Q.The monthly income (X) and monthly savings (Y) of 8 households are plotted on a scatter diagram, and the points are found to cluster closely around an upward-sloping straight line. What does this scatter diagram suggest about the correlation between income and savings, and would you expect the numerical value of $r$ to be closer to $0$ or closer to $+1$?

The scatter diagram method gives only a visual impression of correlation; its main limitation is that it cannot provide the exact numerical value (degree) of correlation.

GSEB Class-12 Statistics, Linear Correlation:

A scatter diagram plots paired observations $(x, y)$ as points and lets us judge whether correlation is positive, negative or absent, and roughly how close the points are.

However, its main limitation is:

• It only shows the direction and approximate strength of correlation visually. …

All points on a single straight line means perfect correlation: $r=+1$ (rising line) or $r=-1$ (falling line).

In a scatter diagram the closeness of points to a straight line indicates the strength of linear correlation. If every plotted point lies exactly on one straight line, the linear relationship is perfect: …

The scatter diagram shows only the direction and a rough sense of the closeness of the relationship; it cannot give an exact numerical value of the correlation coefficient.

Explanation. By plotting paired $(x,y)$ values, a scatter diagram lets us see at a glance whether the relationship is positive, negative or absent, and roughly how close the points lie to a line. However, it is purely visual: two people may judge the same diagram differently, and it provides no formula-based, exact numerical measure of th …