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INSITTUTO DE ESTUDIOS SUPERIORES DE TAMAPULIPAS RED DE UNIVERSIDADES AN�HUAC
M�XICO MMVI
Polynomial Regression through Least Square Method Prof. David Macias Ferrer
[email protected] Madero City, Mexico http://www.geocities.com/dmacias_iest/MyPage.html
Goals To approximate a Points Dispersion through Least Square Method using a Quadratic Regression Polynomials and the Maple Regression Commands.
To show the powerful Maple 10 graphics tools to visualize the convergence of this Polynomials.
Least Square Method using a Regression Polynomials Let [
] ∀k∈ℕ be a dispersion point in
where determined by:
. A general regression polynomials is given by:
etc. According the Least Square principle, the coefficient
can be
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Polynomial Regression through Least Square Method - Application Center
Problem: Supose that we have the follow points dispersion:
To use the Maple Tools to find a Quadratic Regression Polynomials to aproximate the dispersion using Least Square Method. According the Least Square Method, the Regresion Polynomials of second degree is given by:
where
. Then, the coefficient
are given by:
The following spreadsheet showing the points dispersion:
In this spreadsheet, the group of yellow cells represent the points dispersion; H2 represent H3 and I2 represent represent
; J2, I3 and H4 represent
; J3 and I4 represent
, (see green cells). On the other hand, K2 represent
finally, the cell K4 represent
;
; J4
; K3 represent
;
,(see cyan cells).
Using the Spread Tools, we have:
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Polynomial Regression through Least Square Method - Application Center
(3.1)
(3.2)
The coefficients of Quadratic Polynomials are given by:
(3.3)
(3.4)
(3.5)
(3.6)
Finally, the Quadratic Polynomials is:
(3.7)
The above mentioned, shows the habitual procedure in a typical class of numeric methods in engineering, this is, what the student has to make in a written exam. But, in an applied problem of science, the Maple Tools can simplify the solution process.
Now, we have the Statistics Package to find the quadratic polynomials
(3.8)
(3.9)
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Polynomial Regression through Least Square Method - Application Center
(3 9)
Let us see the residual sum of squares and the standard errors:
(
Let us see the graphics of Points Dispersion, p and QuadPoly:
Bibliography Burden R, Faires D., "Numerical Analysis", Fifth Edition, USA, PWS Publishing Company, 1993
Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities. https://www.maplesoft.com/applications/view.aspx?SID=4845&view=html
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Polynomial Regression through Least Square Method - Application Center
Application Details Author:
Prof. David Macias Ferrer
Application Type: Maple Document Publish Date: Created In:
November 20, 2006 Maple 10
Language: Categories:
English Mathematics: Linear Algebra Mathematics: Numerical Analysis Education: Statistics Education: Numerical Analysis Computer Science: Numerical Analysis Statistics & Data Analysis: Statistics Statistics & Data Analysis: Regression
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