WOW: clear explanation, calm background music and being straight to the point. Those ingredients were enough to make me subscribe right away! Looking forward to more videos about statistics!
Now that my hair is all gone from scratching my head because of frustration trying to understand my Professor's lecture, along came this video that basically put a lot of sense into my head in just only about 5 minutes of video, whereas in my Professor's lecture took a whole week to explain to the class. Thanks for the great explanation..
Greeting Dr. Shah, I have a concern that need to share with you, in your video, you proposed about covariance- i.e., Var(xy) = {Exy/n - (Xbar.Ybar)} however it's value is differed by another covariance formula = E{(Xi-Xbar).(Yi-Ybar)}/{n-1}. Request you to suggest.
Agree - the video can calculate the population covariance but not the sample covariance. If we do not subtract it from the 'mean', the division by (n-1) cannot yield the sample covariance.
The variance formula differs from that in wikipedia: The variance of a random variable {\displaystyle X} X is the expected value of the squared deviation from the mean.
Yes, but this is also valid, you just need to keep in mind that it gives you a biased estimate, while n-1 removes the bias introduced by estimating the mean through the same sample.
what you do is distribute the exponent to remove parenthesis x1^2 - xbar^2 + x2^2 - xbar^2 all divided by N Now Xbar^2 can be factored out... it is N * -Xbar^2 .. but remember it is all over N so it cancels the N out. hence Σ(x^2)/N - (xbar)sq * N / N
if I'm not mistaken (you may need to verify my answer), you use n-1 as the divisor because many textbooks use unbiased estimator approach, as in, you don't know the value of all population and using the samples instead. this case use n as the divisor because it used maximum likelihood approach, as in, you know the value of all population (we have all value of x and y). CMIIW.
[SUM( Xi- XBar)^2]/n-1 that is the formula that my statistics lecturer taught me to calculate the varience but yours differs in the sense that you don't subtract one from n
Thank you so much! This cleared things up very quickly! One question I have, You calculate the co-variance do you have to really calculate the variance. Can you not just skip to calculating the sum of xy/n - (mean of x)(mean of y) ??
Dear math master, Could you give me an example of finding a covariance matrix from a Gaussian function fit on a Gaussian data? Cheers. You may suggest a book to read about this kid of fitting problems as well.
***** Yang Mandy Since it is a uniform distribution (all outcomes have the same likelihood) that equation works fine. It's a weighted average but all weights are the same.
in my textbook there is a different formula for the variance ( s² = sigma(x-xbar)²/n-1 ) and here he uses a simplified version of it ( var(x) = sigma X²/n - Xbar² ) but i get 2 different answers with the same sample values... Can anyone help me out there?
Hi Joshua, not sure how you get x1^2 - xbar^2 + x2^2 - xbar^2. using the formula (a-b)(a-b)=a^2-2ab+b^2, i get x^2-x.xbar-x.xbar+xbar^2. not sure whether you can advise me...
your 7 min of explanation is better then 12 pages of stats lecture notes- amazing!
WOW: clear explanation, calm background music and being straight to the point. Those ingredients were enough to make me subscribe right away! Looking forward to more videos about statistics!
Now that my hair is all gone from scratching my head because of frustration trying to understand my Professor's lecture, along came this video that basically put a lot of sense into my head in just only about 5 minutes of video, whereas in my Professor's lecture took a whole week to explain to the class.
Thanks for the great explanation..
This was probably the most concise, clear way anyone has ever explained covariance to me.
Thank you prof . I cant even undertand when my lecturer teached us. Its almost 14weeks of lecture and next week we gonna sit for exam . You help me
This is by far the best explanation for solving for covariance. Thank you very, very much.
simple and straight to the point, amazing explanation overall!
Today I was very afraid that how to calculate this thing and i watch your vedio and clear my all doubt. Thank you sir
I just want you to know and be reminded that you have helped someone even in this year 2021. Thank you.
Better than khan academy and all other youtubers, thanks bald man
So glad I found this video! Thank you for explaining this. I'm taking a summer course and needed to understand covariance quickly!
Great explanation, simple and easy to understand. Thank you for the video :)
Greeting Dr. Shah,
I have a concern that need to share with you,
in your video, you proposed about covariance- i.e., Var(xy) = {Exy/n - (Xbar.Ybar)}
however it's value is differed by another covariance formula = E{(Xi-Xbar).(Yi-Ybar)}/{n-1}.
Request you to suggest.
Agree - the video can calculate the population covariance but not the sample covariance. If we do not subtract it from the 'mean', the division by (n-1) cannot yield the sample covariance.
Thank you so much, Mr. Instructor! This is so much helpful. So easy to understand. Have a wonderful day, and stay safe!
this is still helping me ten years later thank you
YOU ROCK!
OMG!
I WISH YOU WERE MY PROFESSOR!
SHE HAS BEEN TRYING TO TEACH US THAT FOR OVER 5 WEEKS!
AND IT TOOK YOU 7 MIN!
The variance formula differs from that in wikipedia: The variance of a random variable {\displaystyle X} X is the expected value of the squared deviation from the mean.
thanks you very much I spent two months with my lecturer who's so suck finally this minutes video made it more easiest .
Holy moly, thank you SOOOO MUCH for this!! How did you make this so easy to understand??
Wow thank you sooo much! I can't believe that this was what my uni prof was teaching about. I am doubting of the existence of universities nowadays..
The best video about variance, covariance and correlation coefficient together ever..)
Give this guy all the awards
i learned more in this 7 minute vid than i did sitting in class the past 4 weeks
Great video, professor could not teach me this, other videos I look up were not helpful but this video was great.
OH MY WORD!! This has helped me so much! I haven't been able to understand any other video! Thank you so much!
best and most intuitive explination
Very skillful in teaching
amazing clear cut concept very helpful for my data mining paper
After scratching off many papers you came to my rescue. thanks @Two-Point-Four
Thank you for the great explanation!
i rarely comment on videos. But this was fantastic, absolutely superb,
Isn't this a sample? Wouldn't you divide by n-1?
Yes, but this is also valid, you just need to keep in mind that it gives you a biased estimate, while n-1 removes the bias introduced by estimating the mean through the same sample.
what you do is distribute the exponent to remove parenthesis
x1^2 - xbar^2 + x2^2 - xbar^2
all divided by N
Now Xbar^2 can be factored out... it is N * -Xbar^2 .. but remember it is all over N so it cancels the N out. hence Σ(x^2)/N - (xbar)sq * N / N
This explaination is so good
if I'm not mistaken (you may need to verify my answer), you use n-1 as the divisor because many textbooks use unbiased estimator approach, as in, you don't know the value of all population and using the samples instead. this case use n as the divisor because it used maximum likelihood approach, as in, you know the value of all population (we have all value of x and y). CMIIW.
I like how you say calculator. 'Calcalaytah' haha. :)
Definitely cleared some things up. Hopefully the problems I'm doing allow me to use this method.
Thank you Dr. Shah . I am saved :')
[SUM( Xi- XBar)^2]/n-1 that is the formula that my statistics lecturer taught me to calculate the varience but yours differs in the sense that you don't subtract one from n
That is for a sample mean and sample variance. To avoid error and bias, you use Xbar and N-1 for the sample, that is the reason behind the formulas
thanks from my heart
thnx sir your teaching way is very good
You explained in such easy terms, thanks !
Thank you for this, well explained and well understood!!!
Fantastic video. Made a difficult concept for me very easy to understand. Thanks!
So brilliantly explained, thanks so much
Thank you so much! This cleared things up very quickly!
One question I have, You calculate the co-variance do you have to really calculate the variance. Can you not just skip to calculating the sum of xy/n - (mean of x)(mean of y) ??
I love this man
Can we find find the variance of y if we have variance of X and covariance of X and Y
great concise explanation. thank you
You are brilliant Sir ... Love you Sir ...
Thank you holy shit. Going to have to rely on you tube videos in order to pass my stats course, God damn my proff is a worthless bad of shit.
Preach brotha
What are you studying buddy?
Thank you.. It was really helpful 👍
Excellent !!!! Thanks Dr
Thank you so much for your excellent explanation. Keep up the great work.
Thx teacher you are good teacher
I knew math wasn't evil! please make more video
that formula is for sample variance, and yes!
Thank you for making this!! So helpful
Good one. Thanks. Please explain covariance matrix also.
guys, for the variance he used sample variance. so don't be confused, if you are using estimate of variance then use that (:
Very nice explanation, thank you!
Really clear explanation..! Thanks!
Thanks! This was actually very helpful.
THANKYOU SO MUCH!!!
Great job ! Thank you for posting !
Thank you for sharing, very helpful
Thank you, great, simple explanation.
thank you very much dear
Fantastic! Im bout to tell all da homies bout u
Dear math master, Could you give me an example of finding a covariance matrix from a Gaussian function fit on a Gaussian data? Cheers. You may suggest a book to read about this kid of fitting problems as well.
Thanks a lot.
Thank you great all round explanation!
Thank you
Is anyone noticed that the variance equation wrong??
Yang Mandy Yeah, noticed it too :(
***** Yang Mandy Since it is a uniform distribution (all outcomes have the same likelihood) that equation works fine. It's a weighted average but all weights are the same.
Joe Rowley Ah okay, thanks for clearing that up!
okay, I see. Thanks!
No its not wrong
Thanks for the great explanation!
Thank you so much for sharing!
Great explanation!
Very well explained.
Thank you!!
Very good class🥰
You made my doubt clear thanks ❤️
Super useful, thank you.
💞💞💞 great teacher
Lets start a gofundme to get this guy a satva
Whoa this is magic.Thanks.
well explained.. Thank you
superb explanation!!
Very well explained. Thanks :)
finally a video i understand. thanks for sharing :)
in my textbook there is a different formula for the variance ( s² = sigma(x-xbar)²/n-1 ) and here he uses a simplified version of it ( var(x) = sigma X²/n - Xbar² ) but i get 2 different answers with the same sample values... Can anyone help me out there?
did you find the answer?
really well done
Hi Joshua, not sure how you get x1^2 - xbar^2 + x2^2 - xbar^2. using the formula (a-b)(a-b)=a^2-2ab+b^2, i get x^2-x.xbar-x.xbar+xbar^2. not sure whether you can advise me...
Why there are many different formulas for the same thing? I am very confused
waoo.. this is an amazing explanation. thank u
but what about the degree of freedom (9-1) for the denominator?
Thank you soooo much! You are great!
Thank you for this
wait.. why 20/3?
It's 6.6, so he wrote it as 20/3
285/9 - 25 = 6.6 =20/3
thank you this was excellent!
You sir are awesome!!!!!!!!