This book presents a broad range of regression models including count regression models, constrained and penalised regression models such as ridge, LASSO, and elasticnet regression that are used in various applied science fields. The author describes the historical development of the least squares principle, simple linear regression, and Polynomial regression. In addition, logistic regression and multiple linear regression are discussed at length. A novel method to estimate the slope of linear regression is presented along with an emphasis on the importance of numeric problems.