Consider the following statements: 1 If the correlation coefficient `r_(xy)=0`, then the two line of regression are parallel to each other r
2. If the correlation coefficient `r_(xy)=+1` then the two lines of regression are perpendicular to each other Which of the above statements are correct?

Options

A. 1only
B. 2only
C. Both I and II
D. Neither I nor II

Answer

To determine the correctness of the given statements regarding the correlation coefficient and the lines of regression, we will analyze each statement step by step.

### Step 1: Analyze the First Statement
The first statement claims that if the correlation coefficient \( r_{xy} = 0 \), then the two lines of regression are parallel to each other.

- **Understanding Correlation Coefficient**: The correlation coefficient \( r_{xy} \) measures the strength and direction of a linear relationship between two variables \( x \) and \( y \).
- **Interpretation of \( r_{xy} = 0 \)**: When \( r_{xy} = 0 \), it indicates that there is no linear relationship between the variables. In terms of regression lines, this means that the lines of regression are actually perpendicular to each other, not parallel.

**Conclusion for Statement 1**: The first statement is **incorrect**.

### Step 2: Analyze the Second Statement
The second statement claims that if the correlation coefficient \( r_{xy} = +1 \), then the two lines of regression are perpendicular to each other.

- **Interpretation of \( r_{xy} = +1 \)**: A correlation coefficient of \( +1 \) indicates a perfect positive linear relationship between the variables. In this case, the two lines of regression are not perpendicular; instead, they are parallel to each other.

**Conclusion for Statement 2**: The second statement is **incorrect**.

### Final Conclusion
Since both statements are incorrect, the answer to the question is that neither statement 1 nor statement 2 is correct.

**Answer**: Option 4: Neither 1 nor 2.

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