How to calculate linear regression using least square method

An example of how to calculate linear regression line using least squares. A step by step tutorial showing how to develop a linear regression equation. Use of colors and animations.
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Professor of the Universe: David Longstreet / davidlongstreet
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[@anant8342]

Posted this 8 years back and people are still benefiting from it! Awesome work!

[@黃士旻-d4w]

8 mins beats my 3 hrs course, very helpful n thank you!

[@kakablee]

he can do it faster though...

[@pza_eatr]

محمد دین ذو القرنين ناسوتيو

[@henrycheng8094]

You can watch it in 2x speed and get it over with in 4 mins

[@buristongnoi9125]

I like your comment. LoL

[@tomaszyarlett8681]

quality of uni courses gets even worse when the delivery mode shifts to "online" during coronavirus pandemic

[@lexparsimoniae2107]

Einstein said if you couldn't explain something in simple terms, you didn't understand it well enough. Thanks for your clear delivery of concepts that could be quite baffling.

[@statisticsfun]

Lex thank you for such a great comment. I work really hard at creating good visual explanations, so I do appreciate your feedback.

[@nadiabeno467]

Lex Parsimoniae u r right

[@nadiabeno467]

Lex Parsimoniae well said

[@jagadeeshwaranp161]

absolutely you are correct

[@humwishdom]

yes, the smarter and better people are at something, the more simplistic they can explain things, thanks for this video

[@lindawisebear]

I've never watched a maths/stats video which was so CLEARLY EXPLAINED before...in my ENTIRE LIFE. Amazing video making skills sir!

[@statisticsfun]

Linda Zhang Thanks for that. I appreciate that you took the time to write me. Good luck in your classes too.

[@matheusferreira8941]

@@statisticsfun you have a gift! Please continue to make more videos!

[@statisticsfun]

That is a great question. In my lectures I don't emphasis the equations much or how to do calculations by hand. It is important that students understand basic principles though. Such as a regression line goes though the mean of the independent and mean of dependent variable. The point of regression is to help understand correlation and more important causation. I believe it is much more important to understand the meaning of the output than how to plug and chug with a formula or a tool.

[@marcobroca4020]

Thank you so much professor. Could you tell me what's the meaning behind sum(x-x_mean)^2 and sum(x-x_mean)*(y-y_mean). Why doing that we can get the slope?

[@flamboyantperson5936]

what if we have more than 1 independent vairables (x) then we calculate mean?? and how does the line pass through in this case?

[@lsubandtrumpet2014]

How do I find observations? Are they going to be given? I want to do a regression on percentages of order fulfillment rates at our store. What could I use for an independent and dependent variable for omni fulfillment rates as well ?

[@AugustNocturne]

You are awesome!

[@chinmaykhanna6008]

@@marcobroca4020 have you found the reason?

[@pmarilag]

Pure genius! This is my third time to take Statistics and don't have a clue whatsoever about it. I read a lot of easy books to understand it, watch videos and tutorials but to no avail. I watched your videos once and I was hooked! Boy, I understood it in one sitting! Your calm voice and clear/simple explanations plus your awesome graphics/animations just makes it all so EASY to understand. Plus of course your knowledge about what you're talking about. Thank you so very much!You're amazing

[@oldavid1]

Mr. Longstreet, I beg you to publish a statistics textbook. If you title it "Study less, party more, and get good grades", I'm sure it'll be on every Top Ten bestsellers list! Thank you so, so, so, so very much.

[@statisticsfun]

That is a good idea, but I am building a website that will continue to be free for students. One of my pet peeves is the cost of textbooks. As a student you know the cost of textbooks is outrageous.

[@gmchingon]

statisticsfun I hate having to buy textbooks, but if you were to publish such book, I would buy it.

[@netmadefamous]

statisticsfun I know you are building a website, but it wont stop us buying those non reasonably written books which are very hard to understands .Please re consider your thoughts and publish a book on this ..That will be awesome ..your technique are too good and easy to understand for complex formulas as well ..thanks ..thank you very very much ....

[@kannadarecipes-6626]

@@statisticsfun is it live. your explanation was amazing :) I immediately subscribed

[@AugustNocturne]

A textbook wouldn't be as effective as the animations on this video. But I get what you mean.

[@firefrostpeacemaker]

This was without a doubt the best explanation I've ever experienced on this topic.

[@statisticsfun]

Thank you for the compliment, it is much appreciated. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos. Good luck in your classes too.

[@WassupCarlton]

Clean, clear and crispy. I'm glad people are still out here doing things manually instead of immediately hecking off to code. bravo, SF

[@Ornitholestes1]

This is absolutely amazing! I tried to understand this method from written instructions with my limited mathematical skills and failed over and over again. Then I watched this video once and it's perfectly clear! I need a maths teacher like you!

[@statisticsfun]

That is deep! You are right, we should not put emphasis on mechanics but on understanding. I have had students who could do all the mechanics but not understand the underlying concepts. I have had students who could not do the mechanics to safe their life, but understood the underlying concepts very well.

[@kandyslarsen8145]

You actually made my life so much easier. I may actually get an A in statistics because of your videos!

[@marianamtz10]

Your explanations are by far some of the clearest, simplest, smartest (as far as teaching) I've heard! Thank you for doing this, you have saved me!

[@abokbeer]

I spent couple of minutes wondering how can I thank you. Simply thank you

[@statisticsfun]

+mohamed ghoneim Tell your friends and fellow students about my videos. This will help them learn the subject as well.

[@jaforhossain9567]

I spent whole day watching different types of video but i could find final concept. Finally I got this video by suggested option on KZbin. After 12 years latter this video still really helpful.Thank you very much for providing such video with simple explanation with animation.

[@beautifulXXdesasterr]

so helpful us failing university students thank you

[@Yoshikage8008]

Mimi K im in freshman and im learning this lol

[@lucacapperucci8711]

8th here

[@Yoshikage8008]

cool

[@becausescience747]

You're doing this in uni?

[@conordarcy4663]

Lol your in uni

[@stevenyanging]

You're the man for making this video. People who has a teacher that's really bad at explaining it really appreciates this.

[@wasi8u]

you sir are a legend

[@statisticsfun]

Wasi Raza What a nice thing to say, appreciate that.

[@munishgupta7878]

You have no idea what a great work you are doing sir. I just spent 10 days to understand regression theorem but nothing went inside my brain and your 10-15 minutes video cleared all my doubts. God Bless You. Keep doing such humanitarian work.!!

[@terigopula]

If it has cleared all your doubts can you please explain how that equation gave the slope of the regression line? I didn't understand that part. Your help will be appreciated.

[@munishgupta7878]

Their is a separate formula for finding the slope and intercept. The equation is yhat=a+bx finding a: ybar-b(xbar) and finding b:= r(standard deviation of y/standard deviation of x). and I got this equation not from here but from other courses

[@susie519]

Thanks for the lecture! One thing, I wish you explained us 1) 'why' a regression line has to include means of x and y, and 2) 'why' you calculated the slope the way you did. In this way, we may be able to grab conceptual meanings of regression analysis.

[@tbgar1]

Where have you been the last three years of my part-time Masters program...I"ve never seen anyone explain it so plainly & simply. I totally get it now! Thanks so much!

[@comredigital]

Wonderful presentation, simple to understand! The entire world needs teachers like you! Thank you, sir, for your great effort and it is immensely appreciated

[@Zeangjpn]

I am a teacher and I just wanted to say how great your videos are. Your speak with a clear calm voice and the examples are easy to understand. Keep up the great work and thank you so much.

[@prateexit]

Wow. wonderfully explained. I hope my prof gets to check this out and know the right way of teaching these things. Thank you so much Sir :)

[@ethan612]

i have never seen a video like this before. I went thru tons of videos for linear regression, nobody made it simple as you did. This is a great service you are doing here!!!

[@statisticsfun]

Your comments are much appreciated! Yes education is a great and wonderful thing and my plan is to keep making free educational videos.

[@mohammedah25]

Your video is very educative. I got the understanding way better than what I was thought in class. However, I tied using the formula you gave in the video to find the b1 (0.6) but I had zero(0) instead. Can you please help me out?. Thank you.

[@statisticsfun]

Both are valid and the one of the right (y = a +bx) is what is typically taught in algebra. As long as you know what variables represent you should be good to go. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[@rachellemarcial3422]

This is so helpful. I have a short time before my test and I'm learning fast from your videos

[@sowmyasankar1605]

sir , im not a statistic student.. ur video has helped me to overcome the stress I carried to statistic classes . Thanks a ton. God bless u

[@statisticsfun]

dumhead Thanks for letting me know my video are helping. Hopefully you will get a chance to like my FB page (www.Facebook.Com/PartyMoreStudyLess) and like, share the videos. This helps others find the videos. Good luck in your studies too.

[@swaekim9402]

I literally do not understand why some professors struggle to explain concepts in 3 hours as well as you do in 8 minutes. You make it seem so goddamn easy I feel like I'm cheating just watching this video 💀💀

[@hakinadedeji]

it's simple. being an expert is not being a teacher. you might know something excellently but you might find it difficult imparting it unto others

[@TheHarryPotters]

You must be gifted. That was a super clear explanation, so clear that it almost feels like I must have gotten something wrong, because there's no way it could have been so easy. I wonder why I have to pay my Uni if in the end I have to rely on you teachers on youtube, you're the one who should get the money.

[@melliehaider9861]

It just doesn't get better than this. These videos are invaluable to me-- Thank you!

[@statisticsfun]

You are very welcome and that is great to hear. I appreciate the feedback because I am never really certain about the pace! Good luck on your exam too.

[@danageberten]

MUCH better than my course book! Thanks!

[@latifmammadli6815]

yavsaga bak ya

[@saxboss1]

This might be the most well done statistics video on KZbin, Congratulations really

[@MC_lupin]

Me: What’s up with these funky symbols and equations UGH *sees video* Me: ...That’s it?

[@cryptotare]

My sir taught same in 1 hour and I couldn't understand a single thing and now you thought all in 8 minutes. WOW! Awesome. Just amazing. Keep up!

[@NeutralGenericUser]

Thank you so much! This is infinitely better than the explanation provided in my physics lab manual!

[@NvrGvUpEvr]

One of the best explanation on statistics methods I've ever come across...

[@H_Jones]

Why doesn't my professor teach like this? This was extremely helpful!

[@steph5656]

This is the only video I could find that explained how to actually use the formulas, thank you!

[@kamalakerreddy]

Its so so explanatory and useful. Thank you for the video.

[@statisticsfun]

K Reddy You are very welcome. Hopefully you will like, share, subscribe, If you get a chance could you please like our FB page. www.FaceBook.Com/PartyMoreStudyLess It will help others find the videos.

[@Protaug33]

You're amazing! I'm taking a statistics course in grad school and we just hit linear regression. The way you explained this just refreshed my high school course from way back when doing the slope intercept form. The biggest issue I'm having is relearning all this crap with new vocabulary. Two of my classes even overlap with content, but each one uses different terminology for the same junk. Thanks for breaking it down so simply! Mind blown! Great video.

[@thomaseldrup1315]

You are goooooood!!! :) have seen a lot of your vid's now, and every time i'm stunned by how you can make something so complicated sound so simple. good work, appreciate it ;)

[@statisticsfun]

Squaring the X-Xmean in regression is a mathematical technique to get rid of the negative sign. Also we are taking the distance and if you recall the "distance formula" = ((x1-x0)^2 + (y1-y0)^2)^.5 which is part of the Pythagoras theorem. Hope that makes sense.

[@tdm4825-r6r]

Ernest teacher number 1

[@MarsMaher]

no u chatting shit

[@rashadallahverdiyev9877]

I've never seen such an excellent interpretation. Both the way of your explanation and computer presentation have been thought perfectly. Big Thanks.

[@lukebaker8116]

Very helpful thank you!!!

[@statisticsfun]

+Luke Baker You are very welcome. Hopefully you will get a chance to like and share the videos. This will help other students find them.

[@reza13501]

I wonder if there is a better lecturer than you in the world. You are madly brilliant.You just put my over-rated lecturer for post-grad degree into shame

[@Jaynyina]

this is awesome. thank you sooooo much

[@statisticsfun]

+jesse kwaku You are very welcome and good luck in your classes too.

[@Jaynyina]

+statisticsfun Thank you very much. I have got finals tomorrow

[@luna-sv6uf]

I hope you get paid for this because otherwise my heart cannot handle that you put so much effort into all of these videos, even if you do it proves there are good people in the world. love you even though I don't know you!

[@bordeaux1337]

Is there a proof that all regression lines go through the means? And why does that formular later on give the slope ?

[@abhinandansrinivas5831]

i would like to know the answers to these too.

[@terigopula]

Even I am very inquisitive about that formula giving the slope of the line.

[@manikanth2166]

read the book "applied regression analysis. a research tool". you'll get free pdf on google search. chapter 1 has the proof

[@terigopula]

Thank u so much Mani Kanth​ :)

[@fearfullymade8510]

You have probably the best Statistics videos on KZbin. Very helpful, thank you.

[@sarahthompson4191]

This was SO HELPFUL. Thank you! Maybe now I'll pass :)

[@avimehenwal]

Explained like a PRO, beats all 30 pages linear regression chapter in traditional textbooks. Thankyou so much for explaining concept this clearly. (Y) Please keep it up

[@revlmp727]

Only if uni teachers could explain like this and not assume that your super clever..

[@akshaybaghmar254]

i find this the simplest way to explain regression analysis basics, which many books/professors fails to explain clearly . Thanks a lot for the video.

[@jameson4862]

u good ernest?

[@MarsMaher]

ew

[@kellyweaver6870]

You just cleared up for me in 8 minutes what I've been struggling with all day. I am a visual learner, so the colors are lovely. I'm just sorry I found you at the end of my statistics class!

[@kongmagneto12]

Thanks a million!!!!!!

[@statisticsfun]

Thomas Kongolo You are welcome a million too! Thanks for writing me and letting me know my videos are helping you. Hopefully you will like, share, subscribe, If you get a chance could you please like our FB page. www.FaceBook.Com/PartyMoreStudyLess It will help others find the videos.

[@somayyehsedaghatjoo4355]

I watched many clips for linear regression.These series were the best one.It is really well done.Thanks

[@jessepinkman725]

2018 still using this vid for my reference

[@Roman-fk5rl]

2020?

[@statisticsfun]

Great to hear. I think animation really does improve the learning process. As I say a picture may be worth a 1,000 words, but an animation is worth 1 million words.

[@AugustNocturne]

You are so on point!

[@MatrixHound_Dungeon]

You are the man!!! I knew there had to be someone out there like you! With your explanation, coding it should be a breeze! This has to be the best use of 8 1/2 minutes in the past week! Thanks!

[@justineperocho5311]

Thank God, you literally saved my life. Been struggling with this all day. Respect to you

[@akifhuseein1502]

Almost a decade later and still the best explanation out there. You sir are a legend.

[@ajitkumar15]

After struggling to get video to understand the topic, I landed here.. by far this is the best video on this topic,, thank you so much!!!!

[@PraneetCastelino]

Thank you very much. This is absolutely brillant. Having left university many years ago I absolutely don't remember anything and now that I am trying to get into quantitative finance, I need to know all about regression analysis. Your explanation is brillant as you don't skip anything and realise your viewers watching this video have different levels of math skill.

[@MrSajigsnair]

Hi Sir..Intially i tried this concept on my data and got it all wrong. The reason was the way i fitted my regression line. I corrected the mistake and the results are accurate now. Your explanation is so simple and straight forward. I am in love with it now!!..Hats off to you

[@fernandoartmann5626]

I've seen so many different ways to tell this same thing you did, but it ALWAYS sounded completely incomprehensible... you made it easy to understand! Many thanks!

[@shylohgodfrey9761]

I have spent hours trying to do this the way math lab shows and you have taught me how to do it in 8 and a half minutes! THANK YOU.

[@adaoskay134]

Without a doubt the best video on KZbin

[@thoalfiqarhafid7522]

you are the best ever, words can't express who thankful I am, my uni prof spends ages, and he still bad explaining things you did in just 8 minutes

[@scrapbookk8775]

Man, this is the best video on this I've ever seen. Thank you sir. I understood this so well.

[@ikayikay9011]

many years now but still the most explicit explanation. Great

[@SnxadaNx]

Wow! The best explanation and teaching method I have seen online. The simplicity of it all is amazing.

[@mr.a6907]

Hope it wasn't too bad ?? Come on man.. that's the best ever explanation ever I came across.. So much clarity. Hats off !! Love from India

[@anthonyhawkins6138]

You are great at explaining complex statistical concepts! I am a graduate student studying finance & I have found ur channel to be MOST helpful.

[@lone_wolf4530]

One of the best linear regression tutorials I have ever seen.!!! Thanks for explaining the topic.

[@statisticsfun]

Wow! That is great to hear and happy to know my videos are helping you learn.

[@Henry-nk9wx]

My good man, you have saved me many hours and likely a failed exam when they put this in it. You’re equation is similar to my textbooks as in yours is the simplified version

[@sonnyv2007]

Public Policy (MPP) and Public Health (MPH). Our MPP program in policy analysis is intense and all quants. Within 4 minutes of starting our Econometrics class this semester I was lost which was discouraging. I had the high expectations of getting lost by week 2. You've definitely helped make things easier to understand. I go around eager to explain things now lol! You Rock!

[@prasantakarmakar8554]

I never understand this before in this way,.....God sends some special persons to guide all the other persons.....You're one of them special one. Thanks alot....Please share your efforts to do some good in our life. Thank You.

[@statisticsfun]

Good question. Linear regression analysis is a type of bivariate analysis. Bivariate analysis trying to find or establish a relationship between two variables.

[@jedsonguedes]

One of the best Statistics classes I've ever seen. And by far the best least square video I ever saw. Note: at 4:18 you should've put the -2 between parentheses before squaring it. Just a notation issue. The result was correct.

[@mariamajaz1690]

Way better than any textbook that I've looked at!

[@MrJadreemah]

Thank you! I am an MSW research major and we start regression last week and I couldn't grasp the concept. Watching your series on regression I feel a little better about it. I will be running regression for my thesis.

[@Ford-Prefect]

You've taken something that seemed incredibly complicated and made it completely accessible. Thank you.

[@infographic7907]

you are very rare kind of teacher that everyone one should have in a life time sir.

[@lorinichols8882]

I cannot thank you enough for your videos. I appreciate an enormous effort went into each minute and don't know how you find the time. You affect so many students lives in a positive way and career folks who need a refresher here an there. Hats off to you.

[@breadman7733]

This cleared up all my confusion, these channels are fantastic!

[@statisticsfun]

Wow! What a great testimonial and your comments are very much appreciated.

[@JOmondi1]

Thanks a lot Sir for your hard work and thoughtfulness. You may not know the full extent of what you have done to the service of humanity especially to people like us in Africa. Thank you so much and I hope your thoughtfulness finds its way back to you in done way. Asante Sana.

[@statisticsfun]

@climatechangeKE Very cool email and thanks so much for taking the time to write me. Good luck to you in your classes as well. It is a joy to know that I am helping you and others in Africa.

[@yodestinaetion]

You deserve an award sir!!!.LOVE THIS GUY!!!

[@kalpeshm9852]

U have explained me a 2 hour lecture in just 9 minutes thank you man u are the best 😊

[@rodrigocustodio1955]

you are so good at explaining, you should teach other teachers how to teach, break down, make simple, create meaning, and subsequently students will be able to master the subject and approach more abstract concepts with confidence.

[@nataliecho6188]

Words cannot explain how grateful I am for such well explained video. I'm currently self learning so a lot of times I'm struggling to grasp things however this makes it so much easier. Thank you so much

[@muhannedalogaidi4113]

I haven’t seen channel like this. Hope and wish that this channel grows up and more videos created

[@Flumanka]

Omg I have been searching for ages for someone explaining these formulas and I am so happy I found your video! It is really easy to follow along and now I can finally calculate these types of examples myself! Have an exam coming up soon and this was really of great help, THANK YOU!