Least squares | MIT 18.02SC Multivariable Calculus, Fall 2010

[@vuluongtrieu2609]

1:16 least squares explain 4:42 fit line equations 6:39 fit parabola equations

[@mikebmccraw]

Nice explanation!! Very clear!! If you want to know WHY the least squares method works, then watch this explanation. Only three data points are used here so as not to loose the method in a sea of unnecessary complication.

[@vladimircastanon9682]

Very rarely do the presenters on MIT OpenCourseWare ever take the time to SLOWLY and THROUGHLY explain key concepts/steps and methods. This was brilliant, I love the way you broke everything down to a tea and made the learning process so simple. Thank you! Please keep making more videos

[@joyofliving5352]

The best explanation for last decades, and more to come! Linear Least Squares. Could you do a non-linear LS as well? :D We are suckers for real teachers and materials who simplify concepts for the proper digestion.

[@justpaulo]

- Regarding the parabola: With a bit of "contemplation" one can see that the Y values seem to be the ones of a parabola with equation Y = X². However the Y values are not symmetrical with respect to X=0, but rather to X=1. In other words it seems that the parabola Y = X² was shifted to the right by 1. That means the parabola Y = (X - 1)² will fit the data points perfectly, and so that must be the solution: Y = X² -2X +1 .

[@jan-torejakobsen6184]

Finally i found a good explenation for this subject:) Keep up the good work

[@EHBRod13]

OMG!!!!!! We're doing Regression Analysis in Engineering Stats, which is exactly this!!!! Thanks so much for making it SO much easier to understand!!!!!!!! Much love!

[@peterp-a-n4743]

The "challenge" was the real explanation.

[@Zeddy27182]

0:43 She literally went out and came back. she is so cute🤣 not to mention that she is such a great Professor

[@joelngige5776]

This made the concept of lease squares even clearer than i had mastered it before. Thanks for the great Video

[@jeeyabilal1266]

Thankyou you dont how helpful these lectures might be

[@rittwikchatterjee5347]

Really helped me to understand the c program algorithm of it...

[@eddiechen6389]

it would be nice if you can show how u derived those two equations!!

[@michaelgenchi3026]

condensing my 2 and 1/2 hour long lecture into 10 minutes 🙏, thank you

[@theodoresweger4948]

Thanks, very clear by keeping it to it's simplest form.

[@valbercesar]

Perfect class. Nice explanation. Thanks so much! It helped me a lot. :)

[@the_eternal_student]

What function are they putting in terms of a and b at 3:36? i do not see any derivative being taken.

[@faisalmumtaz7363]

the value of b is 11/7 at time 5:43

[@miguelpetrarca5540]

how do we derivive when we have a summation ? would the summation go away since it is like an integral?

[@mohammedmhilal4129]

After solving the problem a = 1, b = -2, c = 1 so y=x^2-2x+1

[@andrewjustin256]

3:25 Hey there, I would like to inquire you regarding the function you mentioned in the timeline; you are asking to take the derivative of the function with respect to a and b, but where is the function of I may ask. Furthermore, if I were to find the equation of the scattered plot, it is evidently incorrect! May I please get your insight and assistance on that?

[@MyScienceSnacks]

This is extremely good. I've been trying to wrap me around this for a bit and this is the clearest explanation.

[@fadiaburaid]

Thanks for the good explanation, couldn't be better!! Awesome work

[@KW-dg6fs]

My thought&guess? : Instead of finding the least squares, what we are finding is the least distance (absolute value since some points are above, some are below the fit function). However, we decide to use least squares because when we take the gradient, it makes it easy to solve the problem.

[@evansodhiambo2030]

OMG you are so good,thanks

[@digigoliath]

TQVM! My first exposure (self study) to Statistics, starting with List Squares.

[@cgleck780]

Amazing explanation as I understood what least squares is at the two minute mark!

[@sarahhope8516]

what if "Y" is a function of a lot of variables say for example 4 or 5 variables and each time we combine values of these variables we get a new value of "Y"......in this case how can i proceed to get an approximate function of y?? THANK YOU SO MUCH :-)

[@jitendranadhpalaparthi6394]

First time I understood why we square values.. Awesome thank you.

[@fatihaydogdu2519]

thank you so much. I need that formules for faster GPS ambiguity estimation

[@zhengwang5828]

brilliant explanation! very clear!

[@boogalooshrimpable]

@SpitTanker Given certain assumptions there are different solutions and estimators. If all gauss-markov assumptions are valid you use the normal OLS which is BLUE under thes assumptions (best linear unbiased estimator). You minimize the summation by minimizing the residuals. the residuals are the difference between the true value of y and the estimated value of y(head). You do this by deriving the regression equation with respect to b (which is the regressor). Kinda complicated on YT

[@kumaransivan]

great lecture and teacher. Thank you!

[@smilex3]

Love it! Great video that I will recommend to my students. Thank you!

[@frankyoung6006]

I think my calculation might be wrong but could anyone tell me if there is a factor of 2 in front of the latter two terms in equation 1 at 3:32 here?

[@panav731]

Thanks for the video, i found it very straight forward. Can you please explain further how you found the two equations you used to solve for a and b. are taking the partial derv. of y=ax+b? And do you have a video for your bonus question. I would like to see if what i worked out is correct. Thanks!!

[@ahmedhisham9420]

i realize this is way too late but ill leave this here in case it helps someone :D kzbin.info/www/bejne/i4rIamt5mN2DmNU

[@pabloramirez9711]

what a legend, thank you

[@dui15pucca]

how could 9 people didn't like this video???!!!! this video is very helpful to understand the least square method!

[@lusinetalawally7611]

They are jealous perhaps. Hahaha

[@krishnar1836]

In the challenge problem how to ensure that error is not maximized, as we are trying to minimise error?

[@OriakoPhi]

Loved the challenge problem! Very engaging recitation video.

[@95Deepanshu]

Thank you professor.

[@MrLongliveAmerica]

Least Square is a data fitting application discovered by Mathematician Gauss. The system of equations that you see are given laws obtained by Trial and Error by the Mathematician and so you don't need to Break your head. Hence by merely plugging in the x values you can not only Interpolate, but also extrapolate the y value. As for the Second question, it is a Challenge Question. If you have done it, you can post it here or hint your way of approach, I can say if you are Right or Not.

[@malluhouston6788]

Thank you. This is the point I was missing!

[@Salahuddin-nv6kh]

Thank you Baris hocam for the video :)

[@BossManTee]

Segmented Least Squares: Multi-way Choices

[@garrettkuketz2715]

Holy crap shes a great teacher

[@aslcesur9243]

We were looking for this explanation thank you so much 😊

[@AlexReyesInHD]

This was a good explanation, but I was kinda disappointed that the instructor didn't explain how she got the equations that were used to find the least squares

[@iraq2011iq-for-every-one]

Thank you very much and best wishes

[@pp7114]

Thank you. Very good session!!

[@d1a2n3i5e8l]

Thank you

[@standman007]

Too Good. Thanks very much

[@nyunai298]

Thanks i found what i was looking for. Non linear model using least square methode

[@nyunai298]

I'm sure you'll bring the non linear model in the exam since you didn't show it on the board

[@armiakrolewska]

You are great teacher.

[@yannis1982]

thnx it was simple and clear and it didnt made me look stupid because i understood 100% of what you said.

[@aram1rasul751]

Hi Madam, Thank you very much indeed for a nice explanation. Really I want ot draw a best curve through all point, curve may have a lot of fluctuations instead of line or parabola, can you tell me how to do that. I am desperately in need of this answer. I appreciate your help in advance . Look forward to hearing from you Aram

[@alexandersoderstrom3610]

Did you solve it sir?

[@asiriindrajith8738]

Hi, How to solve a something like this.. f= 1/{K1(x1^a1)(y1^b1)(z1^c1)} + 1/{K2(x2^a2)(y2^b2)(z2^c2)}: x1,x2,y1,y2,z1,z2 all are variables and a1,a2, b1,b2 c1,c3 K1, K2 all are constants that needed to be find.

[@aditydud]

Very very helpful video... And very easy to understand...also the concept is explained very clearly

[@abhinandankushwaha140]

Very beautifully explained... thanks a lot !! It helped me for my semesters

[@YawnGod]

AWW YEAH MIT.

[@peterp-a-n4743]

Patents and copyrights expire eventually for a good reason. Generally I appreciate that we honor the ones who found something out sooner than the rest of the world, even if in fact that often happens by mere accident.

[@RamilSanchez]

This is very helpful , thanks maam christine!

[@PINEDARONALD]

I don't understand how is 13a + 5b = 14 and then 7 under 6 and 5 a + 3b = 6 and then b = 4 under 7 can someone explain the step the end in that conclusions please?

[@nandinijain2773]

thanku very much...for helping us by spreading knowledge !!!!! truly u r great !!!

[@wade5941]

I got more work to do but that was very helpful. Thank you.

[@zennologyofeverything7265]

she is is mighty smaht - chuckie sullivan of good will hunting

[@ganeshpadesur2944]

Tqvm madam

[@ebrahimmohammadsaleh1427]

very nice explanation. thank you very much

[@mussie2040]

thank you teacher

[@imegatrone]

I Really Like The Video Least squares From Your

[@NehaJain1704]

very nice explanation. thank you very much :)

[@hevi6048]

That would be, no. Differential?

[@lusinetalawally7611]

Awesome!!! Thanks a lot

[@vinayakmallikarjunmali4863]

2 hours of class in 10min

[@LAnonHubbard]

Thank you very much!

[@bobkameron]

nice video!

[@jetskiwillywilly7970]

Mind Blown

[@johnsonekka6397]

Thankyou , that was very helpful

[@jtang105]

very nice!!

[@erikumble]

Did anyone do the challenge? I got a=1, b= -2, and c=1. Can anyone confirm the answers?

[@rebinshw]

very useful video.

[@stewbate70]

Question...Isn't Exi Squared 5 squared5x5 =25, why do you have 13? and kExiyi is 5x6=30, why do you have 14? Just started statistics and I can't see it...help! Stewy

[@nicesacbro4891]

Exiyi is not equal to Exi * Eyi . It's equal to the sum of each xi multiplied by it's corresponding yi.

[@yasmin_jsmn]

thanks

[@duranieleonard7761]

It was very helpful thank you so much

[@yogiwp_]

Holy shit. Now I get it!

[@MultiAnkit1993]

Very good video

[@therasmataz2168]

got lost at 3:20

[@MrLongliveAmerica]

I appreciate your Line of thought, and the way you put forth it. But what would your Opinion be on Patient Policies and Rights. If I am to agree upon your Say, then it would mean no one would ever have a legal right on any thing. In fact, as you said and claimed earlier, some one would, some how, at least stumble on the thought of invention of all the existing concepts and their application, and that means, Rutherford, and J.J. Thompson and Bohr and Einstein were just there by accident?

[@kunjaai]

Nice lecture....thanks a lot....:))

[@KaviPriyan-qt6vc]

great

[@peterp-a-n4743]

That's clearly wrong! Many inventions and discoveries in history were made almost simultaneously and independently. It would've been a mere matter of time till anyone else had found it. And don't get me wrong Gauss was one of the greatest geniuses ever!

[@manawilab5322]

Wow, very illustrative, I wish you were my lecturer Thanks, but how should we send your assignment mentioned at the end of the lecture?

[@janzaibmbaloch5484]

well explained!!!!!!!!

[@mvv.3431]

You are awsome !! Thank you !! Should be cloned and put into every college and school in the world.

[@MrLongliveAmerica]

It would be have been much better if the Instructor had given Due Credits to the Inventor/Discoverer Carl Gauss. After all without him, there would have Never Been a technique as Least Squares.

[@vigneshnagarajan3077]

wow great

[@ahmedsamawe5002]

There is no mathematical proof so far proves that this method is the best way, but I have a simple proof that this method is the best way in this field

[@mallakbasheersyed1859]

Can u provide the proof.I am thinking that we must reduce error so we have that formula of mse, can u explain urs.

[@ass-thetic6035]

I have fallen love

[@jadavgopalsingh1473]

hi sir/mam, iam doing reaseach on image processing so i want to know about local mean estimator using lms algorithm so in this topic i want to find mean of (noise+image) after that i want to find output can u help me sir i have paper with me name is "two dimensional local mean estimator adaptive filter using lms algorithm

[@cloudwalker2730]

Not even close to being correct why is this video still up here...

[@salihduzyol919]

WE STAN