Regression analysis is one of the most commonly used methods in statistics that explores functional relationships between variables of interest. Specifically, it examines the influence of one or more predictors on a response variable. We will review the basics of linear regression analysis in which the relationships between a response variable and predictors are assumed to be linear. The focus will be on a careful and intuitive understanding of fundamental concepts of regression analysis. We will also discuss the case where the relationships between variables are highly nonlinear. Flexible regression models based on splines will be briefly introduced.