### Statistical Data Analysis

#### Learning Outcomes

1. Define main notions in the statistical data analysis
2. Explain mathematical backgrounds of main statistical procedures
3. Apply procedure of data preparation and visualization
4. Apply statistical test on real data
5. Analyze the relation between statistical variables by applying regression analysis and correltion analyis
6. Justify the adequacy of statistical inference for given data
7. Interpret the results of statistical data analysis and explain their practical meaning

#### Forms of Teaching

Lectures

Independent assignments

Laboratory

#### Week by Week Schedule

1. Presentation of statistical data; population and sample; sampling methods; population parameters.
2. Objective of multivariate statistical analysis; Data, objects, variables and scales (Stevens's classification); Classification of multivariate techniques; Summarizing, describing and graphical representation of multivariate data.
3. Measures of central tendency (mean, median, mode); measures of dispersion (standard deviation, variance, quantile, and IQR); Statistical inferences; correlation coefficient; linear correlation.
4. Hypothesis testing; type of errors; parametric hypothesis testing; sampling distributions; Tests for means (one and two sample tests - matched pairs and independent); t-test.
5. Tests for variances (one and two sample tests); Chi-square test; F-test.
6. Difference of means; variance of two normal populations; comparing of two population proportions; Tests for population proportions (one and two sample tests); U-test.
7. Interpretation of the tests results; Sample size; Interpretation of p-value; Example of applications: statistical quality control and control charts.
8. Midterm exam.
9. Advantage, disadvantage and use of nonparametric statistical procedures; Nonparametric tests for single sample; Nonparametric tests for two independent and two related samples; Nonparametric tests for three and more independent and related samples.
10. Data manipulation prior to multivariate analysis (missing data, outlier detection, transformations of data, standardization, normality, linearity, homoscedascity, homoegenity); Data appropriate for multivariate analysis: data, correlation, variance-covariance, sum-of-squares and cross-products matices, residuals; distances (statistical and Mahalanobis); Sample geometry and Random sampling.
11. Analysis of variance (ANOVA/MANOVA) and design of experiment.
12. Simple linear regression; Multiple linear regression.
13. Applied correlation and regression analysis, interpretation and relation to ANOVA.
14. Bayesian versus Frequentist inference.
15. Final exam.

#### Study Programmes

Computing (study)
Elective Courses (5. semester)
Electrical Engineering and Information Technology (study)
Elective Courses (5. semester)

#### Literature

(.), Željko Pauše: Uvod u matematičku statistiku, Školska knjiga, 1992,
(.), Mirta Benšić, Nenad Šuvak: Primijenjena statistika, Sveučilište J. J. Štrosmajera, 2013,
(.), 1) David M. Diez, Crhisopher D. Barr, Mine CerinkayaRundel: OpenIntro Statistics, OpenIntro, 2015.,
(.), 2) L. Fahrmeir, T. Kneib, S. Lang, B. Marx: Regression: Models, Methods and Applications, Springer, 2013.,
(.), 3) G. James, Daniela Witten,Tre vor Hastie, Robert Tibshirani: An Introduction to Statistical Learning with Applications in R, Springer, 2013.,

#### General

ID 183454
Winter semester
5 ECTS
L3 English Level
L1 e-Learning
45 Lectures
0 Exercises
12 Laboratory exercises
0 Project laboratory