Linear Regression

Linear regression is a cornerstone of data-driven modeling; here we show how the SVD can be used for linear regression.

These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz

This video was produced at the University of Washington

[nikosips]

Those videos are the best resource for someone who wants to understand data driven models! Thank you very much for your work from an engineering student!!

[Ash-bcvw]

I don't think anybody is teaching LR with respect to SVD on YouTube right now, hence this video is more informative! Loved it immediately subscribed

[appliedmathness]

I love thiese videos!
But in this one you point out the "squared projection error" while showing the segment going from the biased line to the outlier (like in PCA); instead in case of linear regression residuals should be vertical lines.

[dmitrystikheev]

I was looking for copper, but found gold! Boss, excellent as always. Love your way of conveying the material. I hope you will continue presenting more topics on statistics, cause in the multivariate case it can become really intimidating. Best regards from Russia!

[patrickxu]

The lecture is so clear and well-organized! IT IS IMPRESSIVE!!!!

[SoroushRabiei]

Dear professor, you're a great teacher!
Thank you so much for these videos.

[vahegizhlaryan]

I am honestly surprised(just accidentally discovered this channel) why this coolest recourse is not popular among YouTube algorithms

[shakibyazdani]

Absolutely awesome series, I will finish the whole series today:)

[ParthaPratimBose]

Hi Steve, I am a pharmaceutical data analyst, but you're just outstanding

[linnbjorkholm]

Wow! Great video! I really liked your shirt, where is it from?

[Chloe-tymn]

i've been watching all the videos in this chapter and this is the one that got me to cave and purchase the book!! i was so surprised to see that it was so affordable.

thank you and your team so so so much for the high quality accessible information <3

[hengzhang]

Thank you sir,
your courses are awesome!

[Martin-iwll]

In mechanics, overdetermined is named statically indeterminate

[udriss]

Hello.

In your book DATA DRIVEN SCIENCE & ENGINEERING page 24, relation (1.26), you express the matrix B. In this relation you must write: B = X - X bar and not as one can read B = X - B bar. With here X bar which is the matrix of means.

[ihmvhli]

Interesting. In the first lecture of this series, individual faces (i.e. people) were in the columns, but a face was really a column of many pixels. In this lecture, people are in the rows. So each use of SVD is different. And each setup of a data matrix is different.

[a.danielhernandez]

Excellent explanation!, What happens with the y-interception of the line? Is it b?

[sachavanweeren]

very nice series ... though it has been a while and I might be a bit rusty on my math. But if I recall correctly there is nowhere an explicit link made between the SVD and least squares. It is explained that the there is an SVD and with a theorem that this was the best one in some norm. But I have not seen an explicit link with ols. Would be nice if that would be more explicit in the video series...

[clickle]

Can you explain why in the example at the end, U = a/|a|, is it because U has the only one eigen vector of matrix AA(transpose), which is just itself?

[ralfschmidt]

I am slightly confused: the orthogonal projection of b onto a should minimize the distance between b and its projection - which is ORTHOGANAL to the span of a. If I remember correctly, the minimum least squares, however, should minimize the VERTICAL distance between the projected and the original point. I am sure there is something wrong with my assumptions but maybe someone can point me in the right direction

[SkyaTura]

Besides the undeniable quality of the video overall, isn't awesome that he writes backwards in the air just to explain his points? 🤔