Scatter Diagram and Correlation

A scatter diagram is a graphical representation of the relationship between two variables. It shows the values of the variables as points in a two-dimensional space, with one variable on the x-axis and the other variable on the y-axis.

Correlation is a statistical measure of the strength and direction of the relationship between two variables. It ranges from -1 to +1, with values closer to -1 or +1 indicating a stronger relationship and values closer to 0 indicating a weaker relationship.

Single Line Scatter Diagram

If all the plotted points in a scatter diagram lie on a single line, then the correlation can be either perfect positive or perfect negative. This is because a perfect positive correlation indicates that the two variables increase or decrease together in a linear fashion, while a perfect negative correlation indicates that the two variables move in opposite directions in a linear fashion.

However, it is also possible for a scatter diagram with a single line to have a correlation that is not perfect. This can occur if there is some variation in the relationship between the two variables, even though the overall pattern is linear. In this case, the correlation will be a value between -1 and +1, but it will not be perfect.

Conclusion

In conclusion, if all the plotted points in a scatter diagram lie on a single line, then the correlation can be either perfect positive or perfect negative, but it is also possible for the correlation to be a value between -1 and +1 if there is some variation in the relationship between the two variables. Therefore, the correct answer to the given question is option D, either (a) or (b).