What is the mathematical equation relating the independent variable to the expected value of the dependent variable called?

The mathematical equation that expresses the relationship between an independent variable and the expected value of a dependent variable is known as the regression equation. This equation is derived from regression analysis, a statistical method used to identify and quantify the relationship between variables. Specifically, it allows for predictions about the dependent variable based on values of the independent variable(s).

In a typical scenario, the regression equation will take the form of (Y = a + bX), where (Y) represents the expected value of the dependent variable, (X) is the independent variable, (a) is the intercept, and (b) is the slope of the line, indicating how much (Y) is expected to change with a one-unit change in (X).

By using the regression equation, one can make informed predictions and interpretations about data, relying on the established statistical relationship outlined in the equation. This makes it a fundamental concept in quantitative analysis, particularly in business contexts where understanding relationships between different variables is crucial for decision-making.