Pearson's Correlation, Clearly Explained!!!

Correlation is one of the most basic statistical measures of how two different things might be related, which means it is very important to have a clear understanding of what it means and how it works. This StatQuest walks you through everything you need to know about Correlation. It tells you what it means, how to interpret it, and what its limitations are.
NOTE: This StatQuest assumes you already know about "variance"... • Calculating the Mean, ...
...and covariance... • Covariance, Clearly Ex...
...and if you would like to learn more about R-squared, check out these 'Quests!
R-squared, clearly explained: • R-squared, Clearly Exp...
Linear Regression and R-squared: • Linear Regression, Cle...
For a complete index of all the StatQuest videos, check out:
statquest.org/video-index/
If you'd like to support StatQuest, please consider...
Buying The StatQuest Illustrated Guide to Machine Learning!!!
PDF - statquest.gumroad.com/l/wvtmc
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Patreon: / statquest
...or...
RUclips Membership: / @statquest
...a cool StatQuest t-shirt or sweatshirt:
shop.spreadshirt.com/statques...
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0:00 Awesome song and introduction
0:55 Motivation for correlation
2:32 Strong and weak relationships
3:25 Correlation vs causation
4:26 Correlation quantifies relationships
6:00 Why correlation values need p-values
9:50 Negative correlation values
11:30 Correlation = 0, explained
12:11 Small p-values do not imply high correlations
13:38 How to calculate correlation
16:32 Correlation vs R-squared
17:31 Summary of concepts
#statquest #correlation

[@statquest]

NOTE: Although I do not mention it by name in the video, this StatQuest covers Pearson's Correlation Coefficient. Unfortunately, this did not occur to me until after I posted the video, otherwise I would have mentioned it at least 20 times...so maybe it's better the way it turned out. ;)
Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

[@sunilkumarsamji8507]

Hi Josh Thanks a lot for the wonderful work. it helps learners a lot. My query: At 9 : 08, it is mentioned p = 2.2 * 10 ^ -16 means low probability that a randomly selected point has similarly strong relationship. Does it mean to say that the hypothesis or prediction (line through the data points) of the trend cannot generalize with respect new data point a randomly selected data point? Is that what a low p means to say? At the same time a low p means high confidence level in the trend which means that high confidence level implies that a randomly selected that will have similarly stronger relationship? Let me please know if I am missing some point.

[@statquest]

@@sunilkumarsamji8507 No. The p-value tells us that the probability that random noise could create the relationship we observed, or a stronger relationship. When you have small p-value, that means the probability that the relationship we observed is due to noise is small. This means we can have confidence that new observations will behave similarly to what we have seen before, rather than completely randomly. Does that make sense?

[@inderjeetsinghintech]

@@statquest yes, that is the reason we keep the threshold to only 5% or 0.05.

[@lorisbach9905]

@@statquest Thanks for your amazing videos. I am watchng them all to try to catch up in statistics for my master degree in geology.
In this video, I am unsure on how you calculated the p-values. Can you please explain a little ?

[@statquest]

@@lorisbach9905 Unfortunately, I don't have a video that explains the p-values for Pearson's correlation coefficient in detail. However, I do have a video that explains the p-value for R-squared, which is very, very closely related (and is actually much more useful) here: ruclips.net/video/nk2CQITm_eo/видео.html

[@bigorange6328]

My days spent on statistics before knowing statquest were so wasted

[@statquest]

Wow! I'm glad you like my videos! :)

[@ThinkwithLex]

I can relate

[@kantaphongsaklo102]

Same

[@ahaha731]

Same

[@SumitOli007]

I am crying rn, Statistics was the one thing that scared me in high school, never studied it in engineering & after watching tons of videos & losing hope. I finally found your channel.
I am finally understanding bits and bytes of statistics & I owe everything to this beautiful pedagogy
Infinite BAM

[@statquest]

Hooray! I'm glad my videos are helpful. :)

[@bartgacrama2295]

You are a genius in pedagogy.

[@statquest]

Thank you! :)

[@anitapallenberg80]

100 % agree! I love StatQuest with Josh Starmer!! ♥

[@vikranttyagiRN]

@@anitapallenberg80 Me too. Alot

[@Cat99]

Simple, easy to understand.

[@alberttamazyan]

I am so thankful to you!!! I tried learning statistics multiple times in my life and never succeded with any source. I discovered your stat quests about a week ago and I already feel so comfortable with many concepts in statistics! Huge thanks.

[@statquest]

That's awesome! I'm glad the videos are helpful. :)

[@bubbleworld4172]

Appreciative bäm from Germany.

[@statquest]

That's awesome! I'm glad Bam has an umlaut in German. ;) That makes it twice as cool. TWICE BÄM!

[@TheCJD89]

I just watched the Covariance and Correlation videos back to back. Very well put together and really easy to follow

[@statquest]

Thank you! :)

[@mathavraj9662]

As soon as I started the video, the differences between r-square, covariance and correlation were lingering in my mind. Glad you cleared them all!!

[@statquest]

Glad it was helpful!

[@allthingsconsdrble]

Very much appreciate the crawl, walk, run approach with emphasis on conceptual understanding

[@statquest]

Thank you!

[@Alchemist10241]

I've added this channels videos to my Anki cards and every time I review them I get even deeper insights. well done statquest

[@statquest]

bam! :)

[@arnabchanda2609]

All My Life I have been looking out for you, glad that I found you... BAM!!!

[@statquest]

Hooray! :)

[@zumiao234]

Thank you! You actually help me to understand many basic concepts in a clear and easy-acceptable way, you are so smart and kind-hearted.

[@statquest]

Thank you very much! :)

[@reach2puneeths]

These are the best videos which explains the concept in simple way. Thanks for making these videos.
Please upload Al and deep learning videos.

[@BatkhuuByambajav]

Bam Bam BAM...
Eventually, I've fallen in love with your BAMs :)
Addictive BAMs and gorgeously simple videos!
Thanks a lot!

[@statquest]

Thanks!

[@user-zc5dp1yw6y]

Ohhh man!!! I'm instantly falling in love with this channel, definitly the best sense of humor to learn machine learning.

[@statquest]

Thanks! :)

[@blakebodycote1024]

I have yet to get into most of these concepts in my statistics major, but I am so thankful to have these bite-sized informational videos with lots of visual explanations to explain each concept so I can start practicing and studying machine learning early. Thank you so much for every single video you put out. Truly a blessing.

[@statquest]

Thank you very much! :)

[@kylebecker5083]

I've learned so much from this channel. Thanks, Josh.

[@statquest]

Awesome, thank you!

[@kaigordon2900]

Extremely helpful and clear with good examples and explanation! Wonderful, thank you!
BAM!!!

[@statquest]

Thanks!

[@gtrstreet]

Very well explained. I like that you give lots of examples and answer many of the possible questions in advance. Thanks a lot!

[@statquest]

Thank you very much! :)

[@terryliu3635]

The best intro on correlation, thank you!

[@statquest]

Thank you! :)

[@2002budokan]

I find the best and non-boring stats explanations in this channel.

[@statquest]

BAM! :)

[@shreyastudies4693]

You have a knack for teaching... this was an amazing video, thank you!!

[@statquest]

Thank you! :)

[@pasqualegiorio3651]

Josh you are just a genius of Stat explanations, thank you.

[@statquest]

Thank you very much! :)

[@vamanieperumal5262]

I cant believe how all your videos are so perfect !

[@statquest]

Wow, thank you!

[@Some_random_guy_16]

you are doing a great job enabling us to learn may super tough concepts relatively easy .. that too free of cost...thankss

[@statquest]

Thank you very much! :)

[@tatianajaramillo1148]

Thank you for your time to explain and make this video!!!

[@statquest]

Thank you very much! I really appreciate your feedback.

[@felipebraga7753]

Cara, seu vídeo é mega claro, sem deixar de ser rigoroso! Super obrigado pelo trabalho!

[@statquest]

Muito obrigado!!!

[@shubhamjain2423]

Dear Josh, This video made my endless nights trying to grasp on this topic.

[@statquest]

:)

[@hassanrevel]

Josh you're super great man. I really enjoy listening you.

[@statquest]

Thank you!

[@harithagayathri7185]

Josh, you explain in such a way that even layman can understand easily.
A big shout out to all the hard work you put in for making these videos.👏👏

[@statquest]

Thank you very much!!! :)

[@AnayFereshetyan]

This was so incredibly helpful, thank you!

[@statquest]

Thanks!

[@user-jh4lh1rc7z]

Bam....I started to think that statistics can be fun....Huge thanks from Korea

[@statquest]

Hooray!!!

[@calciumfree9626]

Big thanks! I couldn't get any intuition from my school lecture, and it's lucky for me to find this video a day before my exam for this!

[@statquest]

Good luck on your exam! :)

[@sherrynsherryn5071]

Thank you from Indonesia, I love your videos!

[@statquest]

Thank you! :)

[@LOVEONLYLOVEable]

If anyone finds a better teacher than this guy on you tube, do let me know 😎😎

[@drditup]

you just explained this better than i ever heard. im a phd student (who for some reason wasn't given a decent statscourse through his master degree in robotics engineering. Needless to say, statistics are good for science)

[@statquest]

Thank you! :)

[@sashacollum7583]

Soooo thankful to have found this video. Why did it seem so hard to understand before?!

[@statquest]

bam! :)

[@vedprakash-bw2ms]

Stat quest is the best ..

[@statquest]

Thanks! :)

[@jammabeergood]

Great rhyme!

[@YeekyYeeky]

your video makes it really easy to understand(even my english is not really strong , I can still understand almost all of them) , thank you from Thailand

[@statquest]

Hooray! I'm glad you like my videos. :)

[@sammiechung2711]

Thanks for your detailed and clear explanation. Saving much of my time to read books which hard to understand.

[@statquest]

Thanks! I'm glad the video is helpful.

[@tuankietly6076]

your video is so great and easy to understand!

[@statquest]

Thanks! :)

[@caspase888]

Waiting for your videos is a cause worth waiting for 👍👍👍

[@statquest]

Thanks! :)

[@mostinho7]

Thanks!
Great summary at 9:00
Correlation strength nothing to do with slope, but with how many points the line goes through. Can have correlation of 1 with large slope or small slope as long as the points lie on a line.
14:00 equation cov(x,y) in previous video

[@statquest]

bam!

[@arismenachekanian1804]

Thank you for making this great video!

[@statquest]

My pleasure!

[@taladiv3415]

Guys like this help make the study world a better place!

[@statquest]

Thank you!

[@amizan23]

Your videos are way better than most of the paid courses.

[@statquest]

:)

[@delliscool4924]

thank you , you are distinguished brilliant mind and great teacher for many

[@statquest]

Wow, thank you!

[@wernhervonbraun4222]

I'm very grateful to all of your videos. I want to support you but I am a student in 3rd world country. Even I get capable enough I'll surely contribute to this great project! Thank you

[@statquest]

Thank you very much! BAM! :)

[@PRODKAZ-fy8cx]

Thank you so much! This was so helpful.

[@statquest]

Thanks!

[@thesagecc]

As a graduate level I-O Psychology student.... thank you... I watched the summary first and then went back to watch the entire video

[@statquest]

bam!

[@draviaartistwithbat5756]

Thanks for the video.
And please make next video series on hypothesis testing (z test, t test, anova, chi square)

[@markobe08]

That is right!!!

[@statquest]

If you want to have a super deep understanding on t-tests and ANOVA, you should check out my StatQuest videos on Linear Models: ruclips.net/p/PLblh5JKOoLUIzaEkCLIUxQFjPIlapw8nU

[@draviaartistwithbat5756]

Sure I will check it and let you know if anything else is needed. Thank you very much. You are doing great man keep up the good work.

[@paveldvorak2014]

@Josh, it is great you actually put the text on the screen, I cannot play sound but I can still follow closely what you are saying. Great videos, I hope you will later dive into more advanced topics in time series analysis (unit roots, ARIMA, GARCH, etc). Pls keep it up!

[@statquest]

I'm glad you like my style. :)

[@qiliu4100]

I am familiar with the concepts you talk about.
But I am a fan of your songs, so I am here to listen to the music.

[@statquest]

BAM! :)

[@user-kn9wu7ts9m]

It solves my confusion. Thanks a lot.

[@statquest]

Bam! :)

[@TheEbbemonster]

Very good - I would have liked to see a p-value calculation also :)

[@SaintSaint]

ruclips.net/video/vemZtEM63GY/видео.html ruclips.net/video/5Z9OIYA8He8/видео.html Both answer this.... but I agree... a quick explanation of p values would be the only extra credit that I felt was missing from this video. Much the way he did variance recap at the beginning.

[@yulinliu850]

Good job Josh! Thanks!

[@statquest]

Thanks! :)

[@mohammednadeem662]

StatQeust is really amazing to learn and understand things very easy

[@statquest]

Thanks!

[@OlegGolubev_yolo]

How good you r at this. I tried really hard to understand what it this when i've been in university. but failed. Because there was no explanation why we need this. Only the words that it is "how x related to y"... I figured out what is it actually only 7 years later... Thanks a lot man

[@statquest]

Happy to help! :)

[@santoshbala9690]

Hi Josh.. Very well explained... Thank you
Please do a video on ACF & PACF (Auto Correlation & Partial Auto Correlation)

[@arishali9248]

Love your videos mate

[@statquest]

Thanks! :)

[@amanzholdaribay9871]

Thank you, man!

[@statquest]

Thanks! :)

[@joserobertopacheco298]

the ultimate clearly explanation

[@statquest]

BAM! :)

[@siddharthmishra8233]

always enjoys your song josh!

[@statquest]

Thanks!

[@robertdavis2855]

I didn't think that Machine Learning and humor were correlated but here we are...BAM!

[@statquest]

bam! :)

[@maheshsonawane8737]

Thanks Josh!!!!!!!!!!!!!! Helps lot.

[@statquest]

Thank you! :)

[@maheshsonawane8737]

@@statquest I can't believe u replied. I am pursuing MS Data Science. Your work really give me better understanding. I will pay ur tuition fee when I get job. ✌🤟👆👍😎

[@Bharathkumar-gv4ft]

p-value superbly explained!

[@statquest]

Thanks!

[@emov8326]

I love your work

[@statquest]

Thank you very much!!! :)

[@sheldonsebastian7232]

Amazing Video, Thanks!!!!!!!!!!!!

[@statquest]

Thanks! :)

[@ilhambintang3425]

Best tutorial ever :)

[@statquest]

Thank you! :)

[@jairoalves8083]

how to obtain the p-value from this data?

[@amanmanveen]

@@minhtoto1542 Had the same question. Found this video helpful: ruclips.net/video/8Aw45HN5lnA/видео.html

[@eugenefrancisco8279]

You might be referring to a t-test for slope. You would need to calculate a sample regression line using the data and then obtain a p value by performing a test on the data with some null hypothesis.

[@diegolazareno8020]

Awesome video!

[@statquest]

Thank you!

[@botboy2134]

Wow on to the point video!!!

[@statquest]

Thank you! :)

[@Anteater23]

I love your videos.

[@statquest]

Thank you!

[@usama57926]

amazing explanation....

[@statquest]

bam!

[@Roboticdock]

Excellent!

[@statquest]

Many thanks!

[@ForTheLoveOfHomes]

Fun song! Thanks!

[@statquest]

Thanks!

[@marcoventura9451]

Great video.

[@statquest]

Thank you!

[@user-ew9qv2xn1e]

NICE VIDEO AND EASILY UNDERSHANDING

[@statquest]

Thanks! :)

[@qinqinkong8330]

Triple Bam!! Thanks for the great lecture, although I think the p-Value not only depend on the amount of data we have, but also depend on the strength of relationship. For example, given the same amount of data, the chance to generate stronger relationship from random points is smaller for higher correlation than lower correlation.

[@statquest]

Yes, that's sometimes true, but not always (for example, if your sample size = 2), so I decided to focus on the things that are always true in my video, and that is Correlation is determined by the strength of the relationship and p-values are determined by sample size. In other words, if the sample size is too small you will never have a small p-value, and if the sample size is huge, then it doesn't matter what the correlation is, the p-value will probably be significant. For example, if we have any 2 data points, we can draw a line through them, and correlation = 1, however, the p-value = 1. In contrast, if we have enough data, it doesn't matter how close the correlation is to 0, we can still have a significant p-value.

[@qinqinkong8330]

@@statquest You reply my comments! Bam!!!!

[@statquest]

@@yangyu5525 Corrected!

[@kudimaysey2459]

Thanks statquest

[@statquest]

bam!

[@abhishek-shrm]

Best video ever seen on correlation👍😁

[@statquest]

Thank you very much! :)

[@abhishek-shrm]

@@statquest Welcome and thank you for making these videos😁

[@niveditathatte3170]

lovely explanation following you :-)

[@statquest]

Thank you! :)

[@difflyfe23]

Awesome lecture

[@statquest]

Thank you!

[@kevinwidanagamage2104]

thank you so much for this

[@statquest]

You're very welcome!

[@robertobr234]

I really like it!

[@statquest]

Thanks!

[@1miffy1]

When Phoebe decides to sing stats... xD
Love the videos... lifesavers to sinking ships in the sea of numbers

[@statquest]

Check out: ruclips.net/video/D0efHEJsfHo/видео.html

[@1miffy1]

Omg xD best!

[@vaibhavpandey7398]

Uncle josh, ur only one who answers my query of why can't squiggly line be made. Thanku

[@statquest]

It can be, but it's not as easy (however, modern neural networks can fit a squiggly line to just about anything. For details, see: ruclips.net/video/zxagGtF9MeU/видео.html ). When we use squiggly lines, we use R^2 instead of Pearson's Correlation because Pearson's correlation is explicitly defined for straight lines.

[@vaibhavpandey7398]

@@statquest ok thanku.. It's entirely new for me

[@pritikagowda5513]

CORRELATION ITS THE SENSATION, please make full version songs on stats haha!

[@statquest]

:)

[@prateeknagaich13]

Hi, great video. Can you please provide additional guidance on the following:
a. How do you quantitatively determine the P-value for a correlation?
b. What's the difference, both formulaically and conceptually between R2, Correlation, and Beta/coefficient in a regression?

[@statquest]

For details on p-values and linear regression, see: ruclips.net/video/nk2CQITm_eo/видео.html

[@persephonez7067]

This is much better than the class in uni..

[@statquest]

Thank you! :)

[@jongcheulkim7284]

Thank you.

[@statquest]

Any time! :)

[@aswathyskumar6622]

Thankyou for that intro song though🥺♥️

[@statquest]

Hooray! :)

[@Clarkephix]

First time hearing a female voice on your channel, and it's hilarious. Anyway, thanks for all of your videos, it helps me survive throughout my statistic course

[@statquest]

Hooray! :)

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you are the best :)

[@statquest]

Thank you very much! :)

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BAM.. Get addicted to your video

[@statquest]

Hooray! :)

[@sumitkumar-el3kc]

I love how you teach us like we're bunch of 7-8 year's old kids.

[@statquest]

I just teach the way I teach myself.

[@gdtoob]

Would you consider doing a video on the beta distribution?

[@ifeanyichukwuadibemma9428]

I understand this now! Double Bam!!!

[@statquest]

Hooray!

[@ashbk1911]

You are the best

[@statquest]

Thank you! :)

[@youngmen747]

Good video 👍

[@statquest]

Thank you!