Linear Regression - Least Squares Criterion Part 2

Linear Regression - Least Squares Criterion Part 2.
In this video, I actually find the equation of the linear model and show the formulas to get there. I go into quite a bit of detail about notation and a few other things so the video is a bit long! We are using the Least Squares Criteria in this video.
We use our data set in order to go through all of the computations so there is a bit of grinding to do. In general this is something you'd just use a calculator / software on but it never hurts to see it all the way at least once!
#stats #statistics #linearregression #leastsquares #maths #correction #correlationcoefficient #dataanalysis #datascience

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You are the only reason I am able to be passing my online math course. I am not just scraping by with a D though, I am actually learning and have a B right now! Thanks!

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Thank you so much for posting these. What took me two weeks in class to barely understand I learned in less than 20 minutes here. I need some Gauss-Markov next.

[@SuperMboli]

I basically know most of the things you did but what I didn't know was how to apply linear regression to prediction or estimation model. NOW it's very clear. Thanks a whole bunch for that.

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Thank you sooooooooo much!!!!

[@jingyiwang5113]

I am really grateful for these fantastic videos that you made. I have understood linear regression now. Thanks!

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Patrick, you really help me understand math... I can't say thank you enough. I tell all of my friends to watch your videos when they ask how I do so well in class :)

[@YlmazDALKIRANscallion]

Your handtyping is so clear. Thank you!

[@marlonumali]

very helpful for someone like me who is not really familiar with predictive equation but suddenly find the need to work with it. many thanks...

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Eplained it better than my professor. Thank you, this is going to help alot.

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Thank you so much! I'm programming software for multivariate ridge regression using Python for an assignment and it helps sooooo much to see it worked out by hand.

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[@fmkeane]

Hi patrickJMT - I'm a big fan of your work - I find you to be very clear and easy to understand. I've a few issues with this video. I've been practicing using Excel to solve the regression, my answer is y = 8.6701x - 438.39. I got the same answer using the 'normal formulae' method. Using your least square formula I get 8.67 for the slope. Just a calculating error somewhere. Keep up the great work - Frank

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I've learned more from you in 6 minutes than a single 2 hour lecture from my professor.

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@patrickJMT
Tomorrow I am going to have my pre-calc finals exam! Thanks for uploading your videos. Your videos help me alot and are very easier to understand, not like my teacher. I 'll try to let you know if I passed the exam.

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Thanks for putting "actual" numbers in the equations!! ;-) Very helpful..

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Thanks Mr: Ireally got preave understanding after waching thes explanation . I hope that we have a teacher with same clear examples

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Thanks :)

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finally someone according to whom I am able to write code for least square method

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You made statistics subject easy, thank you.

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Very clear. Great teaching!

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That’s amazing explanation my brother! Thanks for the effort !!

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Thanks a lot. You explain everything so well.

[@mekhalaspencer1370]

really helpful, both this one and part 1. Thanks !!

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love your videos! I'm a math/computer science double major, and your vids have helped me in most of my classes... any chance you're going to upload any vids for topics on complex variables?

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doing great job really helpful

[@patrickjmt]

thanks!

[@VahidAryadoust]

Thanks for the videos. Very helpful. Can we say that the farthest the point from the regression line, the less accurate the prediction of the regression model for that point?

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where can I have more exercices please ?

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this was extremely helpful! thank you so much

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Hi Patrick cheers to this! Clear and simple examples. Do you have lessons for non-linear too?

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Great explanation, Thanks for the effort.

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Helped me a lot. Thx.

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Very clear explanation

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Brilliant!!! This video helps me a a lot.
Actually I'm now having problem with curve fitting by using least square. Could you elaborate on this topic? I'll be so thankful !

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Thank you sir for such good explanation

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Wonder why the professors make it seem so hard though...

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Perfect video. Thank you very much !

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great video, helped me i lot.

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extremely helpful.. i can finish my homework!

[@robertballance6409]

Hi, this is an excellent video, can you tell me where you found the formula? I need to cite it in my math IA (IB Math project) Thank you, this has been the easiest formula to follow, can not seem to find a similar formula to yours.

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ty bro, you really helped me out

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Thank you for the wonderful video, what is the difference between regression an curve fitting.

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Helpful explanation. Thanks

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Absolute god among men, thank you.

[@EngBandar1]

Thank you so much for this real example. This is my Matlab code for your example
-------------------------
clear all
clc
weight = [65; 65; 62; 67; 69; 65; 61; 67];
height = [105; 125; 110; 120; 140; 135; 95; 130];
Swh = sum(weight.*height) - (sum(weight)*sum(height))/size(weight,1);
Sww = sum(weight.^2) - (sum(weight)).^2 / size(weight,1);
b = Swh/Sww;
a = sum(height)/size(height,1) - b*(sum(weight)/size(weight,1));
x= 30:150; % weights
y = a + b*x; % heights
plot(weight,height,'o', x, y)
axis([55 80 65 160])
grid on
------------------------------------------------------------

[@Gavusl]

Why not just plot the x and y values and let matlab do the approximation for you? What's the point of doing the approximation by yourself if matlab already have these functions ready for you?

[@EngBandar1]

No. sometimes the approximation is not clear. I've tried this many times. Actually, my approach is not that well however, the better approach is to acquire the min and max of x-y - axes to plot the data.

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Gustav Johansson how about for the sake of learning? :p

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A tip for people out there who can't remember the formula for b_1:
The bottom line is the same as the top line but with y's replaced with x's :)

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u r really awesome.

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Nice work dude!

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Anchal Singh bro where is the graph diagram??

[@AnchalSingh06]

I'll do it in R tool. :)

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great explanation

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any plan to make videos about multiple regression , logistic , and finally exponential regression ?

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This is great! Thank you!

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Great explanation - thx

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Great Job