Objective To change the common practice of eliminating independent variables from models because they produce multicollinearity in an independent variable of special interest. Methods I supplement my presentation, which is based on the purposes of regression analysis, by using Venn diagrams, simple formulas, and two small simulations. Results Independent variables that when removed from a model substantially change the statistics associated with the independent variable(s) of most interest are variables that should typically be kept in the model. Multicollinearity is not a sufficient reason to drop variables from a model. Conclusion I argue against the routine dropping of variables that cause multicollinearity in an independent variable of interest from regression models. A more important criterion to consider when contemplating dropping a variable from a model is “model influence.”