When r=0 the regression lines are A) parallel to each other B) Perpend...
Parallel or Perpendicular Regression Lines when r=0
Regression lines are used to represent the relationship between two variables in a dataset. When the correlation coefficient (r) between two variables is 0, it indicates that there is no linear relationship between them.
Parallel Regression Lines
- When r=0, it means that there is no correlation between the two variables. In this case, the regression lines will be parallel to each other.
- Parallel regression lines indicate that the two variables do not have a linear relationship with each other, but they may still have a different type of relationship (e.g., quadratic, exponential).
Perpendicular Regression Lines
- When r=0, it does not imply that the regression lines are perpendicular to each other. The correlation coefficient specifically measures the linear relationship between variables, not the angle between regression lines.
Conclusion
- Therefore, when r=0, the regression lines are parallel to each other because there is no linear relationship between the two variables. It is essential to understand that correlation coefficient of 0 does not imply perpendicular regression lines, but rather indicates the absence of a linear relationship.