# 9793940 - STATISTICAL LABORATORY

Docente: ANTONIO PUNZO

## Risultati di apprendimento attesi

1.     Knowledge and understanding (Conoscenza e capacità di comprensione). The objectives aim to introduce the knowledge of the R language for statistical data analysis with a special focus on descriptive statistics, probability distributions, and statistical inference.

2.    Applying knowledge and understanding (Capacità di applicare conoscenza e comprensione). On completion, the student will be able to utilize the R language for i) providing basic statistical analyses of data; ii) simulating data according to given probability distributions; iii) applying main methods of statistical inference.

3.      Making judgements (Autonomia di giudizio). On completion, the student will be able to extract knowledge from data through statistical analyses in R.

4.    Communication skills (Abilità comunicative). On completion, the student will be able how to present the results from the statistical analyses, based on the use of the statistical software R.

5.      Learning skills (Capacità di apprendimento). On completion, students will be able to utilize the statistical software R for basic data analysis and modeling.

## Modalità di svolgimento dell'insegnamento

Lectures and practical activities and data analysis in R.

## Prerequisiti richiesti

Basic notions in statistics, linear algebra, and computing.

## Frequenza lezioni

Highly recommended.

## Contenuti del corso

Getting started with R and RStudio

Descriptive Statistics. Simple Statistical Distributions. Data tables. Frequency distributions. Main summary statistics: arithmetic mean, geometric mean, harmonic mean. Median and percentiles. Variance, standard deviation, relative variation. Graphical representations. Multiple Statistical Distributions. Contingency Tables. Joint distributions, marginal and conditional distributions. Covariance and correlation.

ProbabilityRandom number generation and data modeling according to different probability distributions: uniform, binomial, Poisson, Gaussian.

Statistical inferenceSample distributions: Student-t, chi-square. Confidence estimation. Confidence level. Confidence bounds for means, variances, and proportions. Hypothesis testing. Null hypotheses and alternative hypotheses. P-values. Statistical tests for means, variances, proportions, comparison of means, and comparison of proportions.

Statistical modelsThe simple regression model. Goodness of fit. Residual analysis. Inference on the parameters of a linear regression model.

## Testi di riferimento

·         Dalgaard, P. (2008). Introductory Statistics with R. Germany: Springer New York.

·         Venables, W. N., Smith, D. M. (2009). An Introduction to R: A Programming Environment for Data Analysis and Graphics. United Kingdom: Network Theory.

·         Verzani, J. (2018). Using R for Introductory Statistics. United States: CRC Press.

## Verifica dell'apprendimento

### Modalità di verifica dell'apprendimento

The exam aims to evaluate the achievement of the learning objectives. It is carried out through a practical test concerning the writing of a convenient R code to solve a statistical problem in R.

### Esempi di domande e/o esercizi frequenti

·         Writing an R code to find the maximum likelihood estimates of the parameters of the log-normal distribution

·         Writing an R code to find the maximum likelihood estimates of the parameters of a linear model with covariates both on the mean and on the variance of the normal distribution for the error

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English version