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\nLeast Squares Formula PROOF\n

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\nFirst video Linear least squares is a method commonly used to fit curves to data. The equation used for least squares here is derived using the column space of A. The 'best' value of X is the one that minimizes the distance between the...\nFirst video

Linear least squares is a method commonly used to fit curves to data. The equation used for least squares here is derived using the column space of A. The 'best' value of X is the one that minimizes the distance between the vector b and [A]X. Most math textbooks stop at the result: A^T A X = A b and use different algorithms to find the best X. The pseudo-inverse is commonly used to solve this final equation since it is based on Singular Value Decomposition (SVD) - but that's a talk for another video.

Chapters:
0:00 Intro
0:08 Previous Video Summary
0:36 Problem Definition
1:16 Column Space of A
2:42 Orthogonality
3:40 Calculations & Result
5:16 Confirmation
5:41 Pseudo-Inverse
6:07 Outro

Music:
Nuclear Lynx - Discovery\n
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Resource Details

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Educator Rating
Not yet Rated
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Media Length
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6:21
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Grade
Higher Ed
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Subjects
Math
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Media Type
Instructional Videos
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Source:
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\nVirtually Passed\n\n
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Date
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2022
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Language
English
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Audiences
For Teacher Use
2 more...
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Usage Permissions
Fine Print: Educational Use
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Concepts

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vector, length, orthogonal, linear algebra
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Additional Tags

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column space, least squares, pseudo inverse, matrix, ax minus, vectors a1, dot product, squares method, unknown parameters, error term, vector ax, transpose, video, plane, find, curve, showed, minimize, norm, solve, close, guess, showing, case, expand, means, notice, solution, shown, words
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