Metode procjene i odabira linearnog regresijskog modela

master's thesis

• Title (english): Methods for estimating and selecting a linear regression model
• Author: Josip Mucak
• Mentor: Miljenko Huzak (mentor)
• Committee member: Miljenko Huzak (predsjednik povjerenstva)
• Committee member: Zoran Vondraček (član povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Pavle Goldstein (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-09-22, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovome radu upoznali smo se sa principom i svrhom korištenja linearne regresije u različitim formama. Vidjeli smo kako funkcioniraju neke od osnovnih metoda za pronalazak koeficijenata (i mnogih drugih statistika) linearnog regresijskog modela, odnosno kako ponekad možemo izmijeniti (metode sažimanja) prvobitno dobivene koeficijente ili neke prediktore u potpunosti izbaciti (metode odabira podskupa) u svrhu poboljšanja snage predikcije. Zaključujemo da bez obzira na prednost neke metode s obzirom na druge u određenom problemu, ne postoji savršeni model koji bi u svakome problemu predikcije davao optimalno rješenje, već moramo svaki puta uzeti u obzir više metoda kako bismo pronašli model koji nam u tom trenutku najviše odgovara gledajući kriterij koji nas najviše zanima.

Abstract (english)

In this paper, we are introduced to the principle and purpose of using linear regression in different forms. We have seen how some of the basic methods for finding the coefficients (and many other statistics) of a linear regression model work, that is, how we can sometimes modify (shrinkage methods) originally obtained coefficients or eliminate some predictors completely (subset selection methods) to improve prediction power. We conclude that regardless of the advantage of some methods over others in a certain problem, there is no perfect model that would predict the optimal solution in each problem, instead each time we must consider several methods to find the model that suits us best at that time by looking at the criterion that interests us the most.

• Keywords: linearna regresija; metode sažimanja; metode odabira podskupa; snaga predikcije
• Keywords (english): linear regression; shrinkage methods; subset selection methods; prediction power
• Language: croatian
• URN:NBN: urn:nbn:hr:217:842312
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-10-29 12:29:53