# STATISTICAL LABORATORY

**Academic Year 2021/2022**- 1° Year

## Learning Objectives

**AIMS AND SCOPE**

The aim of the course is introduce the knowledge of the R language for statistical data analysis with special focus on descriptive statistics, probability distributions and statistical inference.

**LEARNING OBJECTIVES**

**Knowledge and understanding (Conoscenza e capacità di comprensione).**The objectives aim at introducing the knowledge of the R language for statistical data analysis with special focus on descriptive statistics, probability distributions and statistical inference.**Applying knowledge and understanding (Capacità di applicare conoscenza e comprensione).**On completion. Students 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.**Making judgements (Autonomia di giudizio).**On completion, students will able to extract knowledge from data through statistical analyses in R.**Communication skills (Abilità comunicative).**On completion, students will be able how to present the results from the statistical analyses, based on the use of the statistical software R.**Learning skills (Capacità di apprendimento).**On completion, students will able how to utilize the statistical software R for basic data analysis and modeling.

## Course Structure

Lectures and practical activities and data analysis in R.

## Required Prerequisites

Basics of linear algebra and statistics.

## Attendance of Lessons

Mandatory.

## Detailed Course Content

**Use of the statistical software in R regarding:**

**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.

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

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

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

## Textbook Information

Documents available on the web page of The R Project for Statistical Computing: https://www.r-project.org and other resources available on the web.

## Course Planning

Subjects | Text References | |
---|---|---|

1 | Introduction to R, Basic Commands in R, Indexing Data, Matrices and Lists, Loading Data | Lecture Notes |

2 | Graphs, Data Types and Structures, Conditional Statements and Loops, Graphs and Data Visualization | Lecture Notes |

3 | Mean, Median, Variance, standard deviation, quantiles, percentiles, interquartile distance, boxplot, outlier detection | Lecture Notes |

4 | Functions in R, data filtering | Lecture Notes |

5 | Bivariate analysis, statistical inference, contingency table, joint probability, marginal probability, chi-squared test, t-test, linear regression. | Lecture Notes |

## Learning Assessment

### Learning Assessment Procedures

Practical activity and data analyis with R

### Examples of frequently asked questions and / or exercises

Perform a univariate analysis considering the attribute X

Report the correlation matrix among the attributes considering 2 digits precision

Perform a Linear Regression analysis of the relationship between the two features X and Y with the variable Z. Report below the output of the summary() function applied on the linear regression model obtained using lm(). Then, comment the results.

Is the dataset balanced with respect to the attribute X?

Visualize the scatter plot considering the variables X and Y. Report below the code used to create the plot.