Applied Statistics

• Mjerne skale i neke distribucije slučajnih varijabli s parametrima koji ih određuju
• Osnove transformacije varijabli, Z ? skor
• Statističko zaključivanje o dva uzorka
• Usporedbe sredina i varijabiliteta
• Testiranje razlike sredina dva uzorka ? zavisni i nezavisni uzorci
• Mjere asocijacije između dvije varijable ? korelacija
• Uvod u bivarijantne podatke i asocijacija (korelacija)
• Jednostavna linearna regresija – Uvod i pretpostavke za provođenje analize
• Testiranje homogenosti varijance, nezavisnosti opservacija
• Utjecajnih opservacija
• Analiza ordinalnih i nominalnih varijabli
• Analiza kontingencijske tablice – jačina asocijacije ? Hi kvadrat test kao zamjena za
• Fisherov točan test
• Relativan rizik i izgledi – Frekvencije i proporcije
• Višestruka regresija
• Procjena parametara metodom najmanjih kvadrata
• Testiranje značajnosti koeficijenta regresije
• Interval pouzdanosti regresijske analize
• Evaluacija regresijskog modela
• Analiza reziduala i utjecajne opservacije
• Selekcija varijabli u konačnom modelu
• Usporedba dva modela
• R2, postotak objašnjenog varijabiliteta, značenje standardiziranih i nestandardiziranih koeficijenata regresije
• Venn dijagram
• Standardna, sekvencionalna i stepwise regresija
• Analiza varijance ? ANOVA
• Testiranje pretpostavki
• Welch ANOVA / regularna ANOVA
• Jednofaktorska i višefektorska analiza varijance
• Omjer varijanci F test
• Kolokvij
• Nema predavanja

1. Comparing the differences and limitations of the data, depending on the measuring scale and distribution as well as an understanding of the distribution parameters.
2. Analyze the differences between dependent and independent samples; the ability to identify a linear connection between two continuous variables
3. define bivariate data; define a scatterplot; define the difference between linear and nonlinear dependence; recognize the negative connection from the scatterplot; define the meaning of the Pearson correlation coefficient; identify the perfect linear dependence; recognize non-linear association of two variables
4. examine the conditions for the implementation of linear regression and interpretation of regression coefficients; least square method
5. analyze and understand the proportions and frequencies, and creating contingency tables
6. formulate a multiple regression; interpretation of the coefficients in the multiple regression and the comparison of the two models in a multiple regression
7. select the significant variables in the regression model; understanding coefficient R2 of the final model
8. testing assumptions for analysis of variance

Required reading

• Obavezna / Mandatory
  Petzoldt, T. (2018). Data Analysis with R: Selected Topics and Examples. Technical University of Dresden. Dresden, Njemačka. Dostupno na / Available at: https://wwwpub.zih.tu-dresden.de/~petzoldt/elements_en.pdf
  Furrer, R i suradnici. (2020). (A Gentle) Introduction to Statistics. University of Zurich. Zurich, Švicarska. Dostupno na / Available at: http://user.math.uzh.ch/furrer/download/intro2stat/script_sta120.pdf
  Lilja, D J. (2016). Linear Regression Using R. An Introduction to Data Modeling. University of Minesota. Dostupno na:
  https://open.umn.edu/opentextbooks/textbooks/linear-regression-using-r-an-introduction-to-data-modeling

Further reading

• Dopunska / Alternative
  Efron, B, Hastie, T. (2016). Computer Age Statistical Inference: Algorithms, Evidence, and Data Science. Cambridge University Press. Cambridge, UK. Dostupno na / Available at: https://web.stanford.edu/~hastie/CASI/
  Faraway, J J. (2002). Practical Regression and ANOVA Using R. R-project. Dostupno na / Available at: https://cran.r-project.org/doc/contrib/Faraway-PRA.pdf