Linear Regression, Clearly Explained!!!

[@statquest]

Correction: 25:39 I should have (Pfit - Pmean) instead of the other way around. Support StatQuest by buying my books The StatQuest Illustrated Guide to Machine Learning, The StatQuest Illustrated Guide to Neural Networks and AI, or a Study Guide or Merch!!! statquest.org/statquest-store/

[@udaychopra4802]

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)

[@udaychopra4802]

we talk in terms of BAMs now. little BAM.

[@statquest]

This is awesome! So many BAMS!!! :) Even a little BAM. :)

[@ah2522]

@@statquest hooray!

[@statquest]

@@ah2522 Yes! Hooray!!! :)

[@vaibhavdani4470]

@@statquest BAM...Hooray are on my tip of tongue now days !!

[@ycao6]

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.

[@statquest]

Thanks! :)

[@Glock_50]

You are awsome explaining!

[@armangilang9654]

ya, you broken the legs of math mistery

[@amanjang7531]

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.

[@tinacole1450]

ha ha.. great comment. Josh does a great job at making complex stuff seem okay to understand.

[@lazarus8011]

The clarity of your speech with no unessesary details in your visuals makes learning these methods so much easier thankyou.

[@statquest]

Glad it was helpful!

[@tonywang7933]

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.

[@statquest]

Thank you! :)

[@AnuragTK]

God bless the friendly folks in the genetics department at the University of North Carolina at Chapel Hill

[@statquest]

Thanks! :)

[@98Luthfi]

amen

[@omar24191]

Amen (2)!!!!

[@ShreyasG-d2n]

haha XD

[@zulucharlie5244]

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.

[@statquest]

Wow! Thank you very much! :)

[@amitlavon1647]

I am a 33 year old computer science PhD student and I still need statistics explained to me as if I'm 6. Thank you for that.

[@statquest]

:)

[@iarasouza8029]

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!

[@statquest]

Wow, thanks!

[@confidenceinterval4849]

You can learn more about linear regression in simple words here kzbin.info/www/bejne/h4KcfnSkjZ5paa8

[@monicakulkarni3319]

You are statistically one of my favourite KZbin channels!

[@statquest]

I love it! Thank you. :)

[@felixwhise4165]

Which are the others? :)

[@TheEverydayAnalyst97]

@@felixwhise4165 For me Brandon Foltz is another awesome channel!

[@rohitamalnerkar2152]

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.

[@statquest]

Thank you very much!!! I really appreciate your feedback.

[@bu8291]

More people should discover your channel, you make it very easy to understand statistics :)

[@kakusniper]

I never understood statistics in my life till now, you make it look so easy. Thanks again.

[@ericstefko4852]

Without a doubt this is the best explanation of Linear Regression to be found anywhere.

[@statquest]

Thank you very much!

[@ssriv47]

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 !

[@statquest]

bam!

[@ali57555]

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.

[@statquest]

Thank you very much! :)

[@AB-iq9tl]

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.

[@statquest]

Thank you very much! :)

[@Privacy-LOST]

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

[@statquest]

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!

[@dominicj7977]

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.

[@prayaglehana7187]

I have gone through all of his videos.. and believe me he is the one that will make your concepts clear !

[@statquest]

Thanks! :)

[@malamals]

couldn't have agreed more on this.

[@rezat.ashtiani1338]

The most clear and simple explanation of multiple linear regression I’ve ever seen, and I’ve seen MANY! Thank you for this video!

[@statquest]

Glad it was helpful!

[@statquest]

Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

[@ramnewton]

Had the same doubt; this clears things up, thanks! Maybe consider pinning this so it shows up on top always?

[@sureshkm]

@StatQuest I think, we need the same correction in the study guide 'statquest_linear_regression_study_guide' Page 5 of 6 as well.

[@ssriv47]

statquest website is not working. It is showing database error. Please look into it.

[@statquest]

@@ssriv47 Thanks! The site is back up.

[@jbtechcon7434]

Is that a typo at 19:25? You said the numerators are the same, but they're not. Are you missing parentheses?

[@cuberootme]

You are the best instructor. I will watch all your videos. It really helps me in ML. Hope I will find a good job!

[@statquest]

I hope so too!

[@swathisukumar2219]

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.

[@statquest]

Wow, thank you!

[@alecvan7143]

Incredibly clear, watching your videos not only do I learn, but I clear up things I hadn't very well understood in the past!

[@statquest]

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.

[@alecvan7143]

@@statquest Definitely! I'm even watching them now to study for my upcoming actuarial exam! :D

[@statquest]

@@alecvan7143 Good luck and let me know how the exam goes.

[@alecvan7143]

@@statquest Will do, thank you :)

[@alecvan7143]

@@statquest Exam went quite well thanks to your videos ;). Cheers!

[@sudhakarmadakaful]

Linear Regression is well-explained in this video. Love the humor in between too!!!!

[@statquest]

Thank you! :)

[@ikechang1967]

You folks are tearing down the barriers that have prevented me from understanding statistics for so many years. Thank you and thank you again!!

[@statquest]

Thanks!

[@AI_Life_Journey]

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

[@statquest]

BAM! :)

[@rutu1011]

All these exams I tok and tortured myself..where were you? This is the first and only channel that makes stat look interesting!!!

[@statquest]

Thank you!

[@silentsuicide4544]

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!

[@statquest]

Glad the video was helpful! :)

[@ZowieFaerieYeah]

These videos are the best! Thank you soooooo much! Big smiles from a recent psych graduate revising stats concepts for a job interview.

[@statquest]

Good luck with the interview! BAM! :)

[@wz5445]

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!!!

[@statquest]

Glad it helped!

[@nguyentuongvy2110]

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.

[@statquest]

Thank you!

[@navjotsingh2251]

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!!!

[@statquest]

BAM! And good luck with your course.

[@PunmasterSTP]

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!

[@statquest]

Glad it was helpful!

[@ramnewton]

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!

[@statquest]

Nice!

[@vijaypawar5003]

Your videos are so simple and easy to grasp with all those conceptual explanations and graphics you use. They make learning fun. Thanks to KZbin for getting this to us and a bigger thanks to you for sharing it with the world.

[@statquest]

Thank you! :)

[@MrMarias1234]

Thanks! It is the most precise explanation I've ever seen. I don't know why professors love to make this topic so complicated and full of fancy notation.

[@statquest]

thank you!

[@autogenes]

I love teachers who can induce interest in their subjects

[@statquest]

Thank you!

[@fatmacoskun6406]

I like not only your videos but also your sense of humor. Thanks!

[@statquest]

BAM! Thank you!

[@pietronickl8779]

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..

[@statquest]

Thank you very much! :)

[@confidenceinterval4849]

You can learn more about intuition of linear regression here kzbin.info/www/bejne/h4KcfnSkjZ5paa8

[@monicasethuraman5772]

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😇😇

[@statquest]

Happy to help! :)

[@ayush612]

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!

[@statquest]

It's really nice to hear how much you like the videos! I'm glad I can help. :)

[@ayush612]

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 ! 😎

[@statquest]

Thanks!!! :)

[@italiandarthvader]

Thanks to this video I can say I built my first (working) linear regression model FROM SCRATCH. What was most amazing was that I got the approximate answer to the one in the book I'm working through. I'm really ecstatic. I know it might sound childish to build something this simple but I found mathematics to be fun and enjoyable during the process. You really have a talent for explaining, thank you.

[@statquest]

BAM! :)

[@derrickc.8486]

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!

[@statquest]

Hooray! I'm glad my video was helpful! :)

[@Relative0]

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.

[@statquest]

Double BAM!!! :)

[@sharvarisosale2780]

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! 🌟

[@statquest]

Awesome and thank you!

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).

[@statquest]

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!

[@statquest]

Yep, a bracket would make that clearer. You divide [ss(mean) - ss(fit)] by the degrees of freedom. Thanks for pointing that out! :)

[@matthewdong9368]

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!

[@statquest]

Hooray!!!! Thank you so much! I'm so glad to hear that you like my videos. :)

[@arishali9248]

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 !

[@statquest]

Hooray! :)

[@anshulnarela9888]

More power to you Josh!! Nobody eplains these basic concepts like you do. Thanks a lot!

[@statquest]

Thank you! :)

[@trestenpool9045]

I hope I come out as a stats squatch at the end of all your videos!

[@statquest]

Thank you!

[@shekharrudrabhatla8594]

Awesome.. never looked at R-squared this way. Thank you :)

[@statquest]

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

[@Ellielllie]

John Starmer, you are the best thing to happen to the internet.

[@statquest]

Hooray!!! Thank you very much! :)

[@hazel6330]

This is the best explanation that I have ever heard. Truly appreciate your efforts .. true genius👍👍👍

[@statquest]

Thank you! :)

[@malamals]

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.

[@statquest]

My plan is to make a neural network video later in the fall.

[@Privacy-LOST]

3:00 I've been doing this for 10+ years without having ever seen it that way. Brilliant.

[@statquest]

Awesome!!! :)

[@adancastro2220]

I found that this Video explains about 60% of my current understanding of linear regression... Thank you friendly people ;)

[@statquest]

Glad it helped!

[@aarondorcas]

You make statistics that easy to understand, thanks for your extensive work!

[@false_binary]

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!!! 🤯

[@statquest]

Good luck! :)

[@smdsouza8]

I love your videos. It’s a true talent to be able to explain these concepts so clearly

[@statquest]

Thank you so much! :)

[@aureliendaviet5290]

Normally I don't write comments but I really wanted to thank you because your videos are amazing ! You do an tremendous job at explaining things that should be explained by professors (who are unfortunately sometimes bad at explaining it in a simple way). Thank you again (BAM !)

[@statquest]

Wow, thank you!

[@ЕвгенияКазакова-ъ3д]

Oh, I wish I have more hours in a day to watch all of your videos 🤤 I'm crying how good they are! 🤩🤩

[@statquest]

Thank you so much 😀

[@elalaelasariuinjakarta7548]

My background is in public health and I just started to learn PCR and Sequencing. I watch your video step-by-step.

[@statquest]

I hope they help! :)

[@imad_uddin]

What an amazing explanation of r squared. Cant appreciate enough! Subscribed

[@statquest]

Awesome, thank you!

[@drpritamkrdas_official]

BAM! You are enhancing my conceptual clarity day by day. It has a dominos effect as well! Double BAM!!!

[@statquest]

Thank you!

[@michaeld6854]

Explanation so simple, and more importantly fun - thanks!

[@statquest]

Hooray! :)

[@rsnvprasad]

@statquest guru, one observation. While fitting a linear line in a data, a line with non zero Y intercept must be a line that does not pass through origin. For example, line drawn in the example at video time 4:08. Learning many things from your videos. Thank you!

[@statquest]

Yep. The line does not have to pass through the origin.

[@jamesshin4901]

Love your presentation!! What a great job you have been doing to educate people and lessen the confusion!! Many thanks!!!

[@statquest]

Thank you! :)

[@somethingnotspecified]

Don't know how I wrote a statistics test that had a question about this without really understanding the intuition behind the whole thing. Still, I need some extra work on the F-measure to get it 100 % right. Hats off to you as always, Josh! Amazingly well done! :)

[@statquest]

Thanks!

[@meenasirishaallamsetty713]

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

[@statquest]

Thank you very much! The BAM is back!!!! :)

[@extraltodeus]

I'm drunk. I googled "linear regression" to get a better understanding of it and the song really appealing to the wine inside me. Thank you.

[@statquest]

bam

[@yondchang]

Great video, just note Rsqured can actually be negative, it happens when you fit the data worse than a horizontal line.

[@jamiyana4969]

Literally the best explaination you will ever find on KZbin, Thanks a lot!

[@statquest]

Wow, thanks!

[@merryjoy48]

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.

[@sweetmaths4213]

You're the first person I have found who makes stats make sense. Ty ❤

[@statquest]

Thanks!

[@joseangelmartinez308]

How can someone explain so wel?? HUGE BAM!

[@statquest]

Thank you! :)

[@esperanzazagal7241]

I just want to say 14:50 is a brilliant example of what matters to least squares :) thanks!

[@statquest]

Thank you very much! :)

[@salnaud8898]

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,

[@statquest]

Awesome! :)

[@because2022]

Thank you so much. Your dedicated effort in content creation and flawless delivery is awesome. Keep doing well.

[@statquest]

Thank you! Will do!

[@TTortrix]

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.

[@statquest]

BAM! :)

[@xondiego]

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.

[@statquest]

Wow, thank you!

[@sdfsdf5313]

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 :)

[@statquest]

It's a good suggestion. I will put that on the to-do list. And thank you very much for supporting StatQuest!!! BAM!

[@tyronefrielinghaus3467]

Josh...thanks so much. R2 has never been really explained so well. It's normally just given without ANY explanation. For the first time I think I'm ...grokking it. Tyrone from JHB South Africa. Ps...I so value the way you give me an intuitive feel rather than just an equation that I don't -really- understand. Wish my Uni maths teachers had did the same. Thanks again. I'm just beginning your ML book...great!. Also.. Great, clear diction. I loathe when I have to strain to understand some KZbin presenter, esp when it's content is something worthwhile....like it's double the work!😭

[@statquest]

Wow! Thank you very much! :)

[@BrianRisk]

“Womp womp. Here’s the frowny face of sad times.” CRACKED ME UP 😂

[@statquest]

Here's the happy face! :)

[@harshdhaundiyal2241]

I liked and subscribed in the starting minute BAM !!! The graphical approach and the intuitive fun explanation is BAMMM !!! College's and various organisation should put your KZbin playlist as a mandatory course for Machine Learning BAMMMMMMM !!!

[@statquest]

Hooray!!! Thank you very much! :)

[@nathanx.675]

Who’s watching this two days before their midterm? Baaaaaaam!

[@statquest]

Yes! It's that time of year. Good luck!!!! :)

[@saicharangarrepalli9590]

That was a really cool intro. That got me hooked. Then the quality of the lecture was top notch.

[@statquest]

Thank you! :)

[@Dynamite_mohit]

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

[@statquest]

Nice!

[@nachiketpensalwar]

a lot better than other videos... easy to understand concepts this way. thank you for free content.

[@statquest]

Glad it was helpful!

[@seauxmean4074]

the opening theme is awesome

[@statquest]

Ha! :)

[@shubham2488]

Interesting!! At 7:39 I pondered over two questions based on the two graphs: 1. In first graph, ignore the x-axis and imagine a scenario where only mouse sizes are observed. Q1. The only question we can ask here is: Can we predict the next mouse size? Answer: Very intuitive. Take the average (here denoted as the average). Now we may be wrong by some amount and can quantify it using the variance. 2. In second graph, now consider the case when you have some additional readings in your data which are weights. Followings can be asked: Q1. What is the next prediction about reading of weight and size? Answer: Again simple, just take average on both the axes. The variance and covariances can tell some performance guarantee. But this question is pathological. Q2. Given weight, can we predict the size or vice-versa? Why do we have the fitting curve doing best in some metric and lying roughly in the middle of the points? Answer: Theoretically speaking, with the random variable kind of treatment, one can show that the answer lies in the expected value of conditional distribution of Y given X whenever squared loss is considered. Typically in practice, we take a Gaussian assumption on Y given X justified by linear model: y= f(x) + Gaussian noise. And the idea of best f is the one which maximumize the likelihood of y given x which is ultimately minimizing squared loss. And thus, because of Gaussian assumption, we have the fitting curve in the roughly in the middle as the errors can be both positive and negative. Further, the hope is conditional expectation would simply be a straight line that is a linear combination of x with certain coefficients which is indeed true for jointly Gaussian rvs (X,Y).

[@kesavkumar7710]

I never missed intro song of the video.This is real BAM..!! The concepts anyway going to be clear.

[@statquest]

:)

[@tinacole1450]

Your videos are helping to explain what my instructor assumes we know. Thanks!

[@statquest]

Happy to help! :)

[@jackignatev]

Infinity BAM! Your videos are awesome!

[@statquest]

Thank you very much! :)

[@marwolaeth111]

My goodness, StatQuest is exactly the approach I've been seeking for my statistical knowledge reinforcement! Not as shallow as DataCamp or other R courses (‘The math behind this is beyond the scope of this course’). Not as crazy as math lectures. I am a humanitarian. And Salman Khan… well, he is great but way too thorough for a busy man to follow along. I'll resort to him for linear algebra and calculus. Thanks, Josh! StatQuest is marvellous.

[@statquest]

Thank you!

[@xzhou6686]

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.

[@statquest]

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)

[@Brandon-oc8lr]

Probably one of the most informative videos on these concepts I've ever seen. Thank you!

[@statquest]

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

[@joerich10]

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

[@statquest]

You got it! :)

[@alinelermer6664]

The best explanation for Linear Regression ever! Thank you so much. Greetings from Germany.

[@statquest]

Thank you very much!!! BAM! :)