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Master's Dissertation
DOI
https://doi.org/10.11606/D.11.1980.tde-20220207-223005
Document
Author
Full name
Francisco Ademar Costa
Institute/School/College
Knowledge Area
Date of Defense
Published
Piracicaba, 1980
Supervisor
Title in Portuguese
Novo tipo de delineamento ortogonal adequado para a regressão polinomial do segundo grau
Keywords in Portuguese
DELINEAMENTO EXPERIMENTAL
REGRESSÃO POLINOMIAL
Abstract in Portuguese
Um novo tipo de delineamento foi desenvolvido para permitir o ajuste aos dados de um polinômio do segundo com duas variáveis independentes, de modo a oferecer maior flexibilidade na escolha dos delineamentos fatoriais, Foram usados dois fatores, cada um com sete níveis. O delineamento é composto por dois fatoriais de 2 x 2, sendo que no primeiro os níveis estão codificados em -1 e +1 e no segundo em -α e +α, acrescido pelos pontos (0; α√2), (0; -α√2), (α√2; 0), (-α√2; 0) e o ponto central é repetido até 8 vezes. Pesquisando-se a eficiência do delineamento em função do número de repetições do ponto central, chegamos à conclusão de que se deve de preferência utilizar somente um ponto central com α igual a 0,716332 de modo que o delineamento seja mais eficiente.
Title in English
A new type of orthogonal design applied to second degree polynomial regression
Abstract in English
A new design was developed specifically for fitting to data a second degree polynomial with two factors. Criteria in constructing the design were: higher number of levels of each factor, limited number of treatment combinations, and orthogonality of regression coefficients. Treatment combinations (except for the central point) are either at a distance of √2 or α√2 from the center. What interests is the value of α, which makes the design orthogonal as well as the efficiency of the design when more than one central point are used. Formulas were determined which estimate the variances, the estimates, and the sums of squares of the polynomial equation coefficients. It was verified that the variances of the polynomial regression coefficients are smaller when only one central point is used. In this case, α becomes equal to 0.716332.
 
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Publishing Date
2022-02-07
 
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