Usporedba različitih statističkih modela na predviđanje smrtnosti od COVID-a

master's thesis

• Title (english): Comparison of different statistical models to predict mortality from COVID
• Author: Maja Labaš
• Mentor: Siniša Slijepčević (mentor)
• Committee member: Siniša Slijepčević (predsjednik povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-07-11, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad sadržava najbitnije teorijske rezultate vezane za višeparametarsku linearnu regresiju te primjenu tih rezultata na predviđanje smrtnosti od COVID-a. U prvom poglavlju naveli smo neke osnovne definicije iz vjerojatnosti i statistike koji su korisni za ostatak rada. Drugo poglavlje započeli smo s definicijom jednostavne linearne regresije koju smo odmah proširili na složenu linearnu regresiju. Objasnili smo metodu najmanjih kvadrata i dali njezinu geometrijsku interpretaciju. Dokazali smo Gauss - Markovljev teorem i spomenuli test hipoteza. U trećem poglavlju obradili smo metode odabira podskupa uključujući odabir najboljeg podskupa, stepenastu selekciju unaprijed i unazad te etapnu regresiju unaprijed. Osim toga, dotaknuli smo se metoda sažimanja, točnije ridge i lasso regresije. U zadnjem, četvrtom poglavlju počinjemo graditi modele višestruke linearne regresije promatrajući prvo udio zaraženih kao zavisnu varijablu, a nakon toga i udio umrlih od virusa.

Abstract (english)

This paper contains the most important theoretical results related to multiple linear regression and the application of these results in predicting COVID mortality. In the first chapter we mentioned some basic probability and statistics definitions that are useful for further work. We started the second chapter with the definition of simple linear regression, which we immediately expanded to multiple linear regression. We explained the method of least squares and gave its geometric interpretation. We proved the Gauss-Markov theorem and mentioned hypothesis testing. In the third chapter, we covered subset selection methods including best subset selection, forward stepwise selection, backward stepwise selection and forward stagewise regression. Additionally, we touched on shrinkage methods, specifically ridge and lasso regression. In the final, fourth chapter, we begin to build multiple linear regression models, first considering the share of infected as a dependent variable, and then the share of deaths from the virus.

• Keywords: višeparametarska linearna regresija; smrtnost od COVID-a; Gauss - Markovljev teorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:063219
• Study programme: Title: Financial and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Embargoed access; Embargo expiration date: 2025-01-24
• Created on: 2024-07-24 12:14:36