statquest]

Thanks! :)

[@tealbaron]

Outstanding channel! Thank you very much Josh. Request for time series analysis if you have the time!

[@totomo1976]

I really appreciate the effort you put into making these educational videos. You're my hero!

[@statquest]

Thank you! :)

[@tikke8511]

I thought I already knew covariance, but this video gave me new insight. StatQuest videos are very much fun. Thank you and BAM!

[@statquest]

Awesome! :)

[@aartijarwani]

I have never been so interested in Stats than I am right now, after watching this video of yours! thanks Josh:))

[@statquest]

Hooray! :)

[@mohamednassef8612]

Thank you Josh for this amazing work! I really enjoyed your presentations and I appreciate the hard effort made in them :)

[@statquest]

Thank you! :)

[@tatianajaramillo1148]

I love you! Thank you for your videos, they are super clear and entertaining even though is statistics. You have just cleared a huge doubt I had. Also I guess they take a loooot of time to make, so I really appreciate it.

[@statquest]

Wow, thank you!

[@taianeramos6594]

What I like the most in this channel is the "bam" haha I really like that you make drawings to explain things. It is so much easier to understand this way. Thanks for doing all these videos. It is helping me a lot during my PhD!

[@statquest]

Thank you very much! :)

[@james08613]

Love you man !!! You make statistics and machine learning algorithms very easy to understand.

[@statquest]

Thank you! :)

[@sophiahennouni3276]

Brilliant channel, now every time I don't get a statistical concept seen in class I go look for the Quest!!! Actually even when I think I understand I still check the Quest :) Thank you so much for your amazing work, Josh.

[@statquest]

Wow!!! Thank you very much!!! :)

[@pamelavarela1235]

Seriously Josh, you are THE BEST !!! Thanks for such clear explanations.

[@statquest]

Thank you! :)

[@RaynerGS]

Incredible, how he can manage to explain so clearly, way to go!

[@statquest]

Thank you! :)

[@user-gc5ih9fm5y]

I kinda tried to figure out something like this when I was trying to understand covariance few weeks ago but with your visual explaination it is way easier to understand. Thank you very much for StatQuest

[@statquest]

Glad I could help!

[@GauravSharma-ui4yd]

Great explanation 💯, really very interesting. Josh I request you when you get some time please make videos on quantum Gaussian mixture models and deep learning related models like cnn, rnn, lstm etc.

[@waterbottle_9087]

BAM! Thanks Josh. I'm glad I found this channel. Are there quizzes or exercises I can do to test my knowledge on the subject matter after watching the videos?

[@statquest]

I have some quizzes on the StatQuest video index. Look for "StatTest!" statquest.org/video-index/

[@pianobunzz6514]

I want to give you a hundred likes after watching your video. It's very smooth and easy to understand. You're suitable for being called "teacher" in this world. Thanks man.

[@statquest]

I appreciate that!

[@jaouadrahouani4975]

Had problems understanding this for a whole year, you solved all of that in 20 minutes, god bless you

[@statquest]

bam! :)

[@conradsun7160]

thank you for explaining it so well! ive been studying statistics for 4 years + now but because covariance is, as you said, hard to interpret, so I never actually had a firm grasp of what it is (even thou ive used it countless times) this is so helpful

[@statquest]

BAM! :)

[@perrygogas]

You are great! the way you illustrate everything and the animations are awesome!

[@statquest]

Thank you! :)

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Bam!! I really enjoyed watching some of your videos during my free time. Thanks for sharing a nerd thing in the fun way. Thumbs up for you ;)

[@statquest]

:)

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Thank you for your outstanding teaching. This teacher is a legend.

[@statquest]

Wow, thank you!

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Hello Josh! Just wanted to thank you behalf of my friend for helping her to get through an interview with your videos. SO THANK YOU!!!

[@statquest]

Hooray!!! That's great news. Thanks for letting me know. :)

[@marczolghadri]

Thank you. Concepts become easy with these clear explanations.

[@statquest]

Glad it was helpful!

[@dr.bigfudge6497]

your explanation are just too good, I hope every teacher becomes like you

[@statquest]

Thank you!

[@saurabhmahra4084]

Thank you, Josh. I am a university student who just learned covariance like never before. Thank you so much.

[@statquest]

bam! :)

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This channel is awesome. I love your teaching style ❤️❤️❤️

[@statquest]

Thank you very much! :)

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Humor and substance together, legend!!

[@statquest]

BAM! :)

[@rainfeedermusic]

I tried to understand covariance and correlation from 2-3 other sources where I confronted equations and got intimidated quickly. Watching this video and next one helped me gain the confidence to understand these concepts.

[@statquest]

Hooray! :)

[@user-jh4lh1rc7z]

I'm not gonna lie. The best explanation I've ever heard about covariance. so much more worth than 3hours length lecture from my professor

[@statquest]

Thank you! :)

[@mohamedmohamedabdallah13]

dude i have been studying this for years it is the first time to really understand the covariance ty

[@statquest]

bam!

[@MrTimmy23]

Amazing, this was exactly what I was looking for. An explanation for why the formula works

[@statquest]

Glad you liked it!

[@fernleaf1]

appreciate the effort involved in making these videos.

[@statquest]

Thank you very much! :)

[@Mark-vr2nx]

Thanks a lot! I now have a much clearer view of covariance even I've already learned it years ago.

[@statquest]

Awesome! I'm glad the video helped clear things up. :)

[@aakshay8440]

I will be waiting for part 2 of covariance. I got a better understanding of covariance. thank you.

[@statquest]

Part 2 will come out on Monday, August 5th (just a few days from now).

[@thiagomoulinassis]

12:35 : laughed hard at this "bam". thanks for the content Josh! so much value on these videos!

[@statquest]

Thanks! :)

[@erdiozyldrm7108]

So precious, very understandable. Asthonishing job. Thanks a lot.

[@statquest]

Many thanks!

[@tahaelmaliani917]

Very clear and detailed explaintion of covariance. You rock man

[@statquest]

Thank you! :)

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Hooray:) I found a super videos about the basics of statistics on KZbin! Watching your videos like " do do do do do do" and I understood ,BAM!

[@statquest]

Wow, thank you!

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I feel more comfortable and clear listening to these videos than live classroom. And that makes me wonder the point of going to college while I am more efficient study alone at home.

[@statquest]

One day I hope that I can provide a full on-line course in statistics.

[@jaliu]

i love your videos and humor. i'm learning more here than i am in my masters.

[@statquest]

Awesome! :)

[@athomas4875]

best explanation for covariance and correlation. Thanks so much!

[@statquest]

Hooray! Glad it was helpful!

[@aureal710]

Wouuw triple BAM, your explanation is very easy to consume. Great Josh!!!!

[@statquest]

Thank you! :)

[@woodypham6474]

Whats on earth that we have such a good stat teacher like you!!!

[@statquest]

Thanks! :)

[@TheNettforce]

Thanks for the great videos, positive correlation between watching and understanding

[@statquest]

Hooray!!! Thank you so much for supporting StatQuest!!! BAM!!! :)

[@alinelermer6664]

Best Covariance and Correlation explanation ever!

[@statquest]

Thank you! :)

[@Skallagrim1993]

Thank you very much, the video is extremely helpful

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Simply the best! You made my day a little better again 😃

[@statquest]

I'm so glad!

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The best teacher ever. Thank you😊

[@statquest]

Thank you very much! :)

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Thank you so much! You are like a gift ❤️

[@statquest]

Thank you! :)

[@sabrewolf479]

Brilliant explanation. Thank you!

[@statquest]

Glad you enjoyed it!

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Extremely entertaining and helpful. BAM!

[@statquest]

Glad it was helpful!

[@amirmohammadjalili2676]

tnx Josh.You’re great as always.

[@statquest]

I appreciate that!

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Best channel for learning stats

[@statquest]

Thank you!

[@jaredgreathouse3672]

I don't know how familiar you are with it, but I would LOVE tutorials on stuff we do in econometrics such as.... minimization for synthetic control models, like the formula for how weights are generated, distance matching (you know, what we'd do for propensity score analysis), and this one technique called nuclear norm regularization, a cousin of LASSO, Ridge, and Elastic. But other than that, thanks so much for everything you do, this and Khan Academy has carried me from 6th grade to right now in my first semester of Ph.D in public policy.

[@statquest]

I'll keep those topics in mind.

[@vaibhavsahdev6615]

Amazing. thank you for such a fun and informative video

[@statquest]

Thanks!

[@abhishekbhargav9080]

At about 8:50, i got enlightened about the formula of covariance, i will never forget it in my life now, thank you

[@statquest]

BAM! :)

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@@statquest u mean triple BAM

[@user-kn9wu7ts9m]

Thanks a lot ! it give me an intuitive explanation of the covariance !

[@statquest]

Glad it was helpful!

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Thanks so much brother, this is the way everyone should learn. this dude is awesome. Thanks buddy

[@statquest]

Thank you very much!

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Amazing explanation. You save my day

[@statquest]

Awesome! :)

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You make statistics interesting to learn

[@statquest]

Thank you! :)

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Can you please do the "Correspondence Analysis" course ? Your explanation is sufficient and effecient , you have to make more vedios !!

[@VictorCaldo]

I love these videos, thank you sir!

[@statquest]

Thanks! :)

[@Marius-vw9hp]

Very full description made for us that needs the whole picture to understand it. Thanks.

[@statquest]

Hooray! I'm glad the video was helpful. :)

[@Marius-vw9hp]

@@statquest BTW, is there any logical reason for calling it CO variance? Is covariance to variance like cosine is to sine?

[@statquest]

It is called "covariance" in the way we say that two people "Co-operate". In other words, if the covariance is a large value (either positive or negative), than the two variables move together.

[@Marius-vw9hp]

@@statquest ok thanks :)

[@nicolasabino94]

everything Crystal Clear! great video

[@statquest]

Awesome! :)

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great job as always; definitely getting a t-shirt!

[@statquest]

Hooray! :)

[@ssuyash8]

❤ No comments.. Just love and respect

[@statquest]

Thank you!

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possibly one of the best explanation.

[@statquest]

Thanks!

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Your videos are way better than most of the paid courses.

[@statquest]

Thanks!

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Wonderful explanation and edition

[@statquest]

Thank you!

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Crystal clear explanation.

[@statquest]

Thanks! :)

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Great explanation, thanks!!

[@statquest]

Thanks! :)

[@AzureSupremuZ]

Underrated Video. Thanks a lot.

[@statquest]

Thanks!

[@vishalmadaan5668]

Amazing video, Great Explaination !!

[@statquest]

Thank you!

[@EVERYTHIN_007]

You are a great stat teacher on KZbin

[@statquest]

Thank you!