R-squared, Clearly Explained!!!
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- Опубликовано: 29 июн 2024
- 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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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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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.
@@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.
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.
@@mattkilgore7323 Hi Matt can you explain the point you trying to make in a bit more detailed manner
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?
So glad this channel exists. It's rare that RUclips videos on stats are this well done
Thanks!
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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 !
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.
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I can't believe the simple relationship between R^2 and R was never made clear to me! Amazing as always!
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I also appreciated his comments on the subject, and him sharing his opinions and intuitions.
Just a quick question?
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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.
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Thanks!
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.
Thanks! :)
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Just recently found your channel. These are by FAR the most straight forward explanations I found so far. You sir are a godsend.
Thanks!
Added this to my useful tutorials and math playlists.
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I had stats exam coming up and didn't know this particularly well, Thanks for making it much more simpler!
Good luck on the exam! :)
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 !
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Amazing explanation!!Made it very simply for me to understand!! :)
I went through so much content for this..thank you
Hooray! I'm glad the video was helpful.
Josh you are the best!!! Your every video has been helpful to god knows how many times in my studies. Much much love
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I would rather name this video VERY CLEARLY EXPLAINED. Thank you.
Thank you!
cool! you have cleared all the fogs around r2 in my head once for all. appreciate your explanation!
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love the way you explain things in casual manner
Thank you!
Could not have even imagined such intuitive explanation of this topic before watching this video. Thanks Josh!
Thank you!
Just impeccable. I don't think any other better illustration exists other than this. Thank you
Thanks!
Very beautifully explained. Many thanks to the folks of Genetics Department at the University of North Carolina at Chapel Hill.
god bless, i have been searching high and low for this kind of video. Thank you!!!!
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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...
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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.
The introductions are the cutest thing I have ever seen - the videos are also super duper helpful!
Thank you! :)
a simple concept explained simply. thank you for the straight forward explanation
Thank you very much! :)
really boom...I was confused from past 3 days to understand regression value ...now I understand. Thanks
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No one could make me understand R Squared in such easy way. Watched many videos. All made it complicated. Thanks.
Hooray!!! I'm glad to hear the video was helpful! :)
These videos are pretty cool. I can always come back and refresh concepts.
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watching this again, thank you very much. I jumped into more advanced stuff because of your videos. 🙏🙏
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Thank you very much, your video is very easy way to understand, makes me want to go through the Statistics course again.
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I did not see anyone explain the statistics better than you
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Was struggling to understand this concept but this video explained everything!
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Really enjoying your videos. Moreover everything is crystal clear and I am able to understand them. Double BAM
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Ah! this is the best video explaining R squared! Thank a lot!
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Thank you, this was a life-giver! Josh Starmer, you just might have become a part of something which will be big
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Wonderful explanation again. I easily understood the concept. I'm grateful.
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This helped me clearly understand R^2. Trying to grasp this from reading a textbook was impossible for me.
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Working on my MPA stats final and this video has been so helpful
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Thank you for this precious material
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Now I understand the R squared much better! Thank goodness for this video!
Glad it helped!
You know what i decided to start watching your videos from the beginnimg .. baaam .. thanks
Awesome! Thank you!
Beautiful explanation :)
Thank you! :)
Really good explanation as to why r squared is significant in describing variation in data. Thank you!
Glad you liked it!
Thanks for sharing, Sir. It helps me a lot
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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~
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Thanks, every question/doubt that I had instantly got answered about 10 seconds later.
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Undoubtedly d best and to the point explanation. Thanks a lot
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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
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Thank you Josh, this was really a beautiful explanation :-)
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liked, subbed and thank you!
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hats off and thanks a lot you will make me cry. thanks once again.
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Why cry mate???
Well explained. Thank you!!!
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best video explaining R and R squared ever!
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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
I'll keep that in mind.
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Beutifully explained. Thank you so much.
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B - E - A - utiful explanation. Thanks
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Very clear explanation!
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"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....
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One of best videos, thanks
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woah thanks for this one too Josh! finally gets R2
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Thank You Statquest your video and my knowledge of R^2 have a R^2 of 99.99
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this is bizarelly useful for my exam tomorrow
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one of the best explanation, thanks a lot for making this video..
Adding to my previous comment , R2 value can be negative when the variance explained by the line is lesser than the variance explained by mean.
For example var(mean) = 30 and var(line) = 40
Then R2 = -0.3
There exists such models , perhaps that could be worst models.
This is technically correct, but practically speaking, R-squared is always positive because it is used to compare the least squares residuals for the best fitting model to the least squares residuals for the mean, and the best fitting model can't have larger residuals than the mean, otherwise the best fitting model would be the mean. Does that make sense?
Completely agree with you in terms of practicality. It doesn't make sense at all. At the end of day you want a model which performs better than the base model. My point was it can be negative. Nevertheless i really like your videos. That comment of mine was just to clarify my understanding and to reach out to you.
I was thinking more about the negative R-squared and how it could be used in practice. I mean, like you said, even if your model is terrible, worse than the mean, it still might be nice quantify how terrible it is - and that's where the negative R-squared could come in handy. It still has the same meaning, except now you're quantifying how much worse your model is than the mean. Interestingly, it still works out even if var(terrible model) is so bad that the R-squared is less than -1. For example, if var(mean) = 50 and var(terrible model) = 100, then R-squared = (50 - 100) / 50 = -1, so "terrible model" is 100% worse than the mean. If var(terrible model) = 150, then R-squared = (50 - 150) / 50 = -2, and now terrible model is 200% worse.
Right , That's my point. From my own experience , I used to train multiple models on a sample dataset and compute their respected R-squared value to choose the best among those models. There I encountered some models returning negative R-squared value. Those models are practically useless and if you agree that happens when your training data is so huge and the algorithm you are using is so insignificant, like using a multi variant regression for a heavily skewed target variable.That was the motivation behind my comment. I appreciate your time to reply back to my comments. I am glad that it grabbed your attention Mr. Josh.
@@statquest I asked a question about this too and I assumed you meant the best fitting line (even though it was not explicitly stated in the video), or at least one that performed better than the mean line.
Thank you for this easy to understand video :-)
I have two suggestion!
- Time 0:50 -- instead of `strongly related` it is better to say `strongly linear related`! We know that `R` can't explain nonlinear relationships (e.x. Y = X^2)!
- Time 10:00 -- instead of `0.7^2 = 0.5` it is better to say `0.7^2 \approx (is approximately equal to) 0.5` ;-)
Interestingly, and little known, but R^2 can be calculated for equations like y = a + b*x^2. That equation makes a curve, which is not linear, but the equation is _linear in its parameters_ (the parameters are 'a' and 'b', not 'x^2'), and that is what makes a "linear model" linear. A linear model doesn't have result in a straight line, but it must be linear in its parameters. That means you can calculate R^2 for y = a + b*x^2 or even y = a + b*sin(x). Not many people know this though since they don't understand what the "linear" in "linear models" actually refers to.
Yes, and in y = a + b*x^2 or y = a + b*sin(x) it is better to say `y` has a linear relationship with `x^2` or `sin(x)`, not `x`!
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.
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Awesome explanation
Thanks!
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Really awesome lecture
Thanks a lot!