Regression analysis is widely used in many fields to build elegant models that describe how some variables, called explanatory variables, influence another variable, called the response variable. The focus of this course is on the important special cases of (multiple) linear regression (for continuous explanatory variables such as weight) and the classical Analysis of Variance ANOVA (for categorical explanatory variables such as disease category). Besides, we introduce non-linear regression to handle cases in which linearity assumptions do not hold. We approach the subject from a theoretical perspective. We build on the course Foundations of Statistics (2MBS20) and show how to construct parameter estimators, confidence intervals, and statistical tests to analyze multivariate data. We discuss how to verify model assumptions and perform model selection. We pair theory with the use of the R programming language to perform statistical analyses of datasets
Objectives
categorize linear and non-linear regression models based on their definitions, assumptions, and fundamental properties
apply the mathematical theory behind linear regression
conduct estimation and hypothesis testing for linear regression
identify suitable regression models through model selection
evaluate them through model validation
analyze linear and non-linear models with a statistical software
define an appropriate model for the case study in hand
answer real-world modeling questions with linear and non-linear regression