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master's thesis
Jednostavna linearna regresija i polinomijalna regresija - geometrijski pristup
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:571318
Stošić, Nikolina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Stošić, N. (2021). Jednostavna linearna regresija i polinomijalna regresija - geometrijski pristup (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:571318

Stošić, Nikolina. "Jednostavna linearna regresija i polinomijalna regresija - geometrijski pristup." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:571318

Stošić, Nikolina. "Jednostavna linearna regresija i polinomijalna regresija - geometrijski pristup." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:571318

Stošić, N. (2021). 'Jednostavna linearna regresija i polinomijalna regresija - geometrijski pristup', Master's thesis, University of Zagreb, Faculty of Science, accessed 21 June 2024, https://urn.nsk.hr/urn:nbn:hr:217:571318

Stošić N. Jednostavna linearna regresija i polinomijalna regresija - geometrijski pristup [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 June 21] Available at: https://urn.nsk.hr/urn:nbn:hr:217:571318

N. Stošić, "Jednostavna linearna regresija i polinomijalna regresija - geometrijski pristup", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:571318

Metadata
TitleJednostavna linearna regresija i polinomijalna regresija - geometrijski pristup
Title (english)Simple linear regression and polynomial regression - geometric approach
AuthorNikolina Stošić
MentorSnježana Lubura Strunjak (mentor)
Committee memberSnježana Lubura Strunjak (predsjednik povjerenstva)
Committee memberVanja Wagner (član povjerenstva)
Committee memberZlatko Drmač (član povjerenstva)
Committee memberJuraj Šiftar (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-03-05, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu dan je jedan drugi aspekt provođenja regresijske analize. Konkretno, linearnoj i polinomijalnoj regresiji pristupili smo na nešto slikovitiji način, koristeći geometrijski pristup. Kako bismo to izveli, od krucijalne važnosti bili su nam vektori koji su nam omogućili povezivanje znanja iz područja linearne algebre i područja statistike. Naime, podatke s kojima radimo, kao i sam model zapisivali smo u vektorskom obliku. Prilikom provođenja statističke analize, klasičan izračun modelom prilagođene vrijednosti zamijenili smo izračunom ortogonalne projekcije vektora opažanja na prostor razapet samim modelom. Svojstva ortogonalne projekcije poslužila su nam i prilikom provođenja statističkih testova te računanja testne statistike. Dakle, uobičajenim izrazima koje u regresijskoj analizi inače koristimo dodali smo jednu novu interpretaciju te pokazali da je to zaista ekvivalentno. Upravo ta mogućnost sagledavanja problema te pristupa njegovu rješavanju s više točaka gledišta koje vode istom rješenju jedna je od ljepota matematike koja nam omogućuje povezivanje znanja iz različitih područja te pomaže razjasniti eventualne nedoumice.
Abstract (english)
In this thesis, another aspect of conducting regression analysis is given. In particular, we approached linear and polynomial regression in a somewhat more illustrative way, using a geometric approach. To achieve this, the vectors that enable us to connect knowledge from the field of linear algebra and the field of statistics were of crucial importance to us. Namely, the data we work with, as well as the model itself, were written in vector form. When performing statistical analysis, we replaced the classical calculation of model fitted values by calculating the orthogonal projection of the observation vector on the model space. The properties of orthogonal projection also served us when conducting statistical tests and calculating test statistics. So, we added a new interpretation to the common expressions we usually use in regression analysis and showed that it is really equivalent. It is this possibility of perceiving the problem and approaching its solution from several points of view that leads to the same solution which is one of the beauties of mathematics that enables us to connect knowledge from different fields and helps to clarify possible doubts.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:571318
Study programmeTitle: Finance and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-03-25 13:46:20