What is COVARIANCE? What is CORRELATION? Detailed video!

0:00 Introduction | 1:09 Definition | 2:48 Covariance and Correlation from a sample | 9:55 Covariance and Correlation from a probability distribution (using EXCEL) | 18:47 Why do we divide by n-1 for a sample?
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[@maincharacterNRG]

You are a gifted teacher. I am so grateful for your presence on KZbin. I feel I've learned so much more from you than I have from my text. I cannot thank you enough!

[@buildingourdaydream9804]

Your videos and teaching style are SOOOOO critical. Many of us struggle with the non-intuitive formulas and have given up. This stuff CANNOT be applied to real life if we cannot conceptualize what they really mean at their core and why they were derived in the first place. You are bridging that gap Justin, unlike so many others before you, and I am forever grateful. Thank you.

[@aditigangar3133]

Thanks!

[@economicskibaat8013]

Your explanations are so impressive. I just know I can't forget the concepts ever again

[@geoffbakerhytch5623]

Absolutely brilliant presentation! As a (high school/ secondary school) teacher of these topics, I find that you ALWAYS help me clarify my own explanations, making this difficult stuff much easier for students to grasp - I especially agree that overuse of formulae is dangerous: students who overuse formulae without a basic understanding of the processes risk failing to interpret results properly; this problem gets worse NOT better, the more more they do with statistics without such basic understanding! Well done, Justin, and many thanks for all your hard work!

[@dilinijayasinghe8134]

You're a wonderful teacher. Covariance and correlation was a mystery to me before. But you not only explain them in a PDF but also compare with a sample, which makes it extra clear to understand. Thank you so much !!!

[@98ujaal]

Love how you always try to build a strong intuitive understanding of formulae!

[@zedstatistics]

Thanks, SS! Ain't no point teaching people to simply apply formula - that's what you get computers to do :)

[@xXxIMMORTALxXx]

@@zedstatistics Sadly, applying formulas is precisely what most schools teach kids to do in maths classes... maybe not anymore nowadays when lots of schools have incorporated CS into their curriculum? But during my time in elementary up until high school I had been taught only the formulas..urrrgh

[@nildev7264]

This is a stupendous explanation. You've taught us array of concepts in a single video (especially the intuition behind df).

[@howardlau7749]

Can’t appreciate more about your beautiful works. I am studying machine learning, but struggling with some statistics concepts . Your videos really help me out !! You put these knowledge in a structural way, which is really impressive!!

[@DrorProductiones]

It's great to have you! I'm having an exam in statistics soon, and they are going to test us mainly on the theory. It was so hard to find good videos that explain the logic behind everything and not just how to plug numbers in a formula. Many thanks

[@amirmelloul199]

Hi Justin I watched the entire descriptive statistics videos series. I must say all the videos are simply amazing in every imaginable way. I have zero background in statistics and i enjoyed all the videos tremendously. thank you for taking the time to make them as it inspired me to dig deeper into the statistics field. Hope this message will reach you and inspire you to keep making this type of great content.

[@meilinglaw6180]

I am from Asia , and I love you man , Your explanation is so great ‘ easy to understand

[@jonykhan4395]

Good work. I have never watched even one video on KZbin explaining that how statistical formulas are constructed. We just apply them but never learn and taught how to make them instead.

[@QuietLumina]

Thank you so, so much for these videos. They are immensely helpful in actually understanding statistics as opposed to just memorizing things. I’m learning statistics for work and your videos make things so interesting and easy to comprehend. Truly amazing explanations!

[@Karen-2023]

Your presentation skills are great. The visuals and the Excel exercise displays are appreciated. The text/content I have is not as "clear" as your teaching approach via KZbin. Many thanks to you!

[@husinhhoa]

Thank you soooooo muchhhhhh. I've been struggling with statistics for years. Your videos helped me understand much more than my university teachers although English is not my mother tongue.

[@dominiclederer9564]

please make more stats vids ! My lecturers just read off slides and doesn't explain the work. These are excellent !!

[@James-md2xk]

best stats teacher on youtube, thank you so much for your videos here

[@ebukaewuzie3377]

Brooooooooooo it's safe to say teaching is your calling. You're gifted at teaching and your explanations are really top notch. Please i'm struggling with Simple linear Regression and OLS and i'll need your help with that

[@shwetaadvani8941]

What a boon for people new to statistics .Thank you for explaining so logically !:)

[@tsholoMnice2019]

Zedstatistics. You have out done yourself!!!👏👏👏

[@rss1322]

Wish I had this when I was struggling through in college. Excellent video as always!

[@igor-yp1xv]

I'm finishing a Data Science speciaization on Coursera and the current course is dry as hell, feels like I'm eating an yogurt made of sand. This video is an oasis ou clarity and ease. I'm gonna watch all your videos on the same topics of the other course, this one helped me immensely. Thanks a lot!

[@ryany6478]

You explained better than my lecturer and textbook! Thank you.

[@ayoubahabchane]

Sir, you're the best at this. Hands down.

[@firstspar]

Just wanted to say these are great videos and you are doing an amazing job producing these. Please keep them up!

[@taladiv3415]

Your videos greatly aid understanding of a concept. Thank you for your contribution to society!

[@bharanij6130]

Absolute Gold - this series

[@pb3254]

Another great video explanation, reminds me of my A Level stats many moons ago!

[@pp-hiker]

Simply amazing!! Never thought it's so easy!! 🙏

[@RiaziMohandesi]

Thank you very much Sir, one of the best explanation on the planet. From Iran

[@rodlu811]

Fantastic explanation!! Very intuitive and easy to understand .

[@marinabaskakova2333]

So well put together and crystal clear! Thank you!

[@alibinshuja69]

You are a gift to the world!

[@liamhoward2208]

Here is the gist: Covariance gives you one piece of information. It measures the direction of the two variables (positive or negative) positive (direct relationship) means that when one variable increases the other increases and negative means that when one variable increases the other decreases (inverse relationship), whereas, correlation gives you two pieces of information. It gives you the direction (positive or negative) and the strength of the relationship by being a number between (0 and 1). If two variables have a very strong relationship their coefficient might be .90 and if there is a weak relationship the coefficient might be .20

[@sathish297]

Correlation is non negative? So correlation doesn't give direction

[@jinhaosdiary]

@@sathish297 the correlation coefficient can be negative. So it expresses both the direction of correlation and the strength of the correlation.understand now?

[@sathish297]

@jinhaosdiary yep, thanks

[@Engineer78206]

great stat teacher on yt

[@bludbought]

Thank you so so so much! I thank God for you. Keep doing what you are doing.

[@whetstoneguy6717]

Why are statisticians interested in covariance if it is not informative as correlation? EXCELLENT VIDEO.

[@yoshifernando5264]

This is such great prep before doing a business stats unit for the first time. Thanks heaps Justin!!

[@myblankspacee]

I love you man... You saved me 😭❤️

[@michelleraymundo7038]

Great explanation, I love the quick and dirty explanations.

[@ishitaarora281]

this channel is a blessing!

[@meilinglaw6180]

A gifted teacher

[@tjmozdzen]

Nice video and series. Do you have a tutorial on using the covariance matrix to estimate the variance of a sum or product? I recently found out how to do this and realized that people do not cover this very often.

[@mvr192]

Thank you, it was extremely informative 😁. You take your time and explain it very clearly.

[@jacobblack2544]

I bow down to your knowledge sir, Namastey!

[@krishnabarfiwala5766]

I love your videos. Made my concepts clear. Please make videos of design of experiments. All the deisgns . I'm suffering so much in my studies

[@samuelilozumba7459]

Bless your heart, Justin Z.

[@azboshippuden3770]

Thank you for explaining this all easily!!

[@_sun07]

Such a clear and logical explanation! Thanks a lot man!

[@elvinphilip3410]

You are an awesome teacher!!!! Thanks.

[@exploreformore3784]

Brilliant description on covariance

[@mateuszwojnarowicz7650]

Hi! Your series about the regression was perfectly done and it really helps understand the concept. Could you please do the similar one in topic: all about the ANOVA method?

[@xXxIMMORTALxXx]

Check out his video titled: "Regression output Explained", he talks about ANOVA there.

[@gavinaustin4474]

Really enjoying these videos, Justin. Please keep 'em coming. Although I understand the distinction between correlation and interaction, I'd be interested to see how you might explain it in your inimitable fashion.

[@gulcinmmmdova]

You're perfect teacher

[@pranjitborah8752]

I just loved your explanations.it was very helpful

[@I_THE_ME]

Thank you lots for the awesome video that actually focused on what can be accomplished by using the formulas and what they cosist of.

[@vcello6450]

I should give YOU my tuition. Thank you sir!

[@md.shahabulalam9484]

Time series please

[@tanekakutitus50]

perfect explanation👍

[@ARM26878]

Excellent video! Did u happen to cover proof/intuition behind why correlation lies between -1 and 1? Thanks

[@kurmanzhanalimzhankyzy928]

Thank you for all 🤍

[@aminomidi7629]

Thank you for this useful content my friend.

[@spinach7205]

THE CONTENT I NEED- SUBSCRIBED

[@Puhazhenthi]

Very useful, Thank you so much ❤️

[@nia-nshaepcollins7468]

Thank you so much for this explanation!!!!

[@manilambardar3163]

Please make videos on statics in deep learning

[@Ejun0]

Could you please elaborate on why did you use the joint probability of X and Y when calculating the Variance of X?

[@Maihuit]

First! * Could you please make videos about Time series...?

[@zedstatistics]

Been asked about this a few times, actually! Safe to say i should probably get onto it hey!

[@Maihuit]

zedstatistics Love you 🥺 best stats Channel in the history of KZbin😭😭

[@ramakanthrama8578]

@@zedstatistics Hi , Zed , why do we divide covariance by standard deviations, to get correlation. Can you please tell me ?

[@tonimigliato2350]

@@zedstatistics It would be great!

[@Shervind]

@@zedstatistics I love you too, no homo... scedasticity

[@akhilchanganath4103]

Love from India ❤️

[@rezaerabbi2492]

While finding correlation between x & y , we are dividing cov(x,y) by the product of sd(x) and sd(y).What are we actually doing here?How does it work?

[@faheemali6720]

Thanks for the video. If the mean is the average of weighted X, to find the deviation, the X should also be multiplied by the probability weights right?

[@jennymiao2623]

Very good, thank you Justin.

[@PraveenKumar-qn2zh]

Thank you so much clean explanation

[@arundhatisarkarbose5317]

Thank you so much for the videos. They are truly helpful. Can you make videos for time series and panel data analysis?

[@wanderlisi5038]

8:23 how did you get this values of 5.70 and 1.87. I try to understand the calculation. It isn't the variance or standard deviation.. plz help

[@joaoborges2014]

He uses the sample standard deviation, which in numpy can be obtained by passing a second parameter 'ddof=1', like: numpy.std([30, 35, 40, 25, 35], ddof=1)

[@85aayush5]

x = -3 +2 +7 -8 +2 square(x) = 9 4 49 64 4 sum(square) = 130 divide by n - 1 = 130/4 = 32.5 [variance] srqt(variance) = 5.70 [standard deviation] same for y column : )

[@nadiab741]

@@85aayush5 THX (:

[@dineafkir5184]

Great videos. It would be nice with some time series :-)

[@Competent00]

Thank you so much. It was very helpful

[@MitsosDA]

Hey Justin, Can you make some explanatory videos about panel data, fixed effects please? Thank you very much! Love your content!

[@leeris19]

THANK YOU FOR EVERYTHING

[@szilike_10]

You are very good at building intuition, something my university teachers were very lacking. Thank you for this video and your efforts. One question that always bugs me and can't really figure it out is that for me it seems like this kind of thing has to do with the order in which you put the values in the table. I'm more concerned with the theoretical model. Like It would gave the same results if you just shuffled the rows around, but then it wouldn't give the intuition (or not as obvious) of seeing how they are negatively correlated. Like I'm thinking let's say we have a two samples x, y, you can order them of course in whatever way you want cause they were generated or measured randomly (eg. asking people in different order). When I'm thinking graphically, I always see putting the x values in ascending order, but how you draw the y values depends on what order you are taking them, right? And in which order you draw them could can cause positive or negative correlation or none as well. I think I'm kind of confused : )

[@athanasiosklimentidis6975]

Hi zed. You forgot to explain the intuition behind why we divide covariance by the 2 std dev to get the correlation. Could you explain it?

[@suhailawm]

Tnx alot sir. Nice explaining

[@marcussuzuki4031]

Yo. This is what I have been trying to do to gain a better understanding. I would like to see the derivation of all PDFS from scratch . That would be amazing, but it seems like even P.H.D students have a hard time with this for some reason and I havent found it online. Usually the proofs for these things are done through moment generating functions. I believe you would have to start first with chi-quared, then go to something like t because to involves chi-squared.

[@awishkayatiwella]

Marvelous ❤

[@miyamotomusashi4556]

Thank you, just thank you.

[@callppatel1]

Very clear.. Amazing !!

[@akashvani628]

Hey. Can u make a video on step by step course for series of video on stats, to be consumed in your tutorial.

[@ManikHossainKOTHA]

Just a boss public bro🥰

[@bluxer4225]

Блестяще. Как раз мой уровень))

[@tonimigliato2350]

Great lesson. Thank you!

[@deniz-gunay]

why didn't you divide (n-1) at 15:33 ?

[@icb-studies]

In summary, when you're working with a probability distribution, the probabilities already adjust the contribution of each outcome to the covariance, so there's no need to further divide by n or n - 1

[@hamsikakondamudi]

Can you do a series on sampling distribution, pleasee!

[@virajsawant2619]

Can you please tell what is mean by interclass correlation coefficient

[@raphaelg.garces7409]

how do you get the (5.70) and the (1.87) in the CORR formula?

[@Chh_Nour]

Love it! you're amazing, keep going!

[@nadinemoussa2091]

oksh ya noor 😂😂😂

[@magtazeum4071]

Thank you very much!!!!!!

[@couragee1]

many thanks!

[@gameply347]

Is there an video for Z-scores or did i miss that?

[@muhammadfaizan2232]

Excellent