R-squared, Clearly Explained!!!

R-squared is one of the most useful metrics in statistics. It can give you a sense of how good your model is.
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[@statquest]

NOTE: When I first made this video, I was thinking about how R-squared relates to Linear Regression, which will not fit a line worse than the mean of the y-axis values. This is because if the values along the x-axis are truly useless in terms of predicting y-axis values, then the slope of the line used to make predictions will be 0, and the intercept will equal the mean. However, it is possible to simply draw a line that fits the data worse than the mean and get a negative R^2.
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[@mattkilgore7323]

With enough variables in the data set, it would be easy to create a set of r-squared values so that the cumulative percent "explained by" the different variables goes over 100%. That's why I was never a fan of that terminology. Students think it implies causation when it doesn't. Otherwise, great video.

[@statquest]

@@mattkilgore7323 Maybe I should have made it more clear, but if you have a large model with a lot of variables, then you don't add together a bunch of individual R-squared values to find the total R-squared. You calculate a single r-squared value fro the entire model. In other words r-squared refers to the models, not the individual variables.

[@huiwang2854]

StatQuest with Josh Starmer If you only consider all unbiased lines, (mean of predicted ys equal mean of real ys), then no negative R^2.

[@sunilkumarsamji8507]

@@mattkilgore7323 Hi Matt can you explain the point you trying to make in a bit more detailed manner

[@mattkilgore7323]

The phrase "explained by" can be deceptive, as students often think it means "caused by." But this is not what it means in the context of r-squared. Does that help?

[@dannysnee4945]

So glad this channel exists. It's rare that CZcams videos on stats are this well done

[@statquest]

Thanks!

[@shashankkhare1023]

@@statquest You are a lifesaver. I am surprised you dont have more subsciptions. I would recommend your channel to my colleagues, thank you so much :)

[@statquest]

@@shashankkhare1023 Thank you very much!!! Recommending my channel to your colleagues is the best complement you can give me. :)

[@VinodKumar-nn7go]

you can watch and learn from Dr. Ami Gates. Her videos are great..

[@kinvert]

So all this time I spent sniffing rocks to grow bigger was for nothing???

[@statquest]

Ha! You made me laugh. :)

[@PeterXLuo]

haha

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only if you are mouse

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I love you hahahaha

[@muslimmukhtarkhanov8194]

You should have made a powder out of rocks, that would speed up your growing. Especially if your powder of white color🤣🤣🤣

[@ramprakash7872]

You have explained the concept so neatly,clearly ( most importantly in an easier manner ) so that one could get deeper understanding of the concept, a fact that lot many text books / videos / articles failed to do. Keep making such videos !

[@joenah5651]

Thank you so much for making this sooooooo clear, I've struggled to understand the meaning of R2 for a week and you just made it clear to me in 10 min.

[@statquest]

Bam! :)

[@DD-hh4tz]

Your videos are so easy to understand, and also explains the intuition behind. I really love the way you start the video, unlike other bouring lectures.

[@statquest]

Thank you so much! :)

[@muffinman1]

"sniff/weight relationship" debunked by StatQuest. Give this man a Nobel. :)

[@statquest]

Thanks! :)

[@cartulinito]

I started following you 4 months ago, now I'm starting over from the very first video, I'll watch them all and understand everything.
Thank you very much for this content.

[@statquest]

Thanks!

[@dikshyapattanaik3528]

Your channel is blessing in disguise. Visual aids and the explanations are so smooth and easy to understand. Thank you very much.

[@statquest]

Thank you very much! :)

[@gri189]

Just recently found your channel. These are by FAR the most straight forward explanations I found so far. You sir are a godsend.

[@statquest]

Thanks!

[@alecvan7143]

I can't believe the simple relationship between R^2 and R was never made clear to me! Amazing as always!

[@statquest]

Awesome!!!! Thank you very much.

[@pablo_brianese]

I also appreciated his comments on the subject, and him sharing his opinions and intuitions.

[@bleakmess]

Just a quick question?

[@sanketbadhe3572]

I read a lot on R square from different books and articles but this was the really different and very intuitive approach. Visualization is the best way to understand statistics and I think most books lack there.

[@statquest]

Thanks! :)

[@amirmohamed2428]

I had stats exam coming up and didn't know this particularly well, Thanks for making it much more simpler!

[@statquest]

Good luck on the exam! :)

[@vamanieperumal5262]

this is the best channel ever that can exist about statistics :D wonderful explanation and illustrations and the music! :) am glad I found this at the right time !

[@statquest]

Thank you so much 😀

[@baxtables]

Are u glad u found it or are u asking us if u are glad??😆😆

[@yashshah1936]

Josh you are the best!!! Your every video has been helpful to god knows how many times in my studies. Much much love

[@statquest]

Thank you very much! :)

[@ivandeetlefs]

I would rather name this video VERY CLEARLY EXPLAINED. Thank you.

[@statquest]

Thank you!

[@hewhomustnotbenamed5912]

Added this to my useful tutorials and math playlists.
Thanks StatQuests.

[@statquest]

BAM! :)

[@thisis7734]

Amazing explanation!!Made it very simply for me to understand!! :)
I went through so much content for this..thank you

[@statquest]

Hooray! I'm glad the video was helpful.

[@samuelliaw951]

cool! you have cleared all the fogs around r2 in my head once for all. appreciate your explanation!

[@statquest]

Glad to help!

[@prateeksachdeva1611]

Could not have even imagined such intuitive explanation of this topic before watching this video. Thanks Josh!

[@statquest]

Thank you!

[@kowsergazi]

No one could make me understand R Squared in such easy way. Watched many videos. All made it complicated. Thanks.

[@statquest]

Hooray!!! I'm glad to hear the video was helpful! :)

[@ashokcgl]

Just impeccable. I don't think any other better illustration exists other than this. Thank you

[@statquest]

Thanks!

[@tanmaymhatre6370]

love the way you explain things in casual manner

[@statquest]

Thank you!

[@Steve-go3zp]

I have been looking at a variety of stats videos and these are clearly the best. I am so impressed with StatQuest that I renamed my four dogs, "StatQuest," "StatQuest," "StatQuest," and "John Stamos" because, of course...

[@statquest]

BAM! :)

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The introductions are the cutest thing I have ever seen - the videos are also super duper helpful!

[@statquest]

Thank you! :)

[@Love4ever1223]

god bless, i have been searching high and low for this kind of video. Thank you!!!!

[@statquest]

Hooray! :)

[@sanjaykrish8719]

Very beautifully explained. Many thanks to the folks of Genetics Department at the University of North Carolina at Chapel Hill.

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[@statquest]

Hooray!

[@wayne02058]

a simple concept explained simply. thank you for the straight forward explanation

[@statquest]

Thank you very much! :)

[@AdilKhan-sh9fv]

This channel has become my go-to resource for anything stat related.

[@statquest]

Bam! :)

[@khanhdovanit]

@@statquest Love your Bam and your singing

[@rabbisheryl9613]

aha! we meet again, and I thank you again!!! wow, I wish you were teaching my class!!

[@statquest]

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

[@lilmoesk899]

Super useful as always. Please continue with the videos (for example, prediction interval vs. confidence interval or maybe p-values vs. randomization tests or logistic regression...)! I liked your explanation because it never occurred to me that R^2 was basically the same as calculating percent change (diff/original)x100.

[@firasal-nasir1909]

watching this again, thank you very much. I jumped into more advanced stuff because of your videos. 🙏🙏

[@statquest]

Awesome!

[@rajsingh9869]

really boom...I was confused from past 3 days to understand regression value ...now I understand. Thanks

[@statquest]

bam! :)

[@thyang3999]

Thank you very much, your video is very easy way to understand, makes me want to go through the Statistics course again.

[@statquest]

You can do it!

[@fredyrojas7884]

These videos are pretty cool. I can always come back and refresh concepts.

[@statquest]

Glad you like them!

[@goodester6924]

Was struggling to understand this concept but this video explained everything!

[@statquest]

Hooray! :)

[@paololara3115]

Thank you, this was a life-giver! Josh Starmer, you just might have become a part of something which will be big

[@statquest]

Wow, thanks!

[@shinhyelee3169]

Ah! this is the best video explaining R squared! Thank a lot!

[@statquest]

Thank you! :)

[@mohdbasryt]

Great teachers make everything interesting! Thanks Josh

[@statquest]

Thank you! :)

[@stevenpatterson8119]

This helped me clearly understand R^2. Trying to grasp this from reading a textbook was impossible for me.

[@statquest]

bam! :)

[@minilamabianco]

You are a rarity ❤️ really love how you explain statistics! Please tell us more 🙏🏻♥️♥️♥️

[@statquest]

Thanks! :)

[@elfmas]

Thanks, every question/doubt that I had instantly got answered about 10 seconds later.

[@statquest]

BAM! :)

[@MrClevermind]

Thank you, you're helping us with these videos.

[@statquest]

Thank you very much! :)

[@dearwriter9659]

Now I understand the R squared much better! Thank goodness for this video!

[@statquest]

Glad it helped!

[@mohammadhassanjafari481]

I did not see anyone explain the statistics better than you
God bless you ...

[@statquest]

Thank you!

[@AydinCGur]

Wonderful explanation again. I easily understood the concept. I'm grateful.

[@statquest]

Thanks! :)

[@senwang8468]

这样的创作者请给我来一百个！thank you for your videos!I really appreciate what you have done, and look forward to seeing more of them~

[@statquest]

Thank you very much! :)

[@nithyashreevenkataraman3]

Thank you so much, I've learned so much from you in the past week! Very grateful

[@statquest]

Thank you very much! :)

[@nicholesutter80]

Working on my MPA stats final and this video has been so helpful

[@statquest]

bam! :)

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Really enjoying your videos. Moreover everything is crystal clear and I am able to understand them. Double BAM

[@statquest]

Hooray!!! That's great news. BAM! :)

[@samuelgrubb2976]

I never comment, but today is not that day. Thank you so much for this!!!! I am in graduate school and am still struggling to understand these concepts, you're a life saver

[@statquest]

Thanks!

[@sweetheart.nikkilee430]

wow this is the best explanation ive ever seen, thank u!!!!!

[@statquest]

Thank you very much! :)

[@mohitsrivastava5880]

Thanks for the simple explanation. Much appreciated.

[@statquest]

Thanks! :)

[@sebastianc09]

I'm truly grateful for your videos!

[@statquest]

Thank you!

[@sudhitiwaridwivedi3096]

Undoubtedly d best and to the point explanation. Thanks a lot

[@statquest]

Thank you! :)

[@vitulbansal1719]

totally agree!!

[@adnanshahnawaz6808]

"time spent sniffing a rock"! had me cracking😂.... btw thanks josh for putting such great content up... this channel is the my primary source of building my statistics foundations....

[@statquest]

Glad you like them!

[@guthrie_the_wizard]

Thanks very much! Your videos rock. Great pacing, excellent points.

[@statquest]

Thank you very much! :)

[@Gattomorto12]

Nice video! I'll recommend it to family and friends.

[@kumarransing8489]

Really good explanation as to why r squared is significant in describing variation in data. Thank you!

[@statquest]

Glad you liked it!

[@mmhamed1]

You know what i decided to start watching your videos from the beginnimg .. baaam .. thanks

[@statquest]

Awesome! Thank you!

[@pablo_brianese]

Thank you for this precious material

[@statquest]

I'm glad you like it!

[@footballistaedit25]

Thanks for sharing, Sir. It helps me a lot

[@statquest]

Glad to hear that!

[@anacarolinamartinelli9065]

This video is absoluted amazing! R^2 and R finaly understood!

[@statquest]

bam!

[@funnyclipsutd]

After watching your videos, I aced my stats module!

[@statquest]

TRIPLE BAM!!! Congratulations!!! :)

[@KARAB1NAS]

Nice explanation. To the point.

[@PeterXLuo]

best video explaining R and R squared ever!

[@statquest]

Thank you!

[@KIKI-NJ]

So proud of me because I'm watching these videos. Very very goood job thanks 😊 👍 👏

[@statquest]

Nice!

[@emmanuelskywalker1581]

AWESOME! thanks for the explanation.

[@statquest]

Hooray! I'm glad you like the video! :)

[@AmosFolarin]

Beautiful explanation :)

[@statquest]

Thank you! :)

[@mosama22]

Thank you Josh, this was really a beautiful explanation :-)

[@statquest]

Thanks!

[@ricardoagnelo2995]

Good explanation and your videos really are funny... good job

[@statquest]

Hooray! I'm glad you like the videos and my silly jokes. ;)

[@kwanpakshing]

The best explaination I can find

[@statquest]

Thanks!

[@vivekmenon4118]

Well explained. Thank you!!!

[@statquest]

Thanks! :)

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Zedstatistics coupled with statQuest is just absolutely magnifique

[@statquest]

Awesome! :)

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Amazing video! Thank you very much!

[@statquest]

Thanks! :)

[@anilsarode6164]

hats off and thanks a lot you will make me cry. thanks once again.

[@statquest]

Thanks! :)

[@baxtables]

Why cry mate???

[@sheldonsebastian7232]

B - E - A - utiful explanation. Thanks

[@statquest]

Thank you!!! :)

[@toast34]

Came here from the Pearson's correlation video. Thank you so much for this
I just wish that you could show in the video:
• how (Var(mean)-Var(line)) / Var(mean) is equal to [Covar(x,y) / (Var(x)^-2)(Var(y)^-2)]^2
• whether (Var(mean)-Var(line)) / Var(mean) using mean and differences from the x-axis also yields the same value
Again, thank you for the video

[@statquest]

I'll keep that in mind.

[@gbchrs]

woah thanks for this one too Josh! finally gets R2

[@statquest]

Triple bam! :)

[@abdullahattia2491]

my dude I understood and I am happy
8-year-old video is this good
liked, subbed and thank you!

[@statquest]

My dude! Thank you very much! :)

[@isa..333]

this is bizarelly useful for my exam tomorrow

[@statquest]

Good luck! :)

[@mishtimaithli]

phew...!!! finally this concept is clear in my head :) thank you sooo much

[@statquest]

Glad it helped!

[@donfeto7636]

Thank You Statquest your video and my knowledge of R^2 have a R^2 of 99.99

[@statquest]

BAM! :)

[@rashminaik6242]

Very well explained!! Thanks

[@statquest]

Thank you! :)

[@busyshah]

You know only a level of mastery can achieve this level of ease.

[@statquest]

Thanks!

[@amiralessigue9075]

the best explanation as usual

[@statquest]

Thanks! :)

[@gloriachen5050]

I really love this channel, thank you so much! one question is that is the blue line caculated from the least squared method?

[@statquest]

Yes, it is!

[@junepark9591]

Beutifully explained. Thank you so much.

[@statquest]

Thank you!

[@DiegoMachida]

You goddamm beautiful man, Im eating your videos like candy nowadays, Im finishing an electrical and comms engineering degree and working with some computer science and I usually get hammered with statistical questions when I finish presenting my models, thanks to your uploads i've held my own against some nasty expert old timers, thank you for this.

[@statquest]

Awesome! TRIPLE BAM! :)

[@bachxuanquang2837]

Very clear explanation!

[@statquest]

Glad you liked it!

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Mr StatQuest I love you

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Wow is this your login name?

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Dude..this friggin rocks.. THAKS YOU!!!!!

[@statquest]

Thanks!

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This is sooo good... wish i found this video earlier.

[@statquest]

Glad you liked it!

[@amj.composer]

Gosh, this was SO helpful.

[@statquest]

Thanks!

[@RAJIBLOCHANDAS]

Nice explanation!

[@statquest]

Thanks!

[@tymothylim6550]

Great video! Thanks a lot!

[@statquest]

bam!

[@vijaypalmanit]

one of the best explanation, thanks a lot for making this video..

[@unlearningcommunism4742]

I've stared binge watching the entire channel :D

[@statquest]

BAM! :)

[@unlearningcommunism4742]

@@statquest Do you know someone doing TDA (topological data analysis) / AYASDI Software?
Man it's a good stuff...

[@statquest]

@@unlearningcommunism4742 I'll look into it.

[@unlearningcommunism4742]

@@statquest Obscure stuff, my postdoc actually, but it makes everything - better. I've personally tested a lot of things with it from images, to soil samples, languages, FTIR spectra... And it gives the edge every time.

[@intfxdx]

Awesome explanation

[@statquest]

Thanks!