Least squares | MIT 18.02SC Multivariable Calculus, Fall 2010

Least squares
Instructor: Christine Breiner
View the complete course: ocw.mit.edu/18-02SCF10
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@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.

[@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.

[@jan-torejakobsen6184]

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

[@fadiaburaid]

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

[@peterp-a-n4743]

The "challenge" was the real explanation.

[@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!

[@valbercesar]

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

[@joelngige5776]

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

[@theodoresweger4948]

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

[@aslcesur9243]

We were looking for this explanation thank you so much 😊

[@smilex3]

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

[@abhinandankushwaha140]

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

[@OriakoPhi]

Loved the challenge problem! Very engaging recitation video.

[@rittwikchatterjee5347]

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

[@kumaransivan]

great lecture and teacher. Thank you!

[@zhengwang5828]

brilliant explanation! very clear!

[@jitendranadhpalaparthi6394]

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

[@nandinijain2773]

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

[@aditydud]

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

[@MyScienceSnacks]

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

[@iraq2011iq-for-every-one]

Thank you very much and best wishes

[@evansodhiambo2030]

OMG you are so good,thanks

[@pp7114]

Thank you. Very good session!!

[@RamilSanchez]

This is very helpful , thanks maam christine!

[@cgleck780]

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

[@michaelgenchi3026]

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

[@jeeyabilal1266]

Thankyou you dont how helpful these lectures might be

[@pabloramirez9711]

what a legend, thank you

[@ebrahimmohammadsaleh1427]

very nice explanation. thank you very much

[@armiakrolewska]

You are great teacher.

[@NehaJain1704]

very nice explanation. thank you very much :)

[@YawnGod]

AWW YEAH MIT.

[@mohammedmhilal4129]

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

[@wade5941]

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

[@digigoliath]

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

[@fatihaydogdu2519]

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

[@johnsonekka6397]

Thankyou , that was very helpful

[@LAnonHubbard]

Thank you very much!

[@duranieleonard7761]

It was very helpful thank you so much

[@95Deepanshu]

Thank you professor.

[@eddiechen6389]

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

[@imegatrone]

I Really Like The Video Least squares From Your

[@yannis1982]

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

[@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 .

[@mussie2040]

thank you teacher

[@lusinetalawally7611]

Awesome!!! Thanks a lot

[@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

[@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

[@miguelpetrarca5540]

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

[@jetskiwillywilly7970]

Mind Blown

[@kunjaai]

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

[@janzaibmbaloch5484]

well explained!!!!!!!!

[@standman007]

Too Good. Thanks very much

[@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.

[@rebinshw]

very useful video.

[@d1a2n3i5e8l]

Thank you

[@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

[@MultiAnkit1993]

Very good video

[@bobkameron]

nice video!

[@jtang105]

very nice!!

[@garrettkuketz2715]

Holy crap shes a great teacher

[@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

[@BossManTee]

Segmented Least Squares: Multi-way Choices

[@Zeddy272]

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

[@yasmin_jsmn]

thanks

[@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 :-)

[@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!

[@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

[@yogiwp_]

Holy shit. Now I get it!

[@vigneshnagarajan3077]

wow great

[@ganeshpadesur2944]

Tqvm madam

[@faisalmumtaz7363]

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

[@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.

[@KaviPriyan-qt6vc]

great

[@krishnar1836]

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

[@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?

[@zennologyofeverything7265]

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

[@mvv.3431]

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

[@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.

[@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?

[@vinayakmallikarjunmali4863]

2 hours of class in 10min

[@erikumble]

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

[@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?

[@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?

[@hevi6048]

That would be, no. Differential?

[@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.

[@ass-thetic6035]

I have fallen love

[@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!

[@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.

[@damla818]

[@therasmataz2168]

got lost at 3:20

[@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...

[@ahmedismail1018]

not enough

[@salihduzyol919]

WE STAN

[@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.

[@TeddyJohnson]

Regression

[@Petrichor-km6bm]

Thank you prof! Are you Elon's sister...😂