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.

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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! :)

[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.

[thej]

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

[TheNettforce]

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

[think]

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

[Sandeep-zuwe]

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

[moart]

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

[Vierdix]

This is the best resource on learning statistics I've ever seen. I wish I found this channel 2 years ago.

[abhibhargav]

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

[dragonmateX]

As soon as I saw the covariance formula I was like "Hey look its linear regression sum of least squares!"

[rahulv]

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):

[jasonq]

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!

[SantiagoMolano]

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.

[mohamedmohamedabdallah]

dude i have been studying this for years
it is the first time to really understand the covariance
ty <3

[seahseowpeh]

I finally understand what covariance is after YEARS. You are the best teacher.

[iandanforth]

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

[رضافارسیمدان]

this video is great and when i heard the intro i thought Peter Griffin wrote it for you!
(thanks)

[faviorc]

Jesus Christ, this was an amazing explanation. Thank you Sir..

[young]

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.

[irtesamnasrat]

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! :)))