What statistical technique is used to predict a variable when a second variable is known, typically represented as a linear equation?

The correct answer is regression because it specifically relates to the statistical technique where one variable is used to predict another variable through a linear equation. In regression analysis, a dependent variable is predicted based on the values of one or more independent variables. The linear equation derived from this analysis allows researchers to quantify the relationship between the variables and to make predictions about the dependent variable based on known values of the independent variable(s).

This method is particularly valuable in various fields such as economics, psychology, and healthcare, where understanding how different factors influence an outcome is crucial. By establishing the line of best fit through the data points, regression provides insight into how changes in the predictor variable are associated with changes in the predicted variable.

In contrast, correlation measures the strength and direction of a linear relationship between two variables but does not establish predictive capability. Variance analysis, often referred to as ANOVA, focuses on comparing means across different groups and is used primarily for hypothesis testing rather than prediction. Factor analysis is utilized to identify underlying relationships between variables, grouping them into factors; it does not create a predictive model for a dependent variable.