The addition of excessive variables to a model can lead to severe consequences. When a model contains numerous variables, it is likely that some of them will exhibit strong correlations. However, explanatory variables should ideally not possess strong relationships among themselves. This issue, known as multicollinearity, can significantly impact the interpretation of results by causing notable variations between models. Variable selection further compounds this problem by introducing uncertainty as to which subset of potential explanatory variables or predictors should be used. This paper presents a succinct overeview of ten traditional methods for tackling multicollinearity and variable selection in linear regression models. These methods were assessed using a real-life dataset across various sample sizes. The findings suggest that modified group lasso, group lasso, and adaptive group lasso exhibit particular efficacy in estimating variable selection and addressing collinearity issues in this model.