The purpose of a regression equation is to:

The purpose of a regression equation is primarily to predict future outcomes based on the relationships established between the dependent variable and one or more independent variables. In regression analysis, a model is created that describes how the dependent variable changes as the independent variables vary. This predictive capability is essential in many fields, including business, economics, and the social sciences, allowing for informed decision-making based on statistical relationships derived from historical data.

While minimizing total variance is a component of some regression methods (like least squares), it is not the primary purpose of the regression equation itself. Establishing cause-effect relationships is another important aspect of regression analysis but it cannot always be definitively proven, as correlation does not imply causation. Describing characteristics of populations often relies on other statistical methods, such as descriptive statistics, rather than regression equations specifically designed for prediction. Therefore, the focus on using regression equations to yield predictions is the most accurate characterization of their purpose.