Linear regression

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Formative purpose

This course provides the student with the analytical foundations of linear regression analysis, of so that it can approach within a unified framework all the theoretical problems and practices in areas such as multivariate analysis, design of experiments, time series, and linear models, among others. Interpret the hypotheses for the elaboration of forecasts that allow me to determine patterns and trends

Learning objectives

At the end of the course it is planned that the student will be able to: - Acquire the ability to represent using different mathematical models situations. - Solve and analyze problems from a statistical and econometric point of view. - Understand and project the nature of regression research into the process decision-making as a business management tool

Skills to develop

By passing this course the student:

Recognize the importance of data collection for subsequent analysis in dimensionality reduction scopes
Implement the appropriate regression mechanism for a volume of data, recognizing the existence of homoscedasticity or heteroscedasticity
Will formulate corresponding algebraic systems with susceptible problems of maximization or minimization in contexts of least squares
Adequately estimate the parameters present in a phenomenon and the confidence intervals for these
Evaluate the corresponding presence of categorical variables in a model of regression

Learning outcomes

Resolution of a real problem inherent to the Statistics of Optimization phenomena Linear or non-linear and its subsequent presentation at the end of the semester as a colloquium before the course participants and invited teachers. Design statistical models from data for decision making. Theoretical development of a scientific article that involves the implementation of a linear or multilinear regression process when considering the number of free parameters of the information-producing phenomenon

Topics

Introduction to Linear Regression models.

Simple Linear Regression

Regression and model training
Data collection
Uses of regression
Matrix algebra: some applications in statistics simple linear regression
Estimators of the model parameters and their properties, method of minimums squares
Hypothesis test of the slope and the ordinate to the origin
Interval estimation and predictions
Maximum likelihood.
Interpretation of the estimated regression coefficients according to the fitted model

Multiple Linear Regression

Multiple regression model
Estimation of parameter models
Hypothesis test in multiple linear regression
Confidence intervals in multiple regression and tests of hypotheses about the regression coefficients.
Evaluation of the assumptions of the model.

Regression with dummy co-variables

Categorical variables in linear regression models and their modeling through of dummy variables.
ANOVA: one way, two ways and super parametric model
Selection of variables and construction of models.
Multicollinearity

Methodology

The professor explains the topic and some exercises, and the students should ask questions this for helping to build the knowledge

First cort (20 pts): Case study simple linear regression
Second cort (30 pts): Case study multiple linear regression and final project purpose
Third cort (50 pts): Case study regression with dummy variables and final project

FINAL PROJECT

Resolution of a real problem inherent to the Statistics of Optimization phenomena Linear or non-linear and its subsequent presentation at the end of the semester as a colloquium before the course participants and invited teachers. Design statistical models from data for decision making. Theoretical development of a scientific article that involves the implementation of a linear or multilinear regression process when considering the number of free parameters of the information-producing phenomenon.