Applied Statistics

Recommended Prerequisites

Linear Algebra and Analytic Geometry, Calculus I,II and III.

Teaching Methods

In the theoretical classes the relevant concepts are introduced supported by examples taken from the real world . The exposition is supported by power points presentations followed by face to face interactions of the key points. Discussions of practical cases will also be done inside the classes or/and assigned as homework to the students. A mini project to be done in groups of three students is distributed in the beginning of the course. A report of the data treatment miniproject is supposed to be concluded for evaluation by the last class of the course.

Learning Outcomes

To identify the characteristics of the random phenomena. To characterize the random variables in terms of theoretical distributions. To acknowledge the parameters of a distribution. To get acquainted with the different ways of representing samples from a population. To know the different sampling methods. To distinguish parameters from statistics calculated from samples. To construct normality plots. To understand the central limit theorem and its consequences. To be able to do estimation of parameters via point or interval methods as well as hypothesis testing. To understand the statistic approach of linear regression.

The course aims at developing the following skills: Ability in analysis and synthesis; generalization and abstraction; computer skills relating to the scope of the study; ability to formulate and solve problems; Teamwork; independent and critical thinking; capacity of autonomous learning; competence in applying theoretical knowledge in practice.

Work Placement(s)

No

Syllabus

Measuring and measurement errors. Random phenomena: characterization. Randomness and complexity. Different definitions of probability. Probabilistic calculus. Theoretical models for random variables. Distributions and their parameters. Central limit theorem and its implications. Estimation theory and its limitations. Point estimators and their properties. Estimation methods: least squares and maximum likelihood. Confidence intervals for different parameters and sample sizes. Hypothesis tests: formulation and definitions of different error types. Relation between hypothesis testing and confidence intervals. Non parametric testes. Least square method. Linear regression (one and multivariable). Statistic approach to linear regression. Variance analysis (ANOVA).

Head Lecturer(s)

António Alberto Torres Garcia Portugal

Assessment Methods

Assessment
Synthesis work: 20.0%
Resolution Problems: 20.0%
Exam: 60.0%

Bibliography

Vining, Geoffrey e Kowalski, Scott M., Statistical Methods for Engineers, Thomson Brooks/Cole, 2nd Edition, 2006.

Guimarães, R., Sarsfield Cabral, J. A., Estatística, McGraw-Hill, 1999.

Dougherty, E. R., Probability and Statistics for the Eng., Comp. and Physical Sciences, Prentice Hall, New Jersey, 1990.