Which statistical method utilizes linear equations to model the relationship between variables?

The statistical method that utilizes linear equations to model the relationship between variables is linear regression. This technique is foundational in statistics and machine learning, as it allows analysts to understand how changes in one or more independent variables affect a dependent variable.

In linear regression, a linear equation is formulated, which represents the relationship among the variables. The model estimates the coefficients that quantify this relationship, enabling predictions about the dependent variable based on new inputs of the independent variables. It assumes a linear relationship, meaning that it can be graphically represented as a straight line on a two-dimensional plot, where one axis represents the dependent variable, and the other represents the independent variable(s).

Understanding this concept is crucial because it serves as the groundwork for more complex modeling techniques in data analysis, helping practitioners to make informed decisions based on statistical inference drawn from the data. In contrast, the other options do not pertain to statistical modeling in the same way. For instance, long-short-term memory refers to a type of neural network architecture designed for sequence prediction, loss function pertains to the objective measure of how well a model performs, and levels of autonomy relate to the degree of independence of an automated system. Each of these serves distinct purposes in their respective fields and does not specifically utilize linear equations