What does regression analysis provide in terms of mathematical relationships?

Regression analysis is a statistical method used to examine the relationship between one dependent variable and one or more independent variables. The purpose of regression analysis is to determine how these variables are related and to formulate a mathematical equation that best represents this relationship.

The correct answer highlights that regression analysis yields a best-fit mathematical equation. This equation not only helps predict values of the dependent variable based on different inputs of the independent variables but is also constructed using methods that minimize the differences between actual data points and the values predicted by the equation. This process is fundamental in many fields, including economics, engineering, and social sciences, as it provides a structured approach to understanding relationships within data sets.

Other options do not accurately reflect what regression analysis accomplishes; it does not produce random equations, which implies a lack of reliability or correlation. Subjective evaluation does not typically apply to statistical methods, as regression relies on systematic numerical analysis rather than personal judgment. Lastly, while regression analysis does involve statistical analysis, describing it simply as fixed overlooks the dynamic nature of the best-fit equation that is derived from data and can change with the introduction of new variables or data points.