Linear Regression, Clearly Explained!!!
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- Опубликовано: 26 июн 2024
- The concepts behind linear regression, fitting a line to data with least squares and R-squared, are pretty darn simple, so let's get down to it! NOTE: This StatQuest comes with a companion video for how to do linear regression in R: • Linear Regression in R...
You can also find example code at the StatQuest github: github.com/StatQuest/linear_r...
For a complete index of all the StatQuest videos, check out:
statquest.org/video-index/
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Patreon: / statquest
...or...
RUclips Membership: / @statquest
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0:00 Awesome song and introduction
0:37 The Main Ideas!!!
1:12 Review of fitting a line to data
4:00 Review of R-squared
12:13 R-squared for a multivariable model
14:16 Why adding variables will never reduce R-squared
16:08 Calculating a p-value for R-squared
25:26 The F-distribution
Correction:
25:39 I should have (Pfit - Pmean) instead of the other way around.
#statquest #regression
Correction:
25:39 I should have (Pfit - Pmean) instead of the other way around.
Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/
I have seen almost all the playlists.
BAM!
I have told my many friends about this channel.
Double BAM!!
I come back again and again to revise my concepts.
Triple BAMM!!!
There will be generations who are gonna come back and learn here. More power to you. (so many BAMS)
we talk in terms of BAMs now. little BAM.
This is awesome! So many BAMS!!! :) Even a little BAM. :)
@@statquest hooray!
@@ah2522 Yes! Hooray!!! :)
@@statquest BAM...Hooray are on my tip of tongue now days !!
God bless the friendly folks in the genetics department at the University of North Carolina at Chapel Hill
Thanks! :)
amen
Amen (2)!!!!
Every time I saw your video, I just feel you’re probably the only person that don’t want to use math to confuse people or destroy people’s confidence. I appreciate that.
Thanks! :)
You are awsome explaining!
ya, you broken the legs of math mistery
30 years old and for the first time i am not afraid of mathematics a big part thanks to finding this channel in Graduate school.
ha ha.. great comment. Josh does a great job at making complex stuff seem okay to understand.
The clarity of your speech with no unessesary details in your visuals makes learning these methods so much easier thankyou.
Glad it was helpful!
Thank you, throughout years of undergrad courses, I have never seen an instructor is willing to take the time to explain all these basic yet extremely important concepts.
Thank you! :)
Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/
Had the same doubt; this clears things up, thanks! Maybe consider pinning this so it shows up on top always?
@StatQuest I think, we need the same correction in the study guide 'statquest_linear_regression_study_guide' Page 5 of 6 as well.
statquest website is not working. It is showing database error. Please look into it.
@@ssriv47 Thanks! The site is back up.
Is that a typo at 19:25? You said the numerators are the same, but they're not. Are you missing parentheses?
You are statistically one of my favourite RUclips channels!
I love it! Thank you. :)
Which are the others? :)
@@felixwhise4165 For me Brandon Foltz is another awesome channel!
I've published high-impact scientific papers in several different life science fields, and this is my go-to source to refresh my memory for all basic statistics knowledge. Most universities should abandon all attempts at teaching statistics to students in lectures, vector them to this channel, and then provide one-on-one tutoring to help students get across the line and master the material. Seriously great stuff here; you have made the world a better place - thank you.
Wow! Thank you very much! :)
This is by far the best resource for someone who does not have any background in math (or even for someone who does) to learn about key concepts of statistics. Thank you!
Wow, thanks!
You can learn more about linear regression in simple words here ruclips.net/video/QQ9MAnX963M/видео.html
More people should discover your channel, you make it very easy to understand statistics :)
I never understood statistics in my life till now, you make it look so easy. Thanks again.
This is the most intuitive explanation I have seen of these terms. Although I have known these since a couple of years, I have never seen or read a similar kind of explanation anywhere else.
Mr. Josh
Me and my friend circle thoroughly watch your all videos related to data science and we all think you are doing an amazing job. The amount of efforts you put make our ideas more and more clearer. I can't thank you enough for your generous work. Keep it up. Love from India.
Thank you very much!!! I really appreciate your feedback.
You are the best instructor. I will watch all your videos. It really helps me in ML. Hope I will find a good job!
I hope so too!
I really like how you explain things in the most simple way. I thought I knew what Adj R^2 is, but watching your video made me really understand it. Thank you a lot. Please don't stop making our world simpler to understand.
Thank you very much! :)
Linear Regression is well-explained in this video. Love the humor in between too!!!!
Thank you! :)
The most clear and simple explanation of multiple linear regression I’ve ever seen, and I’ve seen MANY! Thank you for this video!
Glad it was helpful!
Your videos are so simple and easy to grasp with all those conceptual explanations and graphics you use. They make learning fun. Thanks to RUclips for getting this to us and a bigger thanks to you for sharing it with the world.
Thank you! :)
I have gone through all of his videos.. and believe me he is the one that will make your concepts clear !
Thanks! :)
couldn't have agreed more on this.
Without a doubt this is the best explanation of Linear Regression to be found anywhere.
Thank you very much!
I love this channel and your explanations are amazing! It's so lucid and I actually feel like making an effort into understanding things. Your channel is one of the main reasons I have a job now. I've been recommending your channel and courses to every person I know!
Triple BAM! 🌟
Awesome and thank you!
You make statistics that easy to understand, thanks for your extensive work!
Hi Josh, your videos are so explicit that learning statistics seem less challenging. I can't express my gratitude for you in mere words, nonetheless "Thank you so much". The concepts are so clearly explained. You are such an amazing teacher and with your generosity and passion, you are helping so many of us out here across the world. May God bless you always. More power and love to you from India.
Wow, thank you!
your channel is THE BEST in explaining core concepts of stats and ML. I would have been lost without it. Your way of explanation is just amazing..its basically what i like..short, crisp, clear and precise. So many people are indebted to you for making these videos. Please keep up the good work and i cant THANK YOU enough for your hard work.
Thank you very much! :)
Awesome.. never looked at R-squared this way. Thank you :)
Hooray!! I'm glad you like the video :)
This is the best statistics channel on youtube! Thanks Joshua and the friendly folks.
I love your videos. It’s a true talent to be able to explain these concepts so clearly
Thank you so much! :)
Thank you so much ;-; this is so helpful!!! Our school literally threw us course notes without much of an explanation, and this video is so useful!!! Triple kudos!!!
Glad it helped!
This is amazing !!! Thank you !! I have been using linear regression for years and this is the first time I understood R squared so clearly! BAM !
Hooray! :)
This is literally the BEST materials on stats fundamentals I could ever find, thank you so so much, Josh!!! I wish I watched your vids way earlier!
Hooray!!!! Thank you so much! I'm so glad to hear that you like my videos. :)
Mind Blown at 7:37. The most obvious things are sometimes the most striking.
I have been hammered these concepts at college with barely any context and now it all makes sense thanks to you sir
Hooray!! Yes, that's the big moment for me, too. I realized that R^2 made much more sense if I could "see it". Once I made that realization, I knew I had to make this video. I'm glad you appreciate it too!
More power to you Josh!! Nobody eplains these basic concepts like you do. Thanks a lot!
Thank you! :)
Holy crud StatQuest w/Josh Starmer, this vid just catapulted me into my first grad school course I started this pm! OLS is primary focus and this vid was the perfect primer for our assigned readings ahead. TY!!! 🤯
Good luck! :)
Probably one of the most informative videos on these concepts I've ever seen. Thank you!
Hooray!! I'm so glad you like my video. :)
Thank you so much for the videos you upload... I am actually wasting my time trying to describe in words how helpful and intuitive your videos are in understanding pillar concepts of statistics... Thank you so much!
It's really nice to hear how much you like the videos! I'm glad I can help. :)
Sorry josh, can't stop myself from appreciating you.. I guess I qualify to be called a fan of your channel and your voice.. Will definitely buy your tracks from my first income ! 😎
Thanks!!! :)
Love your presentation!! What a great job you have been doing to educate people and lessen the confusion!! Many thanks!!!
Thank you! :)
Thank you so much for dissecting the terminology along with highlighting equations as you explain. Great way to understand and build the right intuition. The confusing usage of terminology and equations are the hardest and time consuming part that delays the learning process. This is so far the right mix of theory and equations I have come across. Cheers.
I was in search for few days how to learn stats for ML.
BAM! I stumbled upon this channel and everything is so bright and clear like a pleasant sunny day.
It seems we have to learn how to pronounce BAM correctly and everything else is transferred to our mind between a BAM and double BAM.
God bless Josh Starmer !
bam!
better than several stats courses I took 🙃 thanks a lot for your work! really appreciate the focus on getting an intuition for the formulae. Too many courses just state them without communicating that..
Thank you very much! :)
You can learn more about intuition of linear regression here ruclips.net/video/QQ9MAnX963M/видео.html
Honestly, you are saving people all around the world! Currently doing a data analysis course in the UK and these videos are helping me understand statistics better!!!
BAM! And good luck with your course.
Using size and transparency of ink to represent the 3rd dimension is a brilliant idea. I have struggled with visualizing 3D graphs, this is by far one of the best ways I've seen. Kudos!
Nice!
Awesome! Riveting, straightforward, and jam-packed with well-taught information ❤️❤️❤️
Thanks so much!
I'm learning concepts from machine learning and beside courses and books I'm trying to come back to this channel on daily basis since i find the content very straight forward. For example, i find statistics and probability the hardest to learn and i really struggle when it comes down to feature selection as i don't get for example all those statistical tests to determine the significance, as i cannot understand why for example we use f-distribution to determine r^2 p-value, and here we go, plain and simple, it took few minutes and i get the concept whereas learning from Google can be sometimes really challenging. Thanks again!
Glad the video was helpful! :)
Explanation so simple, and more importantly fun - thanks!
Hooray! :)
You are such an amazing teacher, Josh !! Respect !! Please keep doing the awesome work. I learn so much from your videos. Thank you..
I appreciate that!
You folks are tearing down the barriers that have prevented me from understanding statistics for so many years. Thank you and thank you again!!
Thanks!
Really thankful for all the mesmerizing videos. Throughly enjoyed the content (Purchased few study guides. Quite helpful) . I am still struggling to get a good video on linear regression assumptions with code ( all 10 assumptions) with full explanation on how to detect when the assumptions are violated and what to do next. Just a suggestion :)
It's a good suggestion. I will put that on the to-do list. And thank you very much for supporting StatQuest!!! BAM!
Even with a PhD in engineering from a top 100 university in the world with lots of publications, this is the first time when F test synched with me, Thank you Josh
BAM! :)
This is the video I share to friends interested in machine learning (*not* demos of python that show model creation in a few lines of code that give no context for what's actually happening + why it works!)
Bam! :)
Incredibly clear, watching your videos not only do I learn, but I clear up things I hadn't very well understood in the past!
You're totally binging! And that's awesome. TRIPLE BAM!!! I'm so glad that you like my videos and they are helping you understand statistics etc.
@@statquest Definitely! I'm even watching them now to study for my upcoming actuarial exam! :D
@@alecvan7143 Good luck and let me know how the exam goes.
@@statquest Will do, thank you :)
@@statquest Exam went quite well thanks to your videos ;).
Cheers!
What an amazing explanation of r squared. Cant appreciate enough! Subscribed
Awesome, thank you!
Thank you very much. Good on ya mate.
Finally I got the answers of my questions that I was looking for a long time.
Cheers,
Awesome! :)
a lot better than other videos... easy to understand concepts this way. thank you for free content.
Glad it was helpful!
These videos are the best! Thank you soooooo much! Big smiles from a recent psych graduate revising stats concepts for a job interview.
Good luck with the interview! BAM! :)
This is the best explanation that I have ever heard. Truly appreciate your efforts .. true genius👍👍👍
Thank you! :)
Great video, just note Rsqured can actually be negative, it happens when you fit the data worse than a horizontal line.
I've used regression lines relatively frequently while tutoring students, but it's always good to review the logic and concepts. Thanks for another awesome vid!
Glad it was helpful!
"This is the frowny face of bad times" got a hearty laugh out of me.
Bam! :)
Wow, I took Statistics I and II at the doctoral level and struggled through Stats I, but II was a bit easier. I wish my Statistics professor had made it as interesting, meaningful, and easy to learn and understand as you did in this video. I have a much better understanding of what linear regression is about and I've a renewed interest in learning more about the hows and whys of statistics so I can apply it in my profession. Thank you!
Hooray! I'm glad my video was helpful! :)
Waiting eagerly for the video on degrees of freedom a topic that has eluded me for a very long time. Can't wait for the BAMS on that one.
I wish I could have seen your video when I was in university. You have made it so clear and easy to understand. Thanks for making these videos!
The way you visualised those ols at the beginning, BAM!
Thanks! :)
Oh, I wish I have more hours in a day to watch all of your videos 🤤
I'm crying how good they are! 🤩🤩
Thank you so much 😀
I never missed intro song of the video.This is real BAM..!! The concepts anyway going to be clear.
:)
You explain the material so well. Thank you very much and please keep up the great work!
You're welcome!!! I'm glad that you like the videos. :)
Your videos are absolutely fantastic. You present the information and terminology in a consistent and easy to follow way, and you never make any big leaps between steps (which is unfortunately too common with math teachers who just assume intuition which may not be immediately obvious to everyone).
Thanks so much! Yes, I try to keep the leaps as small as possible and I try to make sure I can "draw" the math. My rule is this - if I can draw a picture of what an equation is doing, than I understand it.
Great way to teach, humans are very visual creatures... I am wondering if there should be a bracket around ss(mean)-ss(fit) in the formula for F @ 19:15 ? Also looking forward to your video of degrees of freedom!
Yep, a bracket would make that clearer. You divide [ss(mean) - ss(fit)] by the degrees of freedom. Thanks for pointing that out! :)
OMG!!! you are so helpful, before I saw your videos, all these topics didn't make sense. On by the way please bring the BAM back!!! kind of liked it
Thank you very much! The BAM is back!!!! :)
How can someone explain so wel?? HUGE BAM!
Thank you! :)
These videos are great, I have been on a binge this weekend :) Your explanations have really taken away my confusion. I would really like to see that video about degrees of freedom.
Thank you! Yes, I'd love to do one on degrees of freedom. I'm working it out in my head and hopefully will get to it soon. :)
@@statquest Still Waiting for this one DoF. Thanks for all the good stuff.
Your channel the new year's gift to me. Thank you thank you, thank you.
Wow, thank you
Hey Josh, thanks for the great videos! One quick question. At 19:13 where the equation for F turns up, should the numerator be (SS(mean)-SS(fit))/(pfit-pmean) or SS(mean)-SS(fit)/(pfit-pmean)? wondered if there is a pair of bracket missing there.
You are correct, a pair of brackets would have made this clearer! Sorry for the confusion. It should be: [SS(mean)-SS(fit)] / (pfit-pmean)
3:00 I've been doing this for 10+ years without having ever seen it that way. Brilliant.
Awesome!!! :)
Geez, such a beautiful explanation. God bless you. Normally when you're doing the computation, all the teachers I had never explained with the ssmean minus the ssfit over ssmean, but that made heaps of sense why... Lovely.
Wow, thank you!
Flabbergasted by the simplicity of the explanations!
Thanks!
“Womp womp. Here’s the frowny face of sad times.” CRACKED ME UP 😂
Here's the happy face! :)
This is my 7+ time on this video,
I just love to revise. :)
In case anyone wondering why we are using mean here,
For a single variable the best fit line is Mean
Example : You tell me what's the average height of your class?
You will calculate mean right?
That's why mean
Nice!
Your videos are super easy to have an intuition, about what we are studying without having the intuition. i'm truly great-full for that. Please make videos on Neural network concepts. A much needed in the largely developing technological world.
My plan is to make a neural network video later in the fall.
Literally the best explaination you will ever find on RUclips, Thanks a lot!
Wow, thanks!
the opening theme is awesome
Ha! :)
Infinity BAM!
Your videos are awesome!
Thank you very much! :)
Thank you so much. Your dedicated effort in content creation and flawless delivery is awesome. Keep doing well.
Thank you! Will do!
That was a really cool intro. That got me hooked. Then the quality of the lecture was top notch.
Thank you! :)
I wish i would have found this when I was in my statistics class. Then I would have been like "Bam!", I understand P values, R^2, and SS.
BAM! :)
Another fantastic vid. Just to clarify, the p value of the F statistic is to be interpreted as the probability that the R2 was obtained by random chance alone. If it is
You got it! :)
I love teachers who can induce interest in their subjects
Thank you!
Really love the way you teach. Thanks!
Who’s watching this two days before their midterm?
Baaaaaaam!
Yes! It's that time of year. Good luck!!!! :)
Hi I have 2 questions:
1) When we are creating the histogram with different F values, where are these random datasets coming from? are they related to our original dataset in someway? I mean are comparing the same features (eg predicting mouse height from mouse weight?)
2)I didn't get the part about p-value being defined as the number of more extreme values divided by all values. From your lecture on p-values explained- a p-value was defined was the sum of probability of current event + anything with an equal probability + rarer events.
1) Those random datasets are related to the original dataset in that they have the same number of points and the same range along the y-axis and the same domain along the x-axis. Other than that, they are just random values. The idea is to compare what you observed to noise. If the noise generated a lot of F-values that were larger than the F-value we got from the observed data, then we wouldn't think that the observed data is all that special (and thus, the observed data would have a large p-value).
2) That's a little bit of a typo - I mean to say, "the number of randomly generated F-values equal to or more extreme divided by the all of the values". The "division" is what turns the values into a probability. Does that make sense?
@@statquest Thank you! can you please confirm whether my thought process is correct or not for the 2 points above:
1) So these random datasets have the same range and domain but can be unrelated to the our dataset in terms of the list of features. We use these datasets to create our histogram (and then the curve) to see how does our observation fair. If there are a lot of f-values greater than ours in the curve, then our observation is not good?
2) For the p-value we take the probability of distribution which is equal, less or rarer than our the point on the distribution, this point is determined by our calculated f-value?
@@pi2019 You are 100% correct for point #1. For point #2 you are 99% correct. The only thing is that the F-distribution isn't symmetric (like the normal distribution) and F-values can only be positive. Thus, we don't have to look at values "less than" the observed F-value when calculating the p-value. Does that make sense?
One thing I would like to make sure is clear is that the randomization in the video is only intended to illustrate how the p-value is calculated. In practice, we just refer to the F-distribution and don't do the randomization.
@@statquest Thank you it makes perfect sense!!
I like the way to review the previous concept , before heading to the other concept. It is really helpful. Ur voice goes very well , increasing an interest to listen and learn more. Thank you so much for sharing your knowledge😇😇
Happy to help! :)
You are the best! And you certainly got even better through the years (I just watched the "R^2 explained" video from 8 years ago).
Thank you!
When will the video on degrees of freedom be coming out? :D :D :D
Good question. One day! :)
In the Hindi language 'Josh' = 'Energy', I just realized the meaning
That's awesome! :)
As the variation of the sum of the squares around the line taking in to account the mouse weight is less than the variation of the sum of the squares around the line average mouse size alone: "some of the variation in mouse size is explained by taking weight in to account" DOUBLE BAM! Thanks a lot Josh, you really help make sense of this stuff.
Double BAM!!! :)
All these exams I tok and tortured myself..where were you? This is the first and only channel that makes stat look interesting!!!
Thank you!
This introduction of R^2 makes much more sense than the typical confusing RSS TSS terms!
Thanks!
This is the first time I have watched a intelligible video about R. Thanks really much for your sharing. Love you and wish you healthy.
Thank you!
What a great video that explains abstract concepts very graphically. This way, a whole complex chapter of a statistical book is presented here so interesting! My compliments to the author of the graphics, the video and the content of it. I owe you big time....thanks so much! You got a new faithful subscriber and promoter of the channel !!! 😃🙏😃🙏👏🏻👏🏻👏🏻
Thank you very much! :)
What a great video! it's absolute a clear explanation! Thank you Josh!
Thank you very much! :)
I like the way you say "DOUBLE BAAAAM" :D , at that moment I understand what I couldn't get it by watching tons of videos before
Double bam!!! :)