Calculus and Linear Algebra

OBJECTIVES: The objective of this course is for the student to acquire a set of competencies related to Statistics both at a theoretical and applied level.

LEARNING OUTCOMES: - Understand the fundamentals of probability and statistics. - Understand and analyze problems about random phenomena. - Manage and understand parameter estimation techniques, confidence intervals and hypothesis tests. - Correctly interpret the statistical conclusions of scientific publications in which the simplest statistical methods are used. - Carry out these analyzes yourself (without making conceptual errors or abuses of interpretation) in your future professional activity and manage the appropriate computer tools. - Apply statistical methods to the analysis of specific problems - Interpret world news based on physical, economic, social and cultural diversity. - Maintain an ethical commitment. - Propose projects and actions in accordance with the principles of ethical responsibility and respect for fundamental rights and duties, diversity and democratic values.

Chapter I: Univariate Descriptive Statistics 1.1 Introduction. The purpose of Statistics. 1.2 Description of data by tables 1.3 Description of data by graphs 1.4 Characteristics measures of a variable Chapter II: Bivariate Descriptive Statistics 2.1 Introduction. 2.2 Bivariate Frequency Tables 2.3 Scatterplots 2.4 Measures of linear dependence 2.5 The regression line Chapter III: Probability 3.1 Introduction 3.2 Probability: definition and properties 3.3 Conditional and total probability 3.4 Independence of events 3.5 Bayes Theorem Chapter IV: Introduction to Random Variables 4.1 Introduction 4.2 Univariate discrete random variables 4.3 Univariate continuous random variables 4.4 Characteristics measures of a random variables Chapter V: Probability models 5.1 Introduction 5.2 Bernoulli process 5.3 Poisson process 5.4 Normal distribution 5.5 Relationship between Normal, Binomial and Poisson distributions 5.6 Simple regression model Chapter VI: Introduction to statistical inference 6.1 Statistical inference. Population and sample 6.2 Estimation and estimators 6.3 Confidence intervals for the mean with large samples 6.4 Determining the sample size 6.5 Other confidence intervals and applications (quality control) 6.6 Introduction to the Hypothesis Testing 6.7 Hypothesis test for the mean with large samples 6.8 Interpreting the test using the p-value 6.9 Diagnosis of the model 6.10 Transformations that improve normality Chapter VII: Comparison of Populations 7.1 Introduction 7.2 Comparing two populations means: Independent samples 7.3 Comparing two populations means: Paired data 7.4 Comparing two population proportions 7.5 Comparing two populations variances (normal populations) Chapter VIII: Introduction to Multiple Regression 8.1 Statistical model for Simple Regression. 8.2 Statistical model for Multiple Regression. 8.3 Estimation of the Multiple Regression parameters. 8.4 Inference for Multiple Regression. 8.5 Test for the Multiple Regression model. 8.6 Regression with binary variables.

The learning methodology consists on the following elements: -Lecture class will be taught in face-to-dace mode: Presentation of the main statistical concepts, with their justification and examples. The instructor will illustrate the methodologies with the computer and real or simulated data. Discussion of the concepts with the students. Discussion of the questions and doubts aroused during the self learning process. -Exercises class. Classes devoted to solving exercises in small groups. -Lab class. The students solve data analysis problems by using a statistical package. They are asked to solve exercises and conceptual problems by using the statistical software. After each class and organized in small groups, they are asked to make a case study that will be evaluated.