Određivanje glavnih prediktora razine adiponektina, homocisteina, cistacina C i ekskrecije albumina u urinu kod dijabetesa tipa 2 koreisteći regresijsku analizu

Šeketa, Valentina (2016) Određivanje glavnih prediktora razine adiponektina, homocisteina, cistacina C i ekskrecije albumina u urinu kod dijabetesa tipa 2 koreisteći regresijsku analizu. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this thesis the emphasis is on regression analysis - theoretical background and its application. Regression analysis is one of the most widely used statistical method because of its flexibility in application. The idea is to describe behaviour of variable of interest (dependent variable) with one or more predictors (independent variable) as equation. The main advantages of this method are simple underlying assumptions and elegant mathematical theory. In the first chapter the use of linear regression analysis is denoted, i.e. the relationship between dependent and independent variable is linear. In the second chapter theoretical background of univariate linear regression is described , i.e. the way we describe relationship between one dependent and one independent variable using a straight line. We have discussed the estimation of parameters from the model in univariate linear regression analysis, testing hypothesis for intercept and slope using t test and F test for the analysis of variance (ANOVA) and estimation of confidence and prediction intervals. These results are generalized in the third chapter to describe multiple regression analysis, i.e. modeling one dependent variable with several independent variables. In the fourth chapter we described testing normality of variables, while the theme of the fifth chapter are transformations of variables for linearization of model and stabilization of variance. In the sixth chapter analysis of residuals to check underlying assumptions. In the end we introduce criteria for validation of models and algorithms for variable selection and model building: all possible regressions, forward selection, backward elimination and stepwise regression. The eighth chapter consists of application of this theory on a concrete problem. The data is from 59 patients with diabetes type II and, for each of them, there are 29 values measured. While working with this data we use the statistical program SAS (University Edition) which makes it quicker and easier to model this problem. The main advantage of SAS is implementation of whole methods as univariate and multiple linear regression and variable selection methods. Our task was to model dependent variables Adiponektin (ApN), Homocistein (HCY), Cystacin C (Cys C) i Albumin Ekskrection in urine (AER) using this data base.

Item Type: Thesis (Diploma thesis)
Supervisor: Jazbec, Anamarija
Date: 2016
Number of Pages: 135
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 16 Nov 2016 12:06
Last Modified: 16 Nov 2016 12:06
URI: http://digre.pmf.unizg.hr/id/eprint/5294

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