In case of perfect positive correlation the two lines of regression are …………….

Answer

To solve the question regarding the nature of the two lines of regression in the case of perfect positive correlation, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Correlation**:
- Correlation measures the strength and direction of a linear relationship between two variables. A perfect positive correlation means that as one variable increases, the other variable also increases in a perfectly linear manner.

2. **Definition of Regression Lines**:
- Regression lines are used to predict the value of one variable based on the value of another variable. There are two regression lines: the regression line of Y on X (denoted as Y|X) and the regression line of X on Y (denoted as X|Y).

3. **Perfect Positive Correlation**:
- In the case of perfect positive correlation (denoted as a correlation coefficient of +1), the relationship between the two variables is such that the points lie exactly on a straight line with a positive slope.

4. **Behavior of Regression Lines**:
- When there is perfect positive correlation, the two regression lines will not only predict values accurately but will also coincide with each other. This means that both regression lines will be the same line.

5. **Conclusion**:
- Therefore, in the case of perfect positive correlation, the two lines of regression are coincident. This indicates that they overlap completely, representing the same linear relationship between the two variables.

### Final Answer:
In case of perfect positive correlation, the two lines of regression are coincident.

---