Pearson's Correlation, Clearly Explained!!!
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- เผยแพร่เมื่อ 22 พ.ค. 2024
- 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...
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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
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. ;)
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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.
@@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?
@@statquest yes, that is the reason we keep the threshold to only 5% or 0.05.
@@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 ?
@@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: th-cam.com/video/nk2CQITm_eo/w-d-xo.html
My days spent on statistics before knowing statquest were so wasted
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@@anitapallenberg80 Me too. Alot
Simple, easy to understand.
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.
That's awesome! I'm glad the videos are helpful. :)
I just watched the Covariance and Correlation videos back to back. Very well put together and really easy to follow
Thank you! :)
I've added this channels videos to my Anki cards and every time I review them I get even deeper insights. well done statquest
bam! :)
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.
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These are the best videos which explains the concept in simple way. Thanks for making these videos.
Please upload Al and deep learning videos.
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!!
Glad it was helpful!
Very much appreciate the crawl, walk, run approach with emphasis on conceptual understanding
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All My Life I have been looking out for you, glad that I found you... BAM!!!
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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.
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Cara, seu vídeo é mega claro, sem deixar de ser rigoroso! Super obrigado pelo trabalho!
Muito obrigado!!!
Very well explained. I like that you give lots of examples and answer many of the possible questions in advance. Thanks a lot!
Thank you very much! :)
Extremely helpful and clear with good examples and explanation! Wonderful, thank you!
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The best intro on correlation, thank you!
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:)
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Thanks! I'm glad the video is helpful.
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Good luck on your exam! :)
Thank you for making this great video!
My pleasure!
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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
Hooray! I'm glad you like my videos. :)
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Amazing explanation! Thank you!
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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
bam!
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)
Thank you! :)
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
Thank you very much! BAM! :)
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
Happy to help! :)
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Hi Josh.. Very well explained... Thank you
Please do a video on ACF & PACF (Auto Correlation & Partial Auto Correlation)
Thank you so much! This was so helpful.
Thanks!
@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!
I'm glad you like my style. :)
I am familiar with the concepts you talk about.
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It solves my confusion. Thanks a lot.
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As a graduate level I-O Psychology student.... thank you... I watched the summary first and then went back to watch the entire video
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Josh, you explain in such a way that even layman can understand easily.
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If anyone finds a better teacher than this guy on you tube, do let me know 😎😎
Thanks for the video.
And please make next video series on hypothesis testing (z test, t test, anova, chi square)
That is right!!!
If you want to have a super deep understanding on t-tests and ANOVA, you should check out my StatQuest videos on Linear Models: th-cam.com/play/PLblh5JKOoLUIzaEkCLIUxQFjPIlapw8nU.html
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.
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Thanks! :)
Very good - I would have liked to see a p-value calculation also :)
th-cam.com/video/vemZtEM63GY/w-d-xo.html th-cam.com/video/5Z9OIYA8He8/w-d-xo.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.
p-value superbly explained!
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the ultimate clearly explanation
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NICE VIDEO AND EASILY UNDERSHANDING
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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.
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.
@@statquest You reply my comments! Bam!!!!
@@yangyu5525 Corrected!
Best video ever seen on correlation👍😁
Thank you very much! :)
@@statquest Welcome and thank you for making these videos😁
Great video.
Thank you!
Best tutorial ever :)
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Uncle josh, ur only one who answers my query of why can't squiggly line be made. Thanku
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: th-cam.com/video/zxagGtF9MeU/w-d-xo.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.
@@statquest ok thanku.. It's entirely new for me
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?
For details on p-values and linear regression, see: th-cam.com/video/nk2CQITm_eo/w-d-xo.html
Would you consider doing a video on the beta distribution?
thank you so much for this
You're very welcome!
When Phoebe decides to sing stats... xD
Love the videos... lifesavers to sinking ships in the sea of numbers
Check out: th-cam.com/video/D0efHEJsfHo/w-d-xo.html
Omg xD best!
lovely explanation following you :-)
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Excellent!
Many thanks!
Thank you for your amazing video!
Could you explain how to calculate the p-value in this video (such as 12:30). I have watched your p-value, but still do not know how to use it in this video's examples' calculation. 🙏🙏🙏
Unfortunately I can't explain it in a comment. Hopefully one day I'll make a video.
@@statquest Great😊😇🤓 I look forward to it😍😍. thank you very much！🙏🙏
Wow on to the point video!!!
Thank you! :)
how to obtain the p-value from this data?
@@minhtoto1542 Had the same question. Found this video helpful: th-cam.com/video/8Aw45HN5lnA/w-d-xo.html
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.
Hi Josh, as always, thank you for your great videos! Would you consider making a video to explain the relationship between correlation and R-squared? I've watched all the videos about these two terminologies, but still can not figure out the relationship.
Presumably you want something other than, "take your correlation value, r, and square it, and that's r-squared". More like, "how does the square of this equation get transformed into this other equation"?
@@statquest So how? I also curious about how/why correlation value^2=r-squared. The equations are so different. Appreciate it if you can kindly explain on that! Thank you, Josh!
@@julieyananzhu1134 I'd have to make a whole video to go through that derivation. Maybe one day I will! :)
I lost it at "small bam" 😂
:)
Thanks statquest
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I really like it!
Thanks!
great video! Is there some place (or maybe a video by you) where I can learn how to calculate the p-value of having a straight line in a 2-d plane?
I have a StatQuest on how to calculate the p-value for linear regression. That might help: th-cam.com/video/nk2CQITm_eo/w-d-xo.html
Fun song! Thanks!
Thanks!
Good video 👍
Thank you!
Great course. May I point out that at (17:38) it is better to say "correlation quantifies the strength of linear relationships"
True! :)
Dear Josh Starmer
,
I am thankful to you for your wonderful videos.
May I know why the numerator of correlation formula is always lower than denominator?
That would take a whole StatQuest to explain. We'd have to go through the Cauchy-Schwarz inequality. However, it's on the to-do list. One day I will do it.
@@statquest It was a great clue. I start reading about Cauchy-Schwarz inequality and look forward to watching your lecture in future.
Still getting this clear in my mind. ..At 13:11 you say that adding data (and a decreased p value) increases our confidence in our guess. I think this may be misleading because it suggests that b smaller p values mean more accurate guesses. I would rather say that smaller p value means more confidence that we are accurately seeing the QUALITY of the guesses we can make (not the guess itself, which is indicated by the correlation value). So with a weak correlation, smaller p value means I am more certain that there is a weak relationship and that my guess will be poor
I hope that makes sense. Thanks for a great series
What I was trying to say was in the picture on the left, we can't be sure if adding more data would give us a totally different correlation value, so we have low confidence in it. In the picture on the right, we have enough data to be confident that the correlation value will not change much with additional data.
Dear professor, at 12:57 in respect to the picture on the left, you said "increase the sample size ,don't increase the correlation". I have a different opinion about the statement. Because that at starting if I have two dots, so no doubt the correlation of the straight line is equal to 1,and P-value =1.then I add randomly some dots to the graph, well the correlation value will be changed , and so the P-value will do .thus, the P-value just tell us if there is a trend or not ,don't tell you how much the difference and how accurate the trend you find close to the actual of the stuff . Alternatively, the accurateness of trend or model you find depends on not only the amount of dots ,but also the development of technology, right?@@statquest
Woaaah thanks for your explanations! Can you make videos about psychometrics too? It would be great!
I'll keep that topic in mind.
@@statquest whoa thankss!! I'm sure lots of people need that 😍
Thank you.
Any time! :)