What type of relationship is described by linear regression?

In linear regression, the primary objective is to model the relationship between a dependent variable and one or more independent variables using a straight line. This method assumes that the change in the dependent variable can be explained by a consistent, proportional change in the independent variables, which is represented mathematically by a linear equation.

The linear relationship is characterized by its constant slope; for any unit increase in the independent variable, the dependent variable changes by a fixed amount. This is fundamental to the linear regression approach, as it allows for straightforward interpretation and predictions based on the derived linear equation. This type of modeling is widely used in various fields, including healthcare, to understand and predict outcomes based on specific input factors.

In contrast, other types of relationships—like exponential, parabolic, or threshold effects—do not maintain this constant rate of change and therefore do not fit within the framework of linear regression. For instance, an exponential relationship suggests a growth pattern that accelerates over time, while a parabolic relationship indicates a curve rather than a straight line, and a threshold effect involves a non-linear interaction where the effects of the independent variable on the dependent variable change at different levels. Thus, these alternatives do not align with the fundamental principles of linear regression.