When does both the regression lines coincide

In the context of regression analysis, two regression lines coincide when they represent the same line of best fit for the data. This occurs when the relationship between the independent and dependent variables is identical in both regression models.

If you're referring to simple linear regression (where there's only one independent variable), the regression lines coincide when the correlation coefficient between the independent and dependent variables is ±1. In this case, the slope of the regression line will be the same, and they will overlap perfectly.

For multiple linear regression (where there are multiple independent variables), the regression lines coincide when the coefficients of the independent variables in both models are exactly the same. This indicates that the relationship between the dependent variable and each independent variable is the same in both models.

In practical terms, coinciding regression lines mean that the relationship between variables is perfectly consistent across different analyses or datasets. However, perfect coincidence is rare in real-world data due to measurement error, sampling variability, and other factors.