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\nFitting a Line using Least Squares #SoME2\n

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\n The Least Squares method is widely used to fit curves to data. This is called Least Squares regression. This video shows how to solve the ordinary least squares minimization problem for 1 unknown and 2 unknowns. In practice though, it...\n The Least Squares method is widely used to fit curves to data. This is called Least Squares regression. This video shows how to solve the ordinary least squares minimization problem for 1 unknown and 2 unknowns. In practice though, it can be used to fit many different types of nonlinear functions too! As long as the minimization can be expressed like this:
min || [A]X - b ||

Then the solution is
X = inv([A]^T[A])[A]^T b

Chapters:
0:00 Intro
0:40 Problem Definition
1:32 Def 1: Vertical Distance: min || r || (1 norm)
2:15 Def 2: Perpendicular distance
2:38 Def 3: Least Squares min || r || (2 norm)
3:28 Calculate Error
5:06 Convex Parabola (1D)
6:06 Proof (1D)
8:51 2D Intro
9:27 Calculate Error in Matrix form
11:52 Convex Parabaloid (2D)
12:45 Proof (2D)
15:58 MATLAB code & summary
16:47 Outro\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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17:05
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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
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Usage Permissions
Fine Print: Educational Use
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Concepts

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linear algebra, data, terms, length, lines, area, values, line of best fit
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Additional Tags

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regression, least squares, optimization, 2 norm, minimization, curve fit, data point, good fit, multivariable calculus, feel free, data set, terms multiplied, error term, error versus, combined length, unknown parameters, hand side, partial derivatives, residual length, minimization problem, matrix times, matrix form, residual vector, matrix equation, matrix, error, point, minimum, side
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