The two regression lines become identical if the correlation coefficient is either +1 or -1.

Here's the step by step explanation:

1. The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1.

2. A correlation coefficient of +1 indicates a perfect positive linear relationship between the variables. This means that as one variable increases, the other variable also increases at a constant rate. In this case, the regression lines of Y on X and X on Y will coincide, i.e., they will be identical.

3. Similarly, a correlation coefficient of -1 indicates a perfect negative linear relationship between the variables. This means that as one variable increases, the other variable decreases at a constant rate. In this case too, the regression lines of Y on X and X on Y will coincide, i.e., they will be identical.

4. For any other value of the correlation coefficient, the two regression lines will not be identical. They will intersect at the point of averages (average X, average Y), but they will not coincide.

Question

The two regression lines become identical if the correlation coefficient is either +1 or -1.

Here's the step by step explanation:

1. The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1.

2. A correlation coefficient of +1 indicates a perfect positive linear relationship between the variables. This means that as one variable increases, the other variable also increases at a constant rate. In this case, the regression lines of Y on X and X on Y will coincide, i.e., they will be identical.

3. Similarly, a correlation coefficient of -1 indicates a perfect negative linear relationship between the variables. This means that as one variable increases, the other variable decreases at a constant rate. In this case too, the regression lines of Y on X and X on Y will coincide, i.e., they will be identical.

4. For any other value of the correlation coefficient, the two regression lines will not be identical. They will intersect at the point of averages (average X, average Y), but they will not coincide.

Knowee AI · Accepted Answer

The two regression lines become identical if the correlation coefficient is either +1 or -1.

Here's the step by step explanation:

1. The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1.

2. A correlation coefficient of +1 indicates a perfect positive linear relationship between the variables. This means that as one variable increases, the other variable also increases at a constant rate. In this case, the regression lines of Y on X and X on Y will coincide, i.e., they will be identical.

3. Similarly, a correlation coefficient of -1 indicates a perfect negative linear relationship between the variables. This means that as one variable increases, the other variable decreases at a constant rate. In this case too, the regression lines of Y on X and X on Y will coincide, i.e., they will be identical.

4. For any other value of the correlation coefficient, the two regression lines will not be identical. They will intersect at the point of averages (average X, average Y), but they will not coincide.

The two regression lines become identical if the correlation coefficient is

Question

Solution

Similar Questions

Upgrade your grade with Knowee