Correlation & Covariance

[chrisxed]

Search for the difference between covariance and correlation and you'll find 1000 confused "answers". Finally, here is the answer in this video. If I'm understanding it correctly, they are essentially measuring the same thing (hence the confusion) but the correlation coefficient is a way to orient this property in a way that makes intuitive sense for humans (a range between -1 and 1 vs. an arbitrary number meaning who knows what out of context).

[bionicturtledotcom]

@chrisxed thanks, that is correct. Both are linear co-movement. As covariance is rendered in the same awkward format as variance (i.e., units^2 or returns^2), correlation translates it into a unitless (intuitive) format.

[onlnr]

Thank you for making this intuitive, makes a lot more sense now.

[MrKernkraft4000]

Another thing that I believe may be tripping people up here is that you forgot to put (n) into the denominator of the equation for covariance (where shown)... unless my eyes are failing me.

[NVRMR08]

Thank you!

[boodai88]

You described it as a piece of cake!

[abxvistro]

he speaks too slowly! I have a test tomorrow I need this info fast

[heraclesX]

@abxvistro dude, you're so fucked.

[leonriv]

Thank you so much for this video. Your explanations are very clear, and simple but quite detailed. I finally understand correlation. This was previously a concept that was very difficult for me to grasp. I apprecitate your contribution very much!!!!!

[sniparag]

I found it very useful

[szlazer]

saved me, thanks man

[lol8789]

U have no idea how much u just helped me. Thanks!!

[galgotias]

You explained very simply.......thanx a lot !

[Theccarr25]

Seriously saved me! I was struggling so much! Thank you!!!

[waem1]

Thank you. You saved my life :)

[ntang92]

great explanation! Thanks a lot!! 

[TheBigNicko]

you simply rock dude!! keep it up

[debbidoots]

you sound like the chef guy from foodwishes! 8D

[04274108]

Perfect! Thanks for the clarification!  Cheers mate!

[04274108]

Great set of videos! Thanks for making the time to create them!

One question. You say to get the correlation coefficient you divide the covariance by the product of the standard deviations. 0.67 / (0.67*0.67) does not equal 1.  Am I missing something?

[bionicturtledotcom]

@04274108 The standard deviations (ie., volatilities) are SQRT(0.67) not 0.67, so correlation = 0.67 / SQRT(0.67)*SQRT(0.67), and since SQRT(0.67)*SQRT(0.67) = 0.67, we have 0.67/0.67.

Thanks for your kind words!

[hawaypg]

@bionicturtledotcom Wait a sec, the std(x) = 1 and the std(y) = 1 and not the sqr(0.67), unless you are considering the standar deviation of a sample formula, in that case is sqrt(0.67) where 0.67 should be the variance but it is not, is just merely coincidence that 0.67 is the product of (x-ux)(y-uy) and then consider the std(x) = sqrt(0.67). Maybe I need a better explanation, thanks for posting

[bionicturtledotcom]

@hawaypg there are no sample statistics here, these are (to keep it simple) merely illustrating "population" -based correlation. As the Average(X) = 3, the (population) variance of X = average[0^2, 1^2, 1^2] = 0.67, such that the StdDev(X) = SQRT(0.67). Similarly, (pop) var(Y) = avg[0,1,1]. It's not meant to be coincident, i just didn't show the StdDev calcs. Hope that explains, thanks, David

[adithyani4]

Its not 0.67 / (0.67*0.67) .It is 0.67 /sqrt(0.67)*sqrt(0.67) which equals 1.Hope it helps.

[anzatzi]

i have been browsing around for something like this--very helpful. statistics suffers from somewhat clunky notation

[jimmyjmv]

I hate why Statistics professors don't teach like this, in this patient way!!!!!!...

[HRSDKK]

Awesome video! This might be a irrelevant question, but what is the reason behind dividing with the product of the standard deviation in order to translate the covariance to correlation?

[aida19751000]

this is good if weights of X and Y are equal (i.e. 1/3 in this example) , but what about covariance of X,Y with different weights?

[karatepopcorndefendr]

Outstanding. Thank you!!!

[jenffemtp]

Thank you, thank you, thank you! This was a great help tying covariance and correlation together. Clear and to the point, can't thank you enough!

[potatopeelingparty]

6 people are dumbasses.. excellent vid, visual aid was fantastic :)

[sovietamerican2]

What the heck?

[ganuongtoi]

sooooooo easy to understand this solve all of my problems in understanding portfolio. Thank you very much sir.

[tooposh1]

thank u! very good explaination!

[ThaFacka]

you've made some points very, very clear. thank you!

[deeejey1]

awesome.... its very helpful

[irfaanfr1]

thanks

[halfstep007]

awesome dude, you are making a great contribution to society.

[the11diesel]

@halfstep007 Here, here. This guy deserves a medal.

[krishnasmurf]

wow that was helpful, thanks!

[siddyt1]

thank you so much, i now understand

[SkyHiRider]

Thank you. Knowledge is golden!

[1Gaggi]

Amazing Explanation..cant thank you enough :)

[meyero90]

I don't understand how stdev(X) = 0.67??? As you said you take the stdev (X) x stdev(Y), but if I compute it, it gives stdev(X)=1 (stdev(3,4,2)) and stdev(Y)=1, so cov(X,Y) / (stdev(X) x stdev(Y)) should equal to 0.67 and not 1. Could you please clarify. Thx

[WGS669]

@meyero90 The example shows the standard deviations to be the square root of 0.67, not 0.67.

Use the series 0, -1, 1 in the STDEVP 'population' function and you'll get his result.

I'd guess you either used the STDEV 'sample' function or you used the wrong series. Or both maybe. Be sure to use the deviations from the mean as the series in standard deviation calculations.

Hope that helps.

[MrSyCoe]

Would there be a bionicturtle complete course which takes the individual through a complete dissertation of these statistical quantities, and then translates them into practical use by application to 'the greeks' components in options?

[rclcryan]

thank you so much for this!

[rclcryan]

thank you so much for this!

[MaritimeGuru]

Thank you for a clear explanation!

[gambart2002]

Wow, thank you very much. I'm studying for CFA and this helped a lot.

[looneycubstar]

thank that makes things so clear for me now !

[jtottonb]

This is a great explanation and interpretation. Most tutorials neglect to give the numbers meaning in-context.

[ap2402]

GREAT! Keep it up!!

[rquinatoa]

You definitely made my day. My Investment Analysis class confused me...but you clarified it for me. Wish more professors could teach like you.

[aishkarbeta]

Seriously you have no idea how much you have helped. I wish everyone taught it this way.

[balnagendra]

How to arrive at -ve correlation. Since both sides are squared, there is no possibility of arriving a negative correlation. So, it will fluctuate between 1 to 0.

[immagathu20]

Thanks so much! This has been very helpful :)

[TSkillaaa]

Missed a tutorial on covariance, found that the suggested reading only made it more difficult, your video on the other hand, was fantastic.

Solved and completed my work in no time at all. Thanks.

Although saying that - I did get a question wrong.

I had a question where the covariance was 0, and it then proceeded to ask if X and Y were independant, i thought yes, but that's apparently incorrect. Do you have any videos explaining why this is?

Thanks x

[TSkillaaa]

just worked out why - thanks a lot. x

[zhsimko88]

very very well put please come teach my finance class!

[71318elmo71318]

Why couldn't my teacher have put it like that? Been struggling over this for weeks, huge THANKYOU! 

[McMahbouba]

Allah bless YOU and USA.

Thanks alot

[pakpride1947]

@ bionicturtledotcom

Thanks a lot brother. It was such a wonderful & simpest explanation. i was confused before; but not any more now. bundle of thanks again.

MAY GOD ALMIGHTY bless you. (Amen)

[aandreya]

I already passed statistics 10 years ago, but I have been asked to tutor. Of course I forgot almost everything, but if your tutorial continues in this direction as some previous I've checked, I might actually remember everything an learn it even better as before.

I only my professor would have thought us in this way. My grade would've been so much better.

Thank you, for making the efford of uploading the videos!

[bnicetm]

You did an excellent job here! Your explanation was clear and concise, who could ask for more.

Chris

B.Nice™

PS If I had to ask for more it would be some formulas that we could copy.

[bnicetm]

You did an excellent job here! Your explanation was clear and concise, who could ask for more.

Chris

B.Nice™

[elpa98]

Really great videos!! Thank you very much!

[kdkdoiew]

Fantastic explanation! Thank you :)

The relationship with finance adds a useful perspective that I hadn't considered before too.

[abyagowi7]

Amazing explanation, keep it up

[scottbroadway]

You have no idea how much you helped! Thank you.

[bionicturtledotcom]

@scottbroadway my pleasure, thanks for you kind feedback, makes my day!

[leotakesleo]

@bionicturtledotcom : How to prove cov(ki,kj) = - n pi pj

[ProgressivPositivity]

Thank you! You explained this wonderfully!

[jim8z3]

Thank you soo much - Perfect explanation of relationships

[bionicturtledotcom]

@jim8z3 thank you, for such kind feedback

[jim8z3]

Thank you soo much - Perfect explanation of relationships

[boodai88]

Thank you very much , what a great expalanation !

Suliman , Kuwait

[shizakhan1]

very helpful !

[sasmalik]

patrickrueegg:........... you are right that at first glance it confuse but we can not say that video is wrong. he written that sqr rout..... sqr rout mean it that when we take square rout of 0.67 and 0.67 and the make product i come 0.67.....

[wengohung]

nice explanation!

[cusanusnicolas]

Think that you'd very much enjoy my paper that derives a formula for calculating average covariance for all combinations of treatment pairs in a randomized block design, then divides that by the average treatment variation across blocks - I call this the r value or the coefficient of covariance (for randomized blocks). The idea is that the r value will vary between 1 and 0 depending on the orientation of blocks (if no sampling errors) in a gradient - or just strength of linear correlation

[69erthx1138]

Even though your aim was financial math, you kept the theory discussion nicely generalized. Great job! What you're saying is that the correlation (functional) is the normalization of the covariance (i.e. makes it a dimensionless metric). I'm certain that the term covariance refers to complimentary-variance similar to the cosine being a complimentary-sine. Is this correct?

[prettykitty00]

The .67 divided by .67 is one though-he didn't multiply it he divided the two numbers at the end. Remember the equation sigma xy over sigma x and sigma y?

best explanation over

[patrickrueegg]

hmm.. the end wasn't clear to me. The product of 0.67 x 0.67 is not 0.67. Then the correlation wouldn't be 1 ?

[exobr]

He made the following calculation: sqrt(0.67) x sqrt(0.67) / 0.67 , which produces a 1, since (sqrt(x) x sqrt(x))^2=1.

[patrickrueegg]

yes, you're right, but its written wrong !!

I mean the standart division of x and y is 0.816497 each. and NOT 0.67 as he wrote !! The variance of each one is 0.67, but not SD as he wrote in the movie.

and 0.816497 x 0.816497 = 0.67

I think this is quite confusing and took 30 minutes of my sleep now.

He should correct this mistake. Do you get what I mean?

[KettlePal]

@patrickrueegg

Actually the standard deviation of both X and Y is 1. However, the variance of both is 0.81649658.

As you have correctly pointed out 0.816497 x 0.816497 = 0.67. The covariance coefficient and the final correlation coefficient remains the same but the denominator he discusses in the correlation formula is entirely wrong. The correlation formula should read: Cov(X,Y) / (σx * σy)

[w201cosworth]

so cool.. top man for this

[kjfksfhk]

THANK YOU!!! This is the best explanation EVER!

[alcowhorelication]

i love you, worked for building my foundation understanding in econometrics!

[alan4cult]

thank you, best explanation of covariance!

[bionicturtledotcom]

i appreciate that, thanks for your support!

[costas020287]

thx u so much

[obesejim]

NICE! Thank you so much!

[jtcra555]

Thank you so much. I received an A on statistics thanks to you!!!!!

[believerofunity]

Thank u sooooooooo much...

[daridaist]

this guy has a talent to teach

[SteVidz]

thank you, it`s much simple now

[Shadyhunter04]

Wow, thank you, I was really about to rip a piece of my hair out because of my econometrics homework.

[lalojefe]

really well donne, keep going.

Thaks

[gobi20]

P.S Greetings from London, UK

[gobi20]

Thank you - Thank you, Sooooo much ! Please do no stop. You do a great JOB!

[rfvo]

100%

[bionicturtledotcom]

1.0

[JulesUCO]

quick question... if two variables have a strong coefficient of correlation, does it mean that there is a causation relationship (one causes the other one)??? thanks...!!!

[bionicturtledotcom]

no, not even, correlation is merely a measure of observed *linear* relationship between two variables. Says nothing about causality; e.g., a third variable can cause them both. Further, it's just linear - variables can be dependent but non-linear. A limited metric.

[rize1337]

that means, if the correlation between X and Y is 1, so X=aY+b

what happens with a relationship between X and Y, if the correlation isnt 1, for example its near 1?

How could the relationship look?

thankss!

[trr12]

if it isn't 1, it means that the relationship resembles a straight line, that is, that you can model it as a linear relationship. The point about causality is very important to understand, by the way, and a lot of people confuse that.

[joolzxx]

thanks so much for posting =D

[rhettintaipei]

Thanks Mr. Harper, My sshool needs you!! Regards, Rhett at National Taiwan University

[MarkaRoxx]

Love all of your videos

[mikeair171]

Thanks for your vids, better than my professor, haha