While drawing a scatter diagram if the plotted lie on a straight line ...
Understanding Scatter Diagrams
Scatter diagrams are graphical representations used to identify relationships between two variables. When plotted on a Cartesian plane, the arrangement of points can provide insights into the correlation and nature of the relationship.
Scatter Plots on Straight Lines
When the points in a scatter diagram lie on a straight line that is either parallel to the x-axis or the y-axis, this indicates specific types of relationships:
Parallel to the X-Axis:
- This configuration suggests that the dependent variable remains constant regardless of changes in the independent variable.
- It indicates a zero correlation. For instance, if temperature (x-axis) is plotted against the number of ice creams sold (y-axis) and the points lie flat, it means ice cream sales do not change with varying temperatures.
Parallel to the Y-Axis:
- Here, the independent variable remains constant while the dependent variable varies.
- This scenario is less common in practical applications but signifies that the dependent variable can take any value regardless of the independent variable's value.
- It implies a vertical line with an undefined slope, indicating that the relationship is not functional (i.e., one value of the independent variable corresponds to multiple values of the dependent variable).
Implications of These Relationships
- Understanding these configurations helps in statistical analysis and predictive modeling.
- They indicate the absence of a linear relationship, prompting further investigation into other types of relationships (e.g., non-linear).
In conclusion, scatter diagrams are instrumental in revealing the nature of relationships between variables, especially when points align along straight lines parallel to the axes, indicating specific correlation types.
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