Management and Corporate Law

GIANCARLO MANZI

The course aims to provide students with the fundamental skills needed to understand, analyse, and interpret data from real-world contexts. First, the course aims to provide an understanding of the fundamentals of probability calculus, which is essential for rigorously addressing uncertainty and building basic statistical models. In the descriptive statistics section, the course aims to develop the ability to describe data sets using synthetic measures such as mean, median, mode, variance, and standard deviation, fostering an intuitive understanding of variability and central tendencies. A further objective is to introduce the principles of graphical data representation, including histograms, scatterplots, and bar graphs, essential tools for communicating information clearly and effectively.
Another key aspect of the course involves learning the concepts of statistical inference: students are guided to understand how, starting from a sample, they can formulate estimates and test hypotheses about the reference population. Finally, the course aims to develop a critical approach to data analysis, fostering the ability to evaluate the quality of information, recognise potential biases, and correctly interpret statistical results. Special attention is paid to simple linear regression models, which will enable students to analyse data with relationships and identify patterns of information. This set of skills forms the basis for more advanced studies and professional applications.

The course aims to provide students with the fundamental skills needed to understand, analyse, and interpret data from real-world contexts. First, the course aims to provide an understanding of the fundamentals of probability calculus, which is essential for rigorously addressing uncertainty and building basic statistical models. In the descriptive statistics section, the course aims to develop the ability to describe data sets using synthetic measures such as mean, median, mode, variance, and standard deviation, fostering an intuitive understanding of variability and central tendencies. A further objective is to introduce the principles of graphical data representation, including histograms, scatterplots, and bar graphs, essential tools for communicating information clearly and effectively.
Another key aspect of the course involves learning the concepts of statistical inference: students are guided to understand how, starting from a sample, they can formulate estimates and test hypotheses about the reference population. Finally, the course aims to develop a critical approach to data analysis, fostering the ability to evaluate the quality of information, recognise potential biases, and correctly interpret statistical results. Special attention is paid to simple linear regression models, which will enable students to analyse data with relationships and identify patterns of information. This set of skills forms the basis for more advanced studies and professional applications.

The course is introductory and requires no particular prerequisites other than a minimal knowledge of basic mathematical concepts, including limits, integrals, derivatives, and matrix algebra.

PART A: Introduction to Statistics - Elements of Probability.
1. Basics of Statistics and Data Science.
2. Probability.
(a) Test, Sample Space, Events, Operations, and Relationships between Events.
(b) Definitions and Properties of Probability.
(c) Conditional Probability and Independence. Marginal Probability.
(d) Bayes' Theorem.
(e) Discrete and Continuous Random Variables.
(f) Probability Function, Probability Density Function, and Distribution Function.
(g) Discrete Distributions: Uniform, Bernoulli, Binomial, and Poisson.
(h) Continuous Distributions: Uniform, Normal, and Exponential.
(i) Mean and Variance Operators and Their Properties.
PART B: Univariate Statistics
1. Types of Statistical variables and Measurement Scales.
2. Measures of Location: Mean, Median, Mode, Quantiles.
3. Measures of Variability: Variance, Simple/Standard Deviations from the Mean/Median, Range, Interquartile Range, Coefficient of Variation.
4. Measures of Skewness.
5. Statistical Plots.
6. Index Numbers.
PART C: Bivariate Statistics
1. Contingency Tables.
2. Joint, Conditional, and Marginal Distributions and Their Relationships.
3. Independence of Random Variables and Bayes' Theorem.
4. Independence Table and Measure of the Relationship between Two Variables.
5. Properties of the Mean and Variance Operators for Multiple Variables.
6. Dependence on Mean.
7. Variance Decomposition.
8. Scatterplot, Covariance, and Correlation.
PART D: Simple Linear Regression (Descriptive Statistics Part)
1. The Simple Linear Regression Model: Assumptions.
2. Least-squares Estimates of the Intercept and Slope.
3. Index of Determination.
4. Prediction.
PART E: Point Estimation.
1. Sampling Distribution, Estimators, and Estimates.
2. Estimates of Means and Proportions and the Central Limit Theorem.
3. Consistency, Bias, and Efficiency of an Estimator.
4. Mean Squared Error.
PART F: Confidence Intervals and Hypothesis Testing
1. Confidence Intervals for the Mean and the Proportion.
2. General Hypothesis Testing: Type I and Type II Errors.
3. Tests on the Population Mean and the Student's t-Distribution.
4. Composite Hypotheses and One-Way Tests.
5. Significance and p-value.
6. Chi-square Test of Independence.
7. Simple Linear Regression (Inferential Part).
8. Tests on the Intercept and Regression Coefficients.

Main textbook: Cicchitelli, D’Urso, Minozzo: ”Statistica: principi e metodi”. Pearson.
Alternative/Optional Readings:
F. Mecatti: "Statistica di base: come, quando e perché", McGraw-Hill.
D. Piccolo: "Statistica", Il Mulino.
Exercise Textbooks:
F. Pauli, N. Torelli, M. Trevisani: "Statistica: esercizi ed esempi", Pearson.
V. Cicogna, D. Olivieri: "Temi svolti di statistica (anni 2005-2012)", Cedam.

Lectures tend to engage students. For example, the provision of additional points for completing small tasks during the course increases student participation. The R/RStudio software tool is also used, especially for completing exercises: this tool also encourages students to consider the potential future use of data analysis for their thesis and, more generally, in the workplace. A good mix of theory and practice (theory, including the formulation of basic theorems in mathematical statistics, and practice, including the presentation of solutions to exercises based on real data) should enhance students' well-rounded preparation.

Class attendance is not mandatory, but we strongly recommend attending classes, at least those covering more difficult topics.

The exam consists of a written test both with exercises to be solved and with multiple choice questions. During the course, non-mandatory tasks will be assigned which can contribute to the final evaluation.

1) Example of an exam question (relating to the probability part) requiring a solution using calculations and formulas:
Scratch-card game. A tobacconist purchased five scratch cards in bulk, each with a 5% probability of winning €50. Suppose the five cards were purchased individually, meaning each customer buys only one card.
a) Determine the exact probability that no one wins the €50 prize.
b) Determine the exact probability that fewer than three people win the €50 prize.

2) Example of an exam question requiring the selection of the most appropriate answer from a given number of possible answers:
What is a fixed-base territorial index number?
a. It corresponds to the population density of a region.
b. It is the ratio, multiplied by 100, of a given quantity of a territorial area to another considered as a reference.
c. It is the ratio multiplied by 100 between a given quantity obtained at a given instant of time and another obtained at another instant considered as a reference.
d. None of the above.

• Knowledge and understanding: students will learn the basics of statistical reasoning and the basic techniques of data analysis for the study and interpretation of phenomena in the socio-economic, business and financial fields.Applying knowledge and understanding: students will be able to apply the main methods of descriptive statistical analysis, the rules of probability calculation, as well as the procedures of statistical inference. The course aims at providing the skills necessary to grasp and describe the core information contained in the data, including the calculation of synthetic indicators, the construction of appropriate graphic representations, as well as the estimation of the parameters of a reference population, evaluating appropriately the margin of uncertainty.Making judgement: students will develop the ability to formalize problems of investigation using statistical-probabilistic language and acquire the necessary tools to solve them independently with a critical judgment based on data processing.Communication skills: students will consolidate the quantitative approach to economic thinking, using statistical evidence to support their decisions.Learning skills: students will be able to continue their training in the economic disciplines, approaching advanced courses of the mathematical-statistical area with a more solid scientific background.
  • Books: Main textbook: Cicchitelli, D’Urso, Minozzo:  ”Statistica: principi e metodi”. Pearson.Alternative/Optional Readings:F. Mecatti: "Statistica di base: come, quando e perché", McGraw-Hill.D. Piccolo: "Statistica", Il Mulino.Exercise Textbooks:F. Pauli, N. Torelli, M. Trevisani: "Statistica: esercizi ed esempi", Pearson.V. Cicogna, D. Olivieri: "Temi svolti di statistica (anni 2005-2012)", Cedam.