Prepoznavanje eksponencijalnog rasta

master's thesis

• Author: Antonija Novački
• Mentor: Miljenko Marušić (mentor)
• Committee member: Miljenko Marušić (predsjednik povjerenstva)
• Committee member: Josip Tambača (član povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Mirko Primc (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-02-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ukratko, ovaj rad sastoji se od dva dijela: teorijskog i eksperimentalnog. Prva dva poglavlja su teorijska i u njima je objašnjena linearna regresija i pojmovi vezani uz nju. Pokazano je kako se metodom najmanjih kvadrata dolazi do parametara linearne regresije. Od velike su važnosti reziduali i njihova distribucija pa je temeljito dokazana tvrdnja da suma kvadrata reziduala ima \(\chi^2\) distribuciju. Treće poglavlje odnosi se na eksperimentalni dio u kojem se medu rastućim podacima, prvo simuliranim, a potom realnim, želi odrediti eksponencijalna faza rasta. Podaci su logaritmirani i na njima se provode dvije metode koje koriste linearnu regresiju. U prvoj metodi uspoređujemo linearni i kvadratični model, a u drugoj uspoređujemo dva linearna modela. Točnost metoda provjeravamo u ovisnosti o različitim razinama značajnosti testova, različitim standardnim devijacijama šuma te različitom duljinom podataka. Simulacije su pokazale da je druga metoda, sa dva linearna modela, u većini slučajeva bolja.

Abstract (english)

In this paper, we have two parts: theoretical and experimental part. First two chapters are theoretical and they explain linear regression and terms related to it. It is shown how one finds parameters of linear regression using the least square method. Residuals and their distribution are very important, therefore is the claim that sum of squared residuals follows \(\chi^2\) distribution proofed in detail. Third chapter refers to experimental part in which one between data, first simulated, then real, wants to find exponential phase of growth. Logarithm of the data is being put through two methods, which use linear regression. In first method linear and quadratic model are being compared, and in the second one, two linear models are being compared. The accuracy of methods are being checked depending on the different levels of significance, different standard deviation of the noise of the data and different length of the data. Simulations have shown that the second method is in most of the cases better.

• Keywords: linearna regresija; reziduali; distribucija reziduala eksponencijalna faza rasta
• Keywords (english): linear regression; residuals; residual distribution; exponential phase of growth
• Language: croatian
• URN:NBN: urn:nbn:hr:217:666829
• 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: 2017-04-26 13:27:11