Statistics and Data Analysis

Recommended Prerequisites

Mathematical Analysis I.     

Teaching Methods

The teaching in this course assumes two formats: theoretical and example classes. During a theoretical class teaching is mostly expository. During an example class teaching consists of problem solving by the students under the guidance of the lecturer. A strong interaction between notions and their practical application is emphasized. In this task, the visualization and the analysis of concrete examples takes on a central role and prepares the way for the abstract definitions. Tutorial support is available to students to help them on the tasks assigned by the lecturers.

Learning Outcomes

The student who successfully completes this course will be able to:

1. Acquire a solid knowledge of statistics for development at the level of subsequent curricular units, research, specializations and the exercise of professional activity.

2. Develop and correctly use data analysis methodologies, ensuring the correct knowledge of concepts, as well as the discussion and proper interpretation of the results.

3. Accurately quantify the intrinsic uncertainty of the data and correctly use statistical software.    

Work Placement(s)

No

Syllabus

1. Probability. Probability concepts; conditional probability and independence of events.

2. Probability distributions: Real random variables; Moments; Usual distributions in Statistics: Poisson, binomial, multinomial, negative binomial, Gauss and Gumbel. Central limit theorem and extremal limit theorem.

3. Data Analysis. Scale, ordinal and nominal data. Numerical summaries and graphs. Outliers. Correlation statistics.

4. Estimation. Point estimation: estimators and methods to obtain estimates. Estimation of extremal parameters. Confidence intervals: generalities, confidence intervals for a population mean, variance and proportion.

5. Hypothesis testing. Generalities. Tests for a population mean, variance and proportion. Two sample tests. Q-Q plot. Qui-Square tests: goodness of fit, independence and homogeneity.

6. Simple and multiple linear regression. Model design; statistical inference for the parameters; predictors’  significance; goodness of fit; prediction intervals.    

Head Lecturer(s)

Maria da Graça Santos Temido Neves Mendes

Assessment Methods

Assessment
2 or more midterm exams: 100.0%

Bibliography

[1] Murteira, B., C. S. Ribeiro, J. A. Silva, C. Pimenta, Introdução à Estatística, 2007, 2ª ed., McGraw-Hill, Lisboa.

[2] Andrews, L.C., Phillips, R.L., Mathematical Techniques for Engineers and Scientists, 2003, Spie, Washington.

[3] Devore, J. L., Probability and Statistics for Engineering and the Sciences, 2000, 5ª ed., Duxbury.

[4] Montgomery, D.C., G.C. Runger, Applied Statistics and Probability for Engineers, 4ª ed., 2007, Wiley.

[5] Moore, D., McCabe, G., Introduction to the practice of statistics, 2006, Freeman, New York

[6] Ross, S. - Introduction to Probability and Statistics for engineers and scientists, 1987, Wiley.