Consider the following statements:1. If the correlation coefficient rxy = 0, then the two lines of regression are parallel to each other.2. If the correlation coefficientrxy = +1 , then the two lines of regression are perpendicular to each other.Q. Which of the above statements is/are correct?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Understanding the statements:
The given statements are about the relationship between the correlation coefficient and the lines of regression. Let's understand what each statement means:

1. If the correlation coefficient rxy = 0, then the two lines of regression are parallel to each other.
- This statement suggests that when the correlation coefficient is zero, the lines of regression will be parallel.

2. If the correlation coefficient rxy = 1, then the two lines of regression are perpendicular to each other.
- This statement implies that when the correlation coefficient is one, the lines of regression will be perpendicular to each other.

Evaluating the statements:
Now, let's evaluate each statement to determine their correctness:

1. If the correlation coefficient rxy = 0, then the two lines of regression are parallel to each other.
- This statement is incorrect. The correlation coefficient measures the strength and direction of the linear relationship between two variables. A correlation coefficient of zero indicates no linear relationship between the variables. However, it does not necessarily imply that the lines of regression will be parallel. The lines of regression depend on the relationship between the independent and dependent variables, not just the correlation coefficient.

2. If the correlation coefficient rxy = 1, then the two lines of regression are perpendicular to each other.
- This statement is also incorrect. A correlation coefficient of one indicates a perfect positive linear relationship between the variables, but it does not imply that the lines of regression will be perpendicular. The lines of regression represent the best-fit line that minimizes the sum of squared residuals, and they are determined by the data points, not just the correlation coefficient.

Conclusion:
Based on the evaluation of the statements, we can conclude that neither statement 1 nor statement 2 is correct. The relationship between the correlation coefficient and the lines of regression is not as simple as suggested by these statements. The lines of regression depend on the data points and the relationship between the variables, while the correlation coefficient measures the strength and direction of the linear relationship.

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