The further the two regression lines cut each other, the …………. Be the degree of correlation.

Answer

To solve the question, "The further the two regression lines cut each other, the …………. Be the degree of correlation," we need to analyze the relationship between the distance of the regression lines and the degree of correlation.

### Step-by-Step Solution:

1. **Understanding Regression Lines**:
- In statistics, regression lines are used to predict the value of one variable based on the value of another. The two regression lines typically considered are:
- Regression of Y on X (denoted as Y|X)
- Regression of X on Y (denoted as X|Y)

2. **Properties of Regression Coefficients**:
- The regression coefficients indicate the strength and direction of the relationship between the two variables.
- If the regression coefficient is zero, it indicates that there is no correlation between the variables, and the regression lines will be perpendicular to each other.

3. **Correlation and Regression Lines**:
- If the correlation is perfect (either positive or negative), the two regression lines will coincide, meaning they will overlap completely.
- If the correlation is weak, the regression lines will be further apart from each other.

4. **Analyzing the Question**:
- The question states that "the further the two regression lines cut each other," which implies that they are moving away from each other.
- This indicates a weaker correlation between the two variables.

5. **Conclusion**:
- Therefore, we can conclude that "the further the two regression lines cut each other, the lesser will be the degree of correlation."

### Final Answer:
The further the two regression lines cut each other, the lesser will be the degree of correlation.

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