Linear Regression

Linear regression is a cornerstone of data-driven modeling; here we show how the SVD can be used for linear regression.
Book PDF: databookuw.com/...
Book Website: databookuw.com
These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Amazon: www.amazon.com...
Brunton Website: eigensteve.com
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-bc8vw]

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

[@patrickxu8795]

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

[@appliedmathness8397]

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.

[@dmitrystikheev3384]

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!

[@SoroushRabiei]

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

[@vahegizhlaryan5052]

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

[@shakibyazdani9276]

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

[@Eigensteve]

Hope you enjoy it!

[@ParthaPratimBose]

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

[@Eigensteve]

Wow, thanks!

[@saitaro]

This is gold, professor!

[@motbus3]

besides the very awesome explanation, the book is awesome and he writes mirrored as it was nothing 😄

[@Chloe-ty9mn]

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

[@hengzhang7039]

Thank you sir, your courses are awesome!

[@PaulNielan]

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.

[@linnbjorkholm9237]

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

[@Eigensteve]

It’s a Patagonia capilene. My favorite shirt. I almost only wear them

[@udriss1]

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.

[@engr.israrkhan]

sir great teacher you are

[@Martin-iw1ll]

In mechanics, overdetermined is named statically indeterminate

[@a.danielhernandez2839]

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

[@kindleflow]

Thanks

[@sachavanweeren9578]

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...

[@spidertube1000]

Good vid bruh

[@ralfschmidt3831]

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

[@robsenponte3308]

Cool

[@anilsenturk408]

How's it going?

[@philrincon]

Is he writing in the reverse?

[@moshuchitu203]

by cross referencing kzbin.info/www/bejne/q5LPnqyQnrWmb9k, one can clearly see the slope derived in the end is nothing but "covariance (a, b)/variance(a)"

[@uzferry5524]

based

[@SkyaTura]

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

[@clickle23]

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?