Simple and Multiple Linear Regression Techniques

REG1

Duration : 1.0 day(s)

:: Course Summary

This workshop deals with simple and multiple linear regression techniques.
Fundamental principles used in linear regression modeling are first introduced. Then focus is put on the conditions of use, tools to assess model performance (mostly plots), and the difference between explanatory and predictive models is explained. Participants will learn which common pitfalls to avoid and the correct interpretation of tables and graphical output produced by statistical software. Advanced methods, such as variable selection methods ("stepwise,"best subset", etc.), the use of categorical explanatory variables, the inclusion of nonlinear and interaction terms (polynomial regression) and ways to deal with the problem associated with correlated explanatory variables (multicolinearity) are also covered.

:: Learning Objectives

Upon completion of this course, participants will understand the underlying assumptions of the techniques and will be able to:

Explain the context of use of simple and multiple linear regression

Construct simple/multiple regression models

Assess the goodness-of-fit of the model to the data

Identify common issues in regression, diagnose problems and fix them

Interpret statistical software output

:: Target Audience

This applied training session in statistics is aimed at all who collect data and who must make decisions based on that data. The regression techniques covered in this session will be particularly useful for people who are interested in relating/predicting a variable to/from a single or a set of explanatory variables.

:: Prerequisite

This one-day training session covers linear regression, a statistical technique used to study the relationship between a continuous dependent variable and a set of explanatory or independent variables.

Participants should know the essential tools in statistics - descriptive statistics, both numerical (mean, standard deviation, standard error, etc.) and graphical (histogram, box-plot, scatter plot, etc.), and hypothesis testing and confidence intervals.

Potential participants should either have attended the training session Fundamental Tools in Statistics or should possess a similar background.

:: Topics Covered

Simple Linear Regression (SLR)
- Objectives
- Terminology
- What is a model?
- Model Specification
- Principle of least squares estimation
- Interpretation of model coefficients
- Difference between correlation and regression
- Example: Data on systolic blood pressure
- Statistical testing on Beta0 (intercept) and on Beta1 (slope)
- Condition of use and diagnostic tools
- Prediction in regression analysis
- Extrapolation
Multiple Linear Regression (MLR)
- Objectives
- Aspects common to SLR
- Interpretation of model coefficients
- Construction of a MLR model
- Adjusted coefficient of determination (adjusted R2)
- Checking model adequacy
- Variable selection
- Multicollinearity
- Special terms in MLR models
Alternatives to Standard Linear Regression
- Nonlinear Regression (NLR)
- Applications of nonlinear regression
- Other ways to handle multicollinearity
Summary
- Steps in model construction
- Robustness of regression to deviations from conditions of application
- Some references

:: Course Content

This one-day session covers linear regression which is a technique used to quantify the relationship between a continuous dependent variable (one taking on a large number of ordered values) and one or several independent variables or predictors. An example data set for which this technique may be relevant could consist of the systolic blood pressure of subjects and corresponding predictors such as age, sex and weight.
The training covers the objectives of linear regression analysis, the principle of modeling, parameter estimation, as well as interpretation of model coefficients, goodness-of-fit and validation measures, and prediction in regression. We place special emphasis on problems commonly encountered in regression, ways to detect these problems and ways to solve them.