Why three are two regression lines?

In statistical analysis, there are typically two regression lines when examining relationships between variables in a context involving both dependent and independent variables, or in cases of different groups within the data. For instance, in a simple linear regression, one line represents the relationship between the independent variable (predictor) and the dependent variable (outcome). Conversely, in a multiple regression scenario, a second line could represent an alternate model or subgroup, allowing for comparisons between different categories or to account for additional predictors. Thus, two regression lines can help illustrate the complexity of relationships in the data.