This is one of the most clear, straightforward stats video I've seen in awhile! 👍

I can't believe how you make things that easy. Thx for this awesome content.

You describe things in absolutely clear and simple way, thx for doing this!!!

You're an amazing instructor and I really enjoy your videos. Great content. Can I make a small suggestion regarding a technicality - the camera seems to be fishing for focus every time you move in closer to it. If you manually focus and fix the focal distance so that the board is in focus, whenever you move closer only you will go out of focus for a brief moment ( not necessarily, if there is sufficient light you can use a small aperture that will allow for a greater focal distance ) and avoid the pitfalls of the slow autofocus.

I like how you give us little refreshers about concepts we may have forgot.

I was following while it was all about apples and bananas, but got lost when you started performing pear-wise operations

Thanks for making an effort to explain things at a slow pace. I love the way you don't use technical terms to explain things immediately, but then you do give us the technical term once it's explained. Much appreciated and subscribed.

Really simple and great explanation of the covariance matrix. It would be great if at the end you tell us what the covariance matrix means in terms of whether there was a relationship between eating a banana and apple - in this case, that yes, there is a positive relationship.

After giving Khan Academy a shot at explaining this poorly I came across this. Perfect. Thank you!

huge thanks for the explanation. i was reading a book about this but i couldn't get my head around it. your explanation clear things up. best of success to you, bro..

thanks. make more videos. you have a talent for keeping thinks understandable

I was struggling with this concept. You made it very simple and easy to understand. Thank you for this amazing content.

To the point, exemplified, condensed and so useful. Thanks for this video!

Excellent presentation but at 2:21 .... confused correlation with covariance with correlation coefficient. Correlation is not bounded between -1 and +1 that is rather the correlation coefficient Correlation coefficient is the one that is bounded. Also the explanation given ... when one is positive and the other is negative ... (that is the definition of correlation) Covariance has to be defined relative to the mean. Please double check in any Standard Statistics Book including Peebles or Papoulis... The presentation style and clarity is excellent. Keep up the good work.

This is one best explanations of the concept I have come across. You truly have a gift! Thank you.

Best explain on this topic! Concise and human friendly

Thank you. Very helpful video. Good luck

Can you do a series leading up to Gaussian process? I like your way of explaining things.

Thank you! This is the best explanation in the world! It really helps me! 👍

your channel deserves way more traction and sub count. keep up the good work. Thanks!!

Great real life explanation - extremely helpful. Thank you so much!!

I want to express my appreciation for tutor. Thank vey much

Excellent explanation. No confusion. No bullshit. Just 100% fruit

Damn where have you been all my life. Thanks dude.

So simple yet so clear. Thank you so much! Subscribed and can't wait to watch your other videos!

You're an excellent teacher! Wish to see more Stat videos from you! Thank you so much!

Amazing explanation! Thank you!

I'm from Germany and I understand you more then every german speaking teacher here

Your lecture is so straight that even non-english speaking student can understand easily. That's me. Thank you for the good lecture

Really good explanations - clear and concise. Thank you.

You are covering some very important topics which are generally not available. Please continue doing so.

Best video on covariance...thnks man

Your video is really easy to understand even someone doesn't have math degree

This video saved my life.

Thank you for that clear explanation. I don't have time to relearn statistics at the moment.

Thanks for this amazing explanation!

Besides StatQuest a really good and growing statistics channel. Subbed.

Hi, Ritvik you are creating awesome content. Please do keep creating such beautiful content.

There's actually an important difference between covariance and correlation. Yes, for both, in general you want that the larger one variable gets the larrger the other gets, and vice-versa. However, for covariance, if the value of one variable were fixed, you will always get a larger covariance if you make the other variable of greater magnitude, with the same sign as first variable. So for instance, if there were values for apple enjoyment of -3, -2, -1, 0, 1, 2, and 3, and they were fixed, you'd increase the covariance by choosing the values of banana enjoyment to be as negative as possible for the negative apple values and as positive as possible for the positive apple values (the 0 one wouldn't matter). On the other hand, (linear) correlation measures the degree to which the variables fall on a line. So, with the same example as above, we'd maximize correlation by choosing values of banana that were, say, equal to each for apple, or any set of values that make a straight line. This clearly means we would NOT want to just choose the largest magnitude, with appropriate sign, banana values that we can.

God Bless YOU! you saved me!

Thank you so much for this very helpful and intuitive video. It really helped me understand specifying mixed models in R!

sir you are awesome thank you second video I stumbled across and it was so clear

I loved this. You are EXCELLENT at explaining mathematics.

Thank you so much for such a clear and detailed explanation, it helped enormously!

Great video!

Great video! Thank you

Great video, would be awesome to give a little more intuition on why these numbers are so insightful ;)

Very well explained. Thank you

Thanks a lot, when you do your advanced stats class you tend to forget the pure basis elements of stats thank you

Great explanation!!!!

Thank you so much. In 10 minutes you explained it so clearly :D keep on with your videos!!!

excellent video, thanks very much

Awesome straightforward explanation thank you

This was an awesome video. Very clear and easy to follow.

Really appreciate the good work

I’ve never taken a stats class in my life and now I have to construct covariant models for NASA.... thank you so much! Now I just gotta apply this to MatLab, can’t be too hard lol

so clear, thank you sir!

I needed this channel in my life so much.

Wow! Now math seems fun and easy!

Your explanation was very clear. Thank you very much

AMAZING! So clear!!!!

Excellent revision

Thank you so much for this video!

Learning in quarantine..thanks man!

Greatly informative video, thank you! :)

Thank you, super clear!

well done

Thank you for making this simple and easy to understand :)

Understanding very well sir

Thank you very much sir. Very helpful!

You are doing a great work... Really appreciate your work, Thanks for the video.

Really awesome explanation

Helped me so much in econometrics! Thanks!

i wish i had professors like this in the uni. maybe i wouldnt have hated statistics so much.

Wow! So happy to have found this channel, you are a great teacher! Thanks!

simple and intuitive! great!

Great style of teaching!

Thanks, helped a lot. Liked and subscribed

Loved the video :D all the best for your channel

excellent stuff bro

Thank you so much for this!

Thanks so much for your clear explanation.

Nice explanations .. thank you

Great explanation Ritvik as always. Please can you make a series of Videos on Financial Calculus....?

This was so helpful. Thank you!

Excellent teaching..

Thank You sooo MUCH!!!!!! This was a brilliant way to teach!

Thank you for making videos

Hi! Shouldn't one devide by N-1 instead of N ? Because we compute the means from the samples. Should Cov(A,B) then not be 2/(3-1) instead of 2/3? Thanks

hey, can we subtract mean from each term to make each column zero mean before calculating covariance matrix. also some texts divide by n-1 instead of n. why is that? Thanks

Thank you! for the video, as always awesome tutorial video.

Great playlist and explanations!! Your camera blurs out at intervals, perhaps you could check that. Thank you for your lessons, they help a bunch!

Super understandable, thank u sm!

Very cool video, thanks for that :)

Solid video. You're good at this

Thank you for making this, very useful!

This is really helpful! Thanks a lot sir!

Fascinating thanks

I understood the concept very well. One question I have (i.e. what type of insights we can achieve by calculating covariance between two elements helps in real life ?)

Great video! I wish I would have some free time to enjoy teaching math and stats on KZfaq!