## Learning objectives

To have a general view of the main concepts of descriptive and inferential statistics, and in particular:

a) Knowledge and understanding. The course provides skills on basic statistical techniques. These techniques include: preliminary data analysis and graphical representations, descriptive statistical indices; confidence intervals and hypothesis testing on the mean and proportion, with the calculation of the corresponding p-values; the simple linear regression model. Carrying out a series of practical analysis taken from economical datasets gives the student the ability to solve simple statistical problems that require the aplication of quantitative tools.

b) Knowledge and understanding of statistical methodology. At the end of the course, the student will be able to independently apply the basic statistical techniques indicated above to business problems. The student will therefore have developed basic analytical skills through the use of statistical methodologies.

c) Autonomy of judgment and critical thinking. At the end of the course, the student will be able to create quantitative reports of company information, and to independently carry out simple market analyses using sample information (such as, for example, an estimate of a brand's market share). Furthermore, the student will be able to correctly interpret the results of these analyses, even when performed by others. By studying the contents of the course, the student therefore acquires a good operational ability on basic quantitative techniques and is able to independently obtain simple business information from company data.

d) Communication skills. At the end of the course, the student will be able to interact with all company components, providing quantitative reports of company information and correctly interpreting the results of simple sample analyses.

e) Learning skills. During the course the student will learn the basic statistical techniques. The skills taught in the course include some basic methodological aspects, essential for understanding the techniques and interpreting the results, and a wide use of the learning by doing approach.

## Prerequisites

Calculus, linear algebra

## Course unit content

Part one

Introduction

• Collecting data, review of available statistical sources

• the data matrix; Graphic representations.

Summary of a phenomenon

• Frequency distributions and double entry tables

• averages (analytical mean and other indexes of position)

• Absolute and relative variability indices, concentration

• the shape of a distributions.

Time series

• Simple mobile and fixed base index numbers

• Time series concatenation with different bases; The average annual rate of variation

• compound price index numbers and deflated values at current prices

Relationships between two variables

• covariance and linear correlation coefficient

• the covariance matrix and correlation matrix

• linear regression: the ordinary least squares method; The interpretation of the parameters; model's goodness of fit;

• linear interpolation of time series

Part II

Introduction to probability and sampling

- Outlook of probability theories

- random variables: general aspects and applications

- theorems

- Sample distribution of statistical indexes

Estimating problems

- Average punctual estimate and relative frequency

- Estimate by average interval in case of large and small samples

- Estimate by relative frequency in case of large samples

Problems of hypothesis verification

- Introduction to statistical tests; Observed significance level (P-value)

- Tests in case of large and small samples - Tests on relative frequency in case of large samples

- Tests on two universes in the case of large samples

Univariate linear regression model

-Deriving the model of linear regression

- Estimation of model parameters and hypothesis testing

- Model checking. The meaning of ANOVA table.

## Full programme

## Bibliography

M.A. Milioli, M. Riani S. Zani, Introduzione all’analisi dei dati statistici, (terza edizione ampliata) Pitagora, Bologna, 2014.

http://www.riani.it/MRZ

Cerioli, M.A. Milioli, Introduzione all’inferenza statistica senza (troppo) sforzo, 3a edizione, Uni.nova, Parma, 2020.

## Teaching methods

Knowledge acquisition: frontal lessons

Acquisition of the ability of applying what has been studied: written tests

Acquisition of judgment: during the course students will be encouraged to detect strengths and weaknesses of the methods and of the basic statistic indices.

Acquisition of learning skills: for each topic we will start from the illustration of the problems which have to be solved and we will analyze critically the adopted solutions.

Acquisition of technical language. While teaching, the meaning of the terms commonly used in statistics will be described.

## Assessment methods and criteria

The assessment is via a written test with use of own PC and MATLAB application. The exam has a maximum duration of 60 minutes. The test generally consists of 3 exercises. A score between 6/30 and 15/30 is given to each exercise, the sum of the single grades is 31/30. The different exercises are in turn divided into subgroups. The first exercise generally concerns the topic of descriptive statistics. The last two refer to probability and inferential statistics. The questions deal with some important points of the theory and practice of statistics and are intended to assess the ability of understanding, independence of judgment and the ability to communicate with appropriate statistical language.

The broad articulation of the questions in the different topics should enable to assess both the learning capacity and the ability to apply the knowledge which has been studied.

The final written test is evaluated in a week period and the results are sent to the students via the institutional email. Registration to the exam on Elly Website is a mandatory requirement.

The honours will be awarded to those students who, in addition to having complied with the requisites necessary to obtain the full grades in the test, have also proved to possess a systematic knowledge of the topic, an excellent ability to apply the knowledge to specific problems, a considerable autonomy of judgement, as well as a particular care in the formal drafting of the test.

## Other information

## 2030 agenda goals for sustainable development