93064 - STATISTICS

Conoscenze e abilità da conseguire

The goal of this course is to introduce statistics, statistical estimation and testing using basic probability models, random variables and discrete and continuous probability distributions.

Contenuti

Part A — Descriptive Statistics

1. Course introduction and data structures
   Statistical surveys; populations vs samples; variables and measurement scales; data matrices.

2. Frequency distributions and graphics
   Univariate tables; histograms, empirical distribution function; cumulative frequencies; statistical ratios; index numbers.

3. Location, variability, shape
   Means, median, mode, quantiles; variance, standard deviation, range, IQR; concentration; skewness and kurtosis; boxplots.

4. Bivariate distributions
   Joint, marginal, and conditional frequencies; conditional mean and variance; decomposition of total deviance; independence vs association; dependence in mean.

5. Scatterplots and association
   Scatter diagrams; covariance; Pearson correlation; introduction to linear regression (idea and interpretation); brief mention of local regression.

6. Towards multivariate thinking
   Multidimensional data matrices; derived matrices (covariance, correlation, distance); dissimilarity and Multidimensional Scaling (MDS); Principal Component Analysis (PCA) (intro and use cases).

R labs: importing data; data cleaning; factor vs numeric types; plotting (base/ggplot); frequency tables.

 

Part B — Statistical Inference

1. Probability and random variables
   Experiments, outcomes, sample space; discrete RVs (Bernoulli, Binomial); continuous RVs (Normal and Student’s t).

2. Sampling and estimators
   Population models and parameters; statistics, estimators, sampling distributions; properties of estimators.

3. Point estimation and confidence intervals
   Methods of point estimation (focus on Maximum Likelihood); CIs for mean and proportion.

4. Hypothesis testing
   Null/alternative; Type I/II errors; significance and power; tests for mean and proportion; non-parametric χ² test of independence.

R labs: simulation of sampling distributions; CI construction; one- and two-sample tests; proportion tests; χ² independence.

 

Part C — Linear Regression

1. Simple linear regression
   Model, assumptions; OLS estimators; interpretation of coefficients; R².

2. Model checking
   Residual diagnostics; departures from assumptions; leverage and influence (intro).

3. Multiple linear regression
   Estimation and interpretation; tests on the model and individual coefficients.

R labs: simple and multiple regression fitting; confidence and prediction intervals; residual and influence plots; model comparison and basic selection.

 

Testi/Bibliografia

Educational material (slides and exercises) on the Virtual Learning Environment platform at the link: https://virtuale.unibo.it.

Suggested texts to complement the slides:

• Statistics: Principles and methods
  Cicchitelli, G., D'Urso, P. ,Minozzo, M. , Ediz. Mylab. Pearson (Chapters 1-5, 9-14, 16-20, 23).
• Elementary Statistics Allan Weiss
  (Chapters 1-10)
• Elementary Statistics Mario F. Triola
  (Chapters 1-3, 5-11)
• Introduction to the Practice of Statistics David S. Moore, George P. McCabe, and Bruce Craig
  (Chapters 1-10)
• Statistics for Business and Economics Paul Newbold, William Carlson, and Betty Thorne
  (Chapters 1-13)

Metodi didattici

Lectures with slides, practical R sessions, and worked exercises during class.

 

As concerns the teaching methods of this course unit, all students must attend Module 1, 2 on Health and Safety [https://www.unibo.it/en/services-and-opportunities/health-and-assistance/health-and-safety/online-course-on-health-and-safety-in-study-and-internship-areas] online.

Modalità di verifica e valutazione dell'apprendimento

The exam assesses students’ mastery of the descriptive, inferential, and regression techniques presented in class, as well as their ability to apply these methods effectively to real data analysis.

 

EXAM

Students may opt for two midterm written exams (partials exams). If both are passed (each ≥ 18/30), the final grade will be the average of the two results; otherwise, students may take a single final written exam.

Both the midterms and the final consist of exercises, multiple-choice items, and open-ended questions, with a duration of 120 minutes. Grades are expressed out of 30.

During the exams, the use of a calculator and statistical tables is permitted. A single two-sided A4 formula sheet is allowed, provided it contains formulas only (no text, notes, worked examples, or datasets).

Strumenti a supporto della didattica

Visit Martina Narcisi's website.

Orario di ricevimento

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