The two regression lines become identical if the correlation coefficient isans.

The two regression lines become identical if the correlation coefficient is 1 or -1. Here's why:

1. Regression lines are used to model the relationship between two variables. In simple linear regression, we have two lines: the regression of Y on X and the regression of X on Y.

2. The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1. A correlation coefficient of 1 means that for every positive increase in one variable, there is a positive increase of a fixed proportion in the other. A correlation coefficient of -1 means that for every positive increase in one variable, there is a negative decrease of a fixed proportion in the other.

3. If the correlation coefficient is 1 or -1, it means there is a perfect linear relationship between the two variables. In this case, the two regression lines would coincide, i.e., they would become identical. This is because the regression line perfectly predicts the relationship between the two variables without any error.

4. In all other cases (when r is not equal to 1 or -1), the two regression lines would not be identical. This is because there would be some error in predicting the relationship between the two variables.