Simple Linear Regression

This chapter presents analyses to determine the strength of the relationship between two variables. It introduces the modeling principles of linear regression, statistical inference of parameters, and the application of regression model. The main task of regression analysis is to study the linear dependence between two variables through a set of sample observations. The chapter introduces two basic measures: coefficient of determination and residual analysis. The regression model can be determined using the least squares estimation to find the optimal estimated values of parameters α and β. It should be noted that the linear regression analysis must make sense, that is, regression analysis is not appropriate if the two phenomena are completely unrelated. It is necessary to determine whether a linear dependence between the two variables is expected according to professional knowledge, practical experience, and analysis purpose.