Beta regresija

delo diplomskega seminarja

Tina Ražić (Author), Jaka Smrekar (Mentor)

Abstract

Beta regresija je regresijski model, kjer je proučevana slučajna spremenljivka zvezna in zavzame vrednosti na intervalu $(0, 1).$ Predpostavimo, da ima slučajna spremenljivka beta porazdelitev, zato je beta regresija primerna za napovedovanje in analiziranje verjetnosti, deležev ali obetov. Transformacija podatkov omogoči uporabo modela tudi za vrednosti na intervalu $[a, b]$, pri čemer je $a < b$. Z beta regresijo se izognemo omejitvam homoskedastičnosti in simetričnosti, ki jih ima linearna regresija. V delu je obravnavan model beta regresije, opisano je pridobivanje cenilk za regresijske koeficiente po metodi največjega verjetja in izpeljana je Fisherjeva informacijska matrika. Predstavljeni so testi za preizkušanje domnev, intervali zaupanja in različne diagnostične metode, s katerimi preverimo ustreznost modela. Teorija beta regresije je aplicirana na primeru iz resničnega življenja in opisan je postopek regresijske analize v programu RStudio.

Keywords

matematika;beta regresija;transformirana linearna regresija;diagnostične metode;regresijska analiza;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[T. Ražić]
UDC:	519.2
COBISS:	18740569
Views:	2109
Downloads:	222
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Beta regression
Secondary abstract:	Beta regression is a regression model for a variable of interest that is continuous and restricted to the interval $(0,1)$. The dependent variable is beta distributed, therefore it is suitable for predicting and analysing probability, proportions or odd ratios. Data transformation enables the use of the model also for variables with values in interval $[a, b]$, where $a < b$. With beta regression we avoid the restrictions of linear regression like homoscedasticity and symmetry. Here we study the beta regression model, maximum likelihood estimation for regression parameters, and Fisher information matrix. We cover hypothesis testing, confidence intervals and different diagnostic measures in order to check the goodness-of-fit of the estimated model. We apply beta regression to real-life data and give a detailed description of the analysis steps in RStudio.
Secondary keywords:	mathematics;beta regression;transformed linear regression;diagnostic measures;regression analysis;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	29 str.
ID:	11221158