Statistics and data science

To acquire the management, under a practical approach, of the different techniques that allow a correct and rigorous approach, collection, analysis and interpretation of data, especially focused on the development of new processes and products, as well as the improvement of the existing ones.

These objectives are focused on the fundamentals and basic models of statistical methods and on the exploratory and inferential analysis of data, especially aimed at chemical engineers.

1. Descriptive Statistics
Introduction to Statistics. Qualitative and quantitative variables. Discrete and continuous variables. Frequency distribution. Graphic representations. Central measurements. Dispersion and shape measurements.

2. Probability
Historical introduction to Probability. Basic concepts. Random experiment. Sample space. Events. Definition of probability. Conditional probability. Independence. Classical theorems: Product rule, Law of total probabilities and Bayes' theorem.

3. Discrete random variables
Definition of random variable. Discrete random variable: probability distribution and distribution function. Main discrete distributions: Bernoulli, Binomial and Poisson.

4. Continuous random variables
Continuous random variable. Density function and distribution function. Characteristic measures of a random variable: mathematical expectation, variance and standard deviation. Typification of a random variable. Uniform distribution. The Exponential distribution. The Normal distribution. Approximation of other distributions by the normal distribution. Central Limit Theorem.

5. Estimation and confidence intervals
Introduction to estimation. Properties of the estimators. Confidence interval concept. Confidence interval for a proportion. Estimation and confidence intervals for the mean and variance of a normal population.

6. Test of hypotheses
The problem of hypothesis testing: types of hypotheses, types of errors and their associated probabilities. Critical level or p-value. Hypothesis testing on a proportion. Tests on the mean and variance of a normal population.

7. Two-sample problem
Paired samples and independent samples. Comparison of two means in paired samples and in independent samples. Testing two variances. Testing two proportions.

8. Linear regression
The simple linear regression model. Estimation of the coefficients by least squares. Covariance and correlation coefficient. Estimation of the error variance. Properties of the estimators. Inference about the parameters. Prediction.

9. Multiple linear regression and analysis of variance.
Multiple linear regression. Introduction to analysis of variance.

10. Introduction to linear programming
Formulation of linear programming problems. Graphical solution of the linear programming problem. Solution using R software.

Basic bibliography:

Notes of the course in the virtual campus and the following books :

Dalgaard, P., 2008. Introductory Statistics with R. Springer (second edition). Accesible en https://link-springer-com.ezbusc.usc.gal/book/10.1007%2F978-0-387-79054…
Holický, M., 2013. Introduction to Probability and Statistics for engineers. Springer. Accesible en https://link-springer-com.ezbusc.usc.gal/book/10.1007%2F978-3-642-38300…


Complementary bibliography:

DEVORE J.L., 2005. Probabilidad y Estadística para Ingeniería y Ciencias. 6º edición. México: Thomson. ISBN 9789706864574
FREUND J.E., MILLER I., MILLER M. 2000. Estadística Matemática con Aplicaciones. 6ª edición. México: Pearson. ISBN 9701703898
MENDENHALL, W, SINCICH, T., 2016. Statistics for Engineering and the Sciences. 6ª edición. Boca Ratón: CRC Press. ISBN 9781498728850
MONTGOMERY D.C., RUNGER G.C., 1996. Probabilidad y Estadística aplicadas a la Ingeniería. 2ª edición. México: Limusa. ISBN 9789681859152
NAVIDI W., 2006. Estadística para ingenieros. México: McGraw-Hill. ISBN 9701056299
PEÑA, D., 2008. Fundamentos de Estadística. 2ª edición. Madrid: Alianza Editorial. ISBN 9788420683805
QUESADA-PALOMA V., ISIDRO A., LÓPEZ L.J., 1982. Curso y Ejercicios de Estadística.2ª edición. Reimpresión. Madrid: Alhambra. ISBN 8420508780

(As it appears in the official curriculum of the degree)

Knowledge
Con18: Knowledge in basic and technological subjects, which enables them to learn new methods and theories, and gives them the versatility to adapt to new situations.

Competences
Comp03: Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial differential equations; numerical methods; numerical algorithms; statistics and optimization.
Comp13: Ability to work in a multilingual and multidisciplinary environment.

Abilities or skills
H/D03: Information management skills.
H/D09: Computer skills.

The methodology will be as follows.

The course has a semester character with six ECTS credits, so it will have 24 hours of expository teaching and 26 hours of interactive teaching, in which computer practices with the statistical software R are included.

Classes will have a duration of 55 minutes and will be developed in the assigned classroom using mainly the blackboard and presentations. The participation of the students in the classes will be encouraged, especially in the more practical aspects. Also will be discussed and solved various exercises set out in bulletins that will be delivered to the students to encourage their personal work, also being used to evaluate their performance.

The tutorials will try to solve the doubts raised by the students about the theoretical-practical classes or about the problems to be solved.

The students will have the support of the virtual campus of the USC, through the course page, to have access to the programs, bibliography and different bulletins of exercises, as well as to notes of some topics and information about additional activities.

The qualification of each student will be done through continuous evaluation and a final exam. This final exam will be theoretical-practical (both in the first opportunity and in the second opportunity), consisting of the interpretation of a series of questions, development of theory questions and problem solving.

The continuous evaluation will account for 30% of the final grade: 15% for the evaluations made in the practices in the R language and 15% corresponding to written controls, tutorials and / or other activities. For the calculation of the final grade the following formula will be used between the continuous evaluation tests (EC) and the final exam grade (EF): 0.3*EC + 0.7*EF.

In the second opportunity a new exam will be taken and the result of the continuous evaluation will be kept. Repeating students will have the same evaluation system.

Any student who has attended the final exam will be considered presented.

For cases of fraudulent performance of tests or exercises, the “Regulations for the evaluation of the academic performance of students and review of grades” will be applied.

(As it appears in the official curriculum of the degree)

Theory lessons 24
Interactive lessons 12
Interactive lessons in the computer room 14
Mentoring in reduced groups 1
Final exam and revision 4
Student's personal work time 95

This represents 55 hours in the class, 95 hours of student work and a total of 150 hours.

In order to successfully pass the course it is recommended:
- Attendance to the expository and interactive classes and the resolution and revision of the proposed problems.
- To dedicate to the study of the subject a time regularly distributed throughout the four-month period.
- To verify the degree of assimilation of the concepts and acquisition of the basic techniques of calculus, solving the exercises proposed in class.
- To use the software of the course during the student's working hours.
- To make use of the tutoring schedule to consult any doubt that may arise.
- With the use of the recommended bibliography it is possible to complete or expand any topic.

The language in which the course will be taught will be Spanish.

Students will have the support of the virtual campus of the USC, through the course page, to have access to the programs, bibliography and different exercise bulletins, as well as notes on some topics and information on additional activities.

The computer exercises will be carried out with the statistical software R.