I am assuming that you got lost when he said that the Expectation of A * Expectation of B cancel out to zero. By that he meant A= 1* 3 * -1= -3, B= 1*0*1=0 So, the Expectation of A = -3, and the Expectation of B=0, now, multiply A(-3) * B(0) = 0;
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.
Thank you so much for the suggestion! I had a couple videos around this time where the focus went in and out and I apologize for that. In my more recent videos, fortunately I did exactly what you suggested so they are easier to watch. Thanks!
i dont mean to be so offtopic but does any of you know of a trick to get back into an instagram account..? I was dumb forgot my login password. I would love any help you can give me!
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.
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..
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.
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
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
He is taking the covariance of entire population i.e. all 3 people therefore, he divides by N. Had he taken a sample out of this population, he would have divided by N-1.
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.
The equation he used for covariance seems to give the same results as another formula I see being used as the standard online, I just can't figure out how to view them as equal. The equation I see online is E[(x_i-E(x)) (y_i-E(y))] Would love some clarification.
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.
Yeah, might want to check your definition of covariance. I'm pretty sure you understand it intuitively but I suggest polishing your definition. It's not so much that two variables "go together." its the measure of how they vary together i.e. if an observed change in x relative to the expected value of x is observed by an equal or similar change in y relative to the expected value of y. It is not dependent on whether the change is in the opposite (+ or -) direction.
"The correlation is standardized covariance, normalizing the covariance with the standard deviation of each variable." From: www.cambridge.org/9780521766333
Very often one can see a formulation like variance-covariance matrix. Is it the same as covariance matrix and are being used interchangeably, or variance-covariance matrix should denote something else?
let me say this once and for all, "there is a huge requirement for professors like you at all the universities on the planet if they have to sustain in future"
Hi there :) Extremely well explained video, thank you! I ended up here as I am trying to run Little's test for missing variables in Stata and the error I am getting says "sample covariance matrix is singular for at least one missing-value pattern" -- Whilst (after some videos)I know what that means in theory, I have no idea what to do with that information now, how it affects my test, and/or if that means I should exclude the 'problem-variable' or use a transformation. Do you have any recommendations? Thank you in advance!
good video. one comment: disable the autofocus in your camera when shoting whiteboard lectures, waiveing the hands in front of the camera puts it out of focus
Thank you very much your explanation was great, the only question is that what is the relation between the curve you plotted at the first of the video and the calculated matrix?
pls mention that this is doing only for the population, not for the sample. because there has another equation for covariance. that can be done both population and sample also. reference: corporatefinanceinstitute.com/resources/knowledge/finance/covariance/
This is one of the most clear, straightforward stats video I've seen in awhile! 👍
I was following while it was all about apples and bananas, but got lost when you started performing pear-wise operations
wow ... hilarious!
@@ritvikmath That's not nice!
I am assuming that you got lost when he said that the Expectation of A * Expectation of B cancel out to zero. By that he meant A= 1* 3 * -1= -3, B= 1*0*1=0 So, the Expectation of A = -3, and the Expectation of B=0, now, multiply A(-3) * B(0) = 0;
@@captincanuckjones1664 The joke was the 'pear'-wise operations (cause you know... fruits), but it's nice of you for explaining!
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.
Thank you so much for the suggestion! I had a couple videos around this time where the focus went in and out and I apologize for that. In my more recent videos, fortunately I did exactly what you suggested so they are easier to watch. Thanks!
thanks. make more videos. you have a talent for keeping thinks understandable
Thank you!
After giving Khan Academy a shot at explaining this poorly I came across this. Perfect. Thank you!
i dont mean to be so offtopic but does any of you know of a trick to get back into an instagram account..?
I was dumb forgot my login password. I would love any help you can give me!
@Jake Maxton instablaster =)
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.
Can you do a series leading up to Gaussian process? I like your way of explaining things.
plus one from my side!
I can't believe how you make things that easy. Thx for this awesome content.
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..
Thank you! This is the best explanation in the world! It really helps me! 👍
You describe things in absolutely clear and simple way, thx for doing this!!!
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.
Don't you need to center the data by subtracting the mean first from all the data?
Thank you. Very helpful video. Good luck
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
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
He is taking the covariance of entire population i.e. all 3 people therefore, he divides by N. Had he taken a sample out of this population, he would have divided by N-1.
I was struggling with this concept. You made it very simple and easy to understand. Thank you for this amazing content.
me: 2 km/h * 1 hour = 2
teacher: 2 what? aPplEs? bAnanAs?
Lol 😆
I'm from Germany and I understand you more then every german speaking teacher here
What does the covariance matrix mean as a whole, i have seen it being used as an entity. Something intuitional as matrix multiplication here?
So simple yet so clear. Thank you so much! Subscribed and can't wait to watch your other videos!
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.
You're very welcome!
Great real life explanation - extremely helpful. Thank you so much!!
Thank you great guy!!!!
how can we calculate correlaion matrix for 3 random variables?
I like how you give us little refreshers about concepts we may have forgot.
The equation he used for covariance seems to give the same results as another formula I see being used as the standard online, I just can't figure out how to view them as equal.
The equation I see online is E[(x_i-E(x)) (y_i-E(y))]
Would love some clarification.
Great explanation, sir. But, what if Apple matrix isn’t real number, I mean Apple matrix is just variable (y1, y2, y3)?
excellent video, thanks very much
You are welcome!
Excellent explanation. No confusion. No bullshit. Just 100% fruit
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.
Yeah, might want to check your definition of covariance. I'm pretty sure you understand it intuitively but I suggest polishing your definition. It's not so much that two variables "go together." its the measure of how they vary together i.e. if an observed change in x relative to the expected value of x is observed by an equal or similar change in y relative to the expected value of y. It is not dependent on whether the change is in the opposite (+ or -) direction.
I actually thought it sounded like correlation just before he said it at 2:08. Like he actually read my mind. 😂
"The correlation is standardized covariance, normalizing the covariance with the standard deviation of each variable."
From: www.cambridge.org/9780521766333
Great video, would be awesome to give a little more intuition on why these numbers are so insightful ;)
Great video!
Thanks!
1. disable auto focus,
2. set camera to manual focus,
3. focus on the white board,
4. thank me later
Very often one can see a formulation like variance-covariance matrix. Is it the same as covariance matrix and are being used interchangeably, or variance-covariance matrix should denote something else?
This means that apples are far better than bananas right? So when I've been told that you cant compare apples and bananas ... thats a lie ...
well done
hi..can you please tell at the last when you have derived the matrix value what does it symbolize ,i mean what does matrix should be interpreted?
Best explain on this topic! Concise and human friendly
thanks!
Greatly informative video, thank you! :)
Thanks!
You are speaking too fast and your example chosen could have been better.
Great video! Thank you
Glad you liked it!
I want to express my appreciation for tutor. Thank vey much
Hi, Ritvik you are creating awesome content. Please do keep creating such beautiful content.
Thank you so much 🙂
So, I didn't understand is there any link between happiness...
something is wrong :(
online calcs don't return the same matrix!
Thanks, helped a lot. Liked and subscribed
I think you are not multiply the bias factor right?
Amazing explanation! Thank you!
Thank you very much sir. Very helpful!
sir
you are awesome
thank you
second video I stumbled across and it was so clear
let me say this once and for all, "there is a huge requirement for professors like you at all the universities on the planet if they have to sustain in future"
Is correlation just normalized covariance?
You're an excellent teacher! Wish to see more Stat videos from you! Thank you so much!
Thanks for this amazing explanation!
seems like a payout matrix from game theory
Hi there :)
Extremely well explained video, thank you!
I ended up here as I am trying to run Little's test for missing variables in Stata and the error I am getting says "sample covariance matrix is singular for at least one missing-value pattern" -- Whilst (after some videos)I know what that means in theory, I have no idea what to do with that information now, how it affects my test, and/or if that means I should exclude the 'problem-variable' or use a transformation. Do you have any recommendations? Thank you in advance!
To the point, exemplified, condensed and so useful. Thanks for this video!
I like pros when they speak about what they know.
your channel deserves way more traction and sub count. keep up the good work. Thanks!!
agreed
Thank you!
Very cool video, thanks for that :)
Besides StatQuest a really good and growing statistics channel. Subbed.
Thanks!
Thank you for that clear explanation. I don't have time to relearn statistics at the moment.
Your video is really easy to understand even someone doesn't have math degree
If the covariance represents how much something and something else are related to each other, why isn’t covariance(A, A) equal to 1 ?
Cov(A,A) is just the variance of A, so the value will be whatever Var(A) is
Best video on covariance...thnks man
Very well explained. Thank you
Hi, What are Correlation range and exponential correlation orders and how we can compute for variables (are in vector form or arrays)?
Nice explanations .. thank you
Thank you so much for this video!
Super understandable, thank u sm!
Thank you so much for this very helpful and intuitive video. It really helped me understand specifying mixed models in R!
Great explanation!!!!
Glad it was helpful!
Thank you for making videos
Great video! I wish I would have some free time to enjoy teaching math and stats on TH-cam!
You can do it!
Don't you divide the sum of squared difference by (n-1) to get the variance? Great video. Thank for explaining so clearly.
You are a wonderful
thanks!
@ritvikmath
So the correlation matrix could be called a normalized covariance matrix ?
Yes you can think of it in that way !
Really appreciate the good work
Thank you, super clear!
Really good explanations - clear and concise. Thank you.
Glad it was helpful!
thank you but we need interpretations
Thank you so much. In 10 minutes you explained it so clearly :D keep on with your videos!!!
Wow! Now math seems fun and easy!
good video. one comment: disable the autofocus in your camera when shoting whiteboard lectures, waiveing the hands in front of the camera puts it out of focus
Noice!
Thank You sooo MUCH!!!!!! This was a brilliant way to teach!
God Bless YOU! you saved me!
i wish i had professors like this in the uni. maybe i wouldnt have hated statistics so much.
so clear, thank you sir!
Thank you very much your explanation was great, the only question is that what is the relation between the curve you plotted at the first of the video and the calculated matrix?
things I don't like your lecture is. You are always covering the board. Can't do screenshot.
Awesome straightforward explanation thank you
Great explanation Ritvik as always. Please can you make a series of Videos on Financial Calculus....?
pls mention that this is doing only for the population, not for the sample. because there has another equation for covariance. that can be done both population and sample also.
reference: corporatefinanceinstitute.com/resources/knowledge/finance/covariance/
very usefull! thanks a lot
The meaning this matrics information out of the covariant matrics must be explained perhaps by salt and sugar percentage as titration process.
Understanding very well sir