Linear regression is used to model the relationship between which of the following variables?

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. This approach is particularly useful for predicting the dependent variable based on the values of the independent variables, allowing for the assessment of how changes in the independent variables affect the dependent variable.

In this context, the dependent variable is the outcome or the variable that you are trying to predict, while the independent variables are the predictors or features that influence that outcome. The essence of linear regression is in establishing this relationship, which is why the correct option is that it involves both dependent and independent variables.

The other options fall short because independent variables on their own do not provide a complete picture of analysis; they need to be related to a dependent variable for modeling purposes. Similarly, using only dependent variables does not facilitate prediction or understanding of their relationships. Lastly, linear regression is not confined to categorical variables; it can include continuous variables as well, making it versatile in modeling various types of data. Therefore, understanding the interaction between both dependent and independent variables is crucial for effective application of linear regression techniques.