Lemmas | Theorems in statistics | Regression analysis

Pyrrho's lemma

In statistics, Pyrrho's lemma is the result that if one adds just one extra variable as a regressor from a suitable set to a linear regression model, one can get any desired outcome in terms of the coefficients (signs and sizes), as well as predictions, the R-squared, the t-statistics, prediction- and confidence-intervals. The argument for the coefficients was advanced by Herman Wold and Lars Juréen but named, extended to include the other statistics and explained more fully by Theo Dijkstra. Dijkstra named it after the sceptic philosopher Pyrrho and concludes his article by noting that this lemma provides "some ground for a wide-spread scepticism concerning products of extensive datamining". One can only prove that a model 'works' by testing it on data different from the data that gave it birth. The result has been discussed in the context of econometrics. (Wikipedia).

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Converse Pythagorean Theorem & Pythagorean Triples

I explain the Converse Pythagorean Theorem and what Pythagorean Triples are. Find free review test, useful notes and more at http://www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage www.YouTube.com/Profro

From playlist Geometry

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Pythagorean Theorem

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From playlist Geometry Video Playlist

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Proving the Pythagorean Theorem

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From playlist Geometry

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Proofs of the Pythagorean Theorem

The Pythagorean Theorem appears in nearly every branch of mathematics. Here are several proofs drawing from algebra, geometry, and trigonometry.

From playlist Lessons of Interest on Assorted Topics

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Pythagorean Theorem II (visual proof)

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From playlist Pythagorean Theorem

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Visual Proof of Pythagoras' Theorem

More resources available at www.misterwootube.com

From playlist Pythagoras’ Theorem

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From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme

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Pythagorean identity explanation

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From playlist Summer of Math Exposition Youtube Videos

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From playlist Mathematics

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Regularity methods in combinatorics, number theory, and computer science - Jacob Fox

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From playlist Mathematics

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From playlist Trigonometry

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9. Szemerédi's graph regularity lemma IV: induced removal lemma

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao explains a strengthening of the graph regulari

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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6. Szemerédi's graph regularity lemma I: statement and proof

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From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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A stable arithmetic regularity lemma in finite (...) - C. Terry - Workshop 1 - CEB T1 2018

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From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields

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7. Szemerédi's graph regularity lemma II: triangle removal lemma

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Continuing the discussion of Szemerédi's graph regularity

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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From playlist Abel Lectures

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10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof

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From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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15. Graph limits II: regularity and counting

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao explains how graph limits can be used to gener

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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a quasi-Pythagorean identity

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From playlist Complex Analysis

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