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master's thesis
Metoda parcijalnih najmanjih kvadrata
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:618422
Jurić Fot, Sanjin
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Jurić Fot, S. (2023). Metoda parcijalnih najmanjih kvadrata (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:618422

Jurić Fot, Sanjin. "Metoda parcijalnih najmanjih kvadrata." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:618422

Jurić Fot, Sanjin. "Metoda parcijalnih najmanjih kvadrata." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:618422

Jurić Fot, S. (2023). 'Metoda parcijalnih najmanjih kvadrata', Master's thesis, University of Zagreb, Faculty of Science, accessed 21 June 2024, https://urn.nsk.hr/urn:nbn:hr:217:618422

Jurić Fot S. Metoda parcijalnih najmanjih kvadrata [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 June 21] Available at: https://urn.nsk.hr/urn:nbn:hr:217:618422

S. Jurić Fot, "Metoda parcijalnih najmanjih kvadrata", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:618422

Metadata
TitleMetoda parcijalnih najmanjih kvadrata
Title (english)Method of partial least squares
AuthorSanjin Jurić Fot
MentorAzra Tafro (mentor)
Committee memberAzra Tafro (predsjednik povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
Committee memberVedran Čačić (član povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-03-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Metoda parcijalnih najmanjih kvadrata (PLS) statistička je metoda koja se koristi za analizu odnosa dvaju slučajnih veličina \( {x}\) i \({y}\), najčešće za predviđanje \( {y}\) preko \( {x}\). Slična je analizi glavnih komponenata (PCA), utoliko što se obje metode bave smanjenjem dimenzije, tj. pronalaze skup novih nekoreliranih varijabli koje će sadržavati maksimalno informacija o početnima; ali za razliku od PCA-a, koji pronalazi komponente za maksimalno objašnjenje varijance u \( {x}\), komponente nastale PLS-om objašnjavaju varijancu u obje veličine, te se stoga mogu koristiti kao ulazi u neki prediktivni model, kao što je linearna regresija. Metoda parcijalnih najmanjih kvadrata posebno je korisna kada je omjer broja opažanja i dimenzije od \( {x}\) malen te kada su kovarijate visoko korelirane. U ovom smo radu opisali metodu i izveli ključne teorijske rezultate vezane uz nju te pokazali kako ona u određenim slučajevima predviđa bolje od linearne regresije i regresije na glavnim komponentama.
Abstract (english)
Partial least squares (PLS) is a statistical method used for analyzing the relationship between two random variables \({x}\) and \({y}\), most commonly to predict \({y}\) from \({x}\). It is similar to principal components analysis (PCA) - both methods deal with dimension reduction, i.e. they construct a set of new uncorrelated variables that will contain maximum information about the initial ones; but unlike PCA, which finds the components that maximally explain the variance in \({x}\), the components generated by PLS explain the variance in both variables, and can therefore be used as inputs to some predictive model, such as linear regression. PLS is especially useful when the ratio of the number of observations to the dimension of \({x}\) is small and when the explanatory variables are highly correlated. In this paper we described the method, derived crucial theoretical results related to it, and showed that in certain cases it performs better than linear regression and principal component regression (PCR).
Keywords
Languagecroatian
URN:NBNurn:nbn:hr:217:618422
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-02-12 08:39:16