How to calculate linear regression using least square method

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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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1 окт 2024

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Комментарии : 1,1 тыс.

@黃士旻-d4w 8 лет назад

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

@kakablee 6 лет назад

he can do it faster though...

@pza_eatr 5 лет назад

محمد دین ذو القرنين ناسوتيو

@henrycheng8094 5 лет назад

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

@buristongnoi9125 5 лет назад

I like your comment. LoL

@tomaszyarlett8681 4 года назад

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

@lexparsimoniae2107 11 лет назад

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 11 лет назад

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

@nadiabeno467 6 лет назад

Lex Parsimoniae u r right

@nadiabeno467 6 лет назад

Lex Parsimoniae well said

@jagadeeshwaranp161 3 года назад

absolutely you are correct

@humwishdom 3 года назад

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

@statisticsfun 11 лет назад

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 4 года назад

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 4 года назад

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 3 года назад

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 3 года назад

You are awesome!

@chinmaykhanna6008 2 года назад

@@marcobroca4020 have you found the reason?

@beautifulXXdesasterr 9 лет назад

so helpful us failing university students thank you

@Yoshikage8008 9 лет назад

Mimi K im in freshman and im learning this lol

@lucacapperucci8711 7 лет назад

8th here

@Yoshikage8008 7 лет назад

cool

@becausescience747 4 года назад

You're doing this in uni?

@conordarcy4663 4 года назад

Lol your in uni

@oldavid1 10 лет назад

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 10 лет назад

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 10 лет назад

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

@netmadefamous 10 лет назад

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 4 года назад

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

@AugustNocturne 3 года назад

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

@lindawisebear 9 лет назад

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

@statisticsfun 9 лет назад

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

@matheusferreira8941 Год назад

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

@statisticsfun 11 лет назад

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.

@anant8342 4 года назад

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

@MC_lupin 5 лет назад

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

@statisticsfun 11 лет назад

Great to hear! Make sure you like MyBookSucks on Facebook (see link in video description). This will help other students with teachers that are "really bad at explaining" statistics find the educational videos.

@statisticsfun 11 лет назад

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

@mohammedah25 2 года назад

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.

@firefrostpeacemaker 11 лет назад

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

@wasi8u 9 лет назад

you sir are a legend

@statisticsfun 9 лет назад

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

@statisticsfun 11 лет назад

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.

@swaekim9402 3 года назад

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 3 года назад

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

@kandyslarsen8145 9 лет назад

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

@prateexit 8 лет назад

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 :)

@abokbeer 8 лет назад

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

@statisticsfun 8 лет назад

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

@jameson4862 4 года назад

u good ernest?

@MarsMaher 4 года назад

@statisticsfun 11 лет назад

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.

@lukebaker8116 9 лет назад

Very helpful thank you!!!

@statisticsfun 9 лет назад

+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.

@jaforhossain9567 6 месяцев назад

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

@H_Jones 10 лет назад

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

@statisticsfun 11 лет назад

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

@Ornitholestes1 11 лет назад

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 11 лет назад

Well, thank you very much. I appreciate the feedback. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@kamalakerreddy 9 лет назад

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

@statisticsfun 9 лет назад

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.

@venkatachalapathibaskar5927 5 лет назад

Sir, one nagging question: b1=slope=(rise/run), how, sum: (x-xbar)×(y-ybar) is equal to the 'rise'. I need to understand this very intuitively.

@vishaldaga3009 5 лет назад

That is why i mentioned him too. It would be great if he has done so

@susie519 11 лет назад

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.

@statisticsfun 11 лет назад

Are you just going to eyeball your line or are you going to derive your line. If you just eyeball it and draw it in, then you are never going to be able to know how well the line fits. If you derive your line, then you will be able to calculate R squared and Standard Error of the Estimate which helps you understand how well your estimated line fits. There is a link in this video description to a playlist on regression. Make sense?

@danageberten 10 лет назад

MUCH better than my course book! Thanks!

@latifmammadli6815 6 лет назад

yavsaga bak ya

@statisticsfun 11 лет назад

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.

@comredigital 5 лет назад

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

@statisticsfun 11 лет назад

Those are good observations and good questions. I will create another video that explains this why the line includes the means and the slope. btw, make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@bordeaux1337 8 лет назад

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

@abhinandansrinivas5831 8 лет назад

i would like to know the answers to these too.

@terigopula 8 лет назад

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

@manikanth2166 8 лет назад

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

@terigopula 8 лет назад

Thank u so much Mani Kanth :)

@statisticsfun 11 лет назад

I don't have anything on moderators or dummy variables yet, but I plan to add something in the near future. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@melliehaider9861 10 лет назад

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

@mohammadsameerkhan937 4 года назад

This video explains how the slope is obtained, but it fails to explain the derivation and principle behind it.

@thomaseldrup1315 8 лет назад

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 11 лет назад

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 3 года назад

You are so on point!

@pmarilag 11 лет назад

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

@statisticsfun 12 лет назад

Thank you very much! Make sure you like MyBookSucks on FaceBook (see link in video description). It will help me help other students find the videos. Good luck in your classes too.

@revlmp727 6 лет назад

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

@statisticsfun 11 лет назад

You are very welcome from Kansas City, USA. Maybe you should go to lectures to learn about where the parties are going to be and to meet new friends, and perhaps your future spouse :).

@tdm4825-r6r 4 года назад

Ernest teacher number 1

@MarsMaher 4 года назад

no u chatting shit

@statisticsfun 11 лет назад

I have an example on using excel using regression. If you click on the playlist on regression (see video description for link), it is the 5th video in the playlist. Good luck!

@rachellemarcial3422 8 лет назад

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

@statisticsfun 11 лет назад

Well thank you very much for that. Make sure you like MyBookSucks on Facebook (see video description for link). This will help others find the educational videos.

@NeutralGenericUser 10 лет назад

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

@statisticsfun 11 лет назад

Thanks! Make sure you like MyBookSucks on FaceBook because this will help others find the educational videos. You can see the link in this videos description.

@Jaynyina 8 лет назад

this is awesome. thank you sooooo much

@statisticsfun 8 лет назад

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

@Jaynyina 8 лет назад

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

@statisticsfun 11 лет назад

You were very welcome, indeed. Make sure you like MyBookSucks on FB (see link in video description). This will help others find the educational videos.

@sarahthompson4191 7 лет назад

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

@statisticsfun 11 лет назад

Does make me wonder, but I try not to pay to much attention because my like rate is 98%. I remind myself that I can't please all the people all the time.

@kongmagneto12 9 лет назад

Thanks a million!!!!!!

@statisticsfun 9 лет назад

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.

@statisticsfun 11 лет назад

The idea of the slope is exactly the same rise/run. The way slope (or b1) is a bit different and tricky. Sorry I don't have anything on PCA, yet.

@jessepinkman725 5 лет назад

2018 still using this vid for my reference

@Roman-fk5rl 4 года назад

2020?

@statisticsfun 11 лет назад

Well thank you very much. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

Many thanks! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

Thanks! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help other students find the educational videos.

@statisticsfun 11 лет назад

Thank you! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

thanks for that! Make sure you like MyBookSucks on FB too (see link in video description). This will help others wowed as well.

@statisticsfun 11 лет назад

Well, there are probably two different ways to handle this. The first is just use elapsed minutes, starting at 10:00 which would be 0, then 10, 20, 30, so on and so forth. The other way would be to convert the time to decimal form, so 10:00am would be 10.00, 10:10 would be 10.17 (10 + 10/60), 10:50 would be 10.83 (10 +50/60). The Excel Formula for converting time is below where A2 is the cell of the time you want to convert. =INT(A2)*24+HOUR(A2)+ROUND(MINUTE(A2)/60,2) Make Sense?

@statisticsfun 11 лет назад

The actual equation is y = b0 +b1x. In this case is it 4 = 2.2 + 1.3(.6). I would encourage to watch the video starting at about 5:25. Take special note on how I solve for b0. I did notice in your equation:4 = b0 + b1*3 = 1.8 ; it should be 4 = b0 + .6*3 ; 4 = b0 + 1.8, then when I subtract both sides of the equation by 1.8, I get 2.2 = b0.

@statisticsfun 11 лет назад

Good to hear and I appreciate the feedback.

@KartikChawla 8 лет назад

this is not the least sqaure method. Where are the normalised equations?

@WassupCarlton 5 месяцев назад

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

@statisticsfun 11 лет назад

Good to hear my videos are helping you. Perhaps you could show my videos to your lectures (or send them a link). Btw, where are you going to school (what country?). Good luck in your classes and do let me know if you have any special requests.

@statisticsfun 11 лет назад

The equation that you describe is a curved line (a parabola). The one I describe is a linear regression or a straight line. Typically linear is discussed prior to curved lines.

@statisticsfun 11 лет назад

Great to hear and good luck writing your EE program. Make sure you like MyBookSucks on FaceBook. This will help others find the educational videos (see video description for link).

@GriddlockCosplay 3 года назад

I know this is an educational video, but the extreme slow grade-2-level multiplication is maddening. If the viewers don't know that 1 x 0 = 0 and 0 x 1 = 0 then they shouldn't be watching this. I don't know if you are just narrating to a slow animation or what, but it is extremely frustrating to watch.

@millykunda4537 3 года назад

My lecturer decides not to teach statistical analysis of analytical data but tells us to expect it in the final exam.... Hence me here panicking... Thank you for making this easy 🙌

@statisticsfun 11 лет назад

Ya know. I don't think it actually has a name (the point where the two means (averages) intersect). Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

Love it! I was going to name my business MyProfessorSucks, but went with MyBookSucks. I could have named it MyProfessor=DumbAss. Good luck in your class and make sure you like MyBookSucks on FaceBook (see link in video description). This will help others with Dumb Ass professors find the videos.

@statisticsfun 11 лет назад

Abhishek... I am not sure I understand your question and what you are trying to accomplish.

@statisticsfun 11 лет назад

Happy to be of service! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos and have their lives saved :).

@statisticsfun 12 лет назад

Great to hear! Make sure you like MyBookSucks on FaceBook (you can see the link in the video description). This will help me get the word out to other self learners. Good luck on your classes!

@statisticsfun 11 лет назад

Great to hear and happy to be of service! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

Interesting. Make sure you let me know if there are any specific subjects you need/want covered. This will help me understand what other needs students need help with. You can post question here, but it may be better to post them on the MyBookSucks FaceBook Page (see link in this video description).

@statisticsfun 11 лет назад

Haha!! You can do it! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos and pass to.

@statisticsfun 11 лет назад

You are very welcome and I appreciate the feedback. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

I am getting ready to post a series of videos this weekend on Multiple Linear Regression, so make sure you subscribe if you have not done so. This way you will be notified when I post.

@statisticsfun 11 лет назад

Thanks for the compliment. I have an entire playlist on ANOVA. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help other students find the educational videos.

@statisticsfun 11 лет назад

Great to hear and I appreciate your feedback. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

I hope you Aced your final! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

Good to hear! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

Thank so much, your feedback is much appreciated. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@plumi75 9 лет назад

All your videos are so useful and can be considered general knowledge. I wonder if you are able to explain Panel Data Analysis as simple as this using any software program. Economics + Statistics(fun) = Econometricsfun :)

@statisticsfun 9 лет назад

plumi75 Hi Berlin, Yes most of my videos are introductory. I do have channel Economicsfun (www.RU-vid.Com/economicsfun). I do have some calculus proofs for microeconomics topics. I have not ventured into any advanced topics for statistics or econometrics but I plan too. In regards, how do that? I use a variety of different tools including flash, illustrator, final cut studio, garage band and a few other tools. Each minute of video takes about 8 hours of work, so these videos take me a long time to produce. I do hope they have a long shelf live.

@statisticsfun 11 лет назад

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.

@statisticsfun 11 лет назад

I don't have that done yet -- but I do plan to create more and more statistics videos including fitting curved lines.

@statisticsfun 11 лет назад

Thank you! While I can't be your prof, you can send me questions. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

It could be used for a bell curve, it is actually an upside down parabola (similar to a bell curve).

@smoke12316 5 лет назад

Why can't my textbook be that simple?

@Klaux 4 года назад

07:27 And this gives me... *2.2* Geometry Dash players: *Breathing Heavily*

@statisticsfun 11 лет назад

Lori, thanks for such a wonderful compliment. Your feedback is much appreciated. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

@statisticsfun 11 лет назад

Well, thank you and what a nice thing to write. I do call myself the professor of the universe :). Make sure you like MyBookSucks on Facebook (see link in video description). This will help others find the educational videos. Btw, what country do you live in? I am in the middle of the USA in Kansas City.

@statisticsfun 11 лет назад

Yes it would be the same exact method if the line was negative sloped too.

@statisticsfun 11 лет назад

Thank you! I have added some links in the video description to a playlist on Regression and a Playlist on Using SPSS for regression analysis.