This article introduces regression modeling, a tool used to understand relationships between variables. It covers various types of regression models, including simple and multiple linear regression, non-linear models, and logistic regression. The researchers delve into matrix algebra and discuss important concepts related to random vectors. They also explore issues like model specification, checking, and selection. Through case studies and examples, the article showcases how regression models can be applied in real-world situations, such as time series analysis and predicting outcomes. The findings in this study offer valuable insights into using regression models for a range of statistical analyses.