# STATISTICS

## Learning outcomes of the course unit

To have a general view of the main concepts of descriptive and inferential statistics

To have a general view of the main concepts of descriptive and inferential statistics

## Prerequisites

Calculus, linear algebra

Calculus, linear algebra

## Course contents summary

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.

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.

## Recommended readings

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, 2a edizione, Uni.nova, Parma, 2004.

A. Cerioli, M. A. Milioli, M. Riani, "Esercizi di statistica", uni.nova, Parma, 2016. http://www.riani.it/CMR

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, 2a edizione, Uni.nova, Parma, 2004.

A. Cerioli, M. A. Milioli, M. Riani, "Esercizi di statistica", uni.nova, Parma, 2016. http://www.riani.it/CMR

## 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.

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, using the same questions for all the students. The exam has a maximum duration of 90 minutes. The test generally consists of 4 exercises. To each is given a score. The different exercises are in turn divided into subgroups. The first exercise generally concern the topic of descriptive statistics. The last three, on the other hand, 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 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.

The Assessment is via a written test, using the same questions for all the students. The exam has a maximum duration of 90 minutes. The test generally consists of 4 exercises. To each is given a score. The different exercises are in turn divided into subgroups. The first exercise generally concern the topic of descriptive statistics. The last three, on the other hand, 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.