Q.A scatter diagram of two variables shows points that lie very close to a straight line running from the upper-left to the lower-right of the graph. What does this tell you about the direction and degree of correlation between the variables?

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.

• It does not give a precise numerical measure of the degree of correlation (unlike Karl Pearson's coefficient), so exact comparison is not possible.

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:

• if the line rises from left to right (positive slope), $r=+1$ (perfect positive correlation);

• if the line falls from left to right (negative slope), $r=-1$ (perfect negative correlation).

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 the degree of correlation. For that, a method such as Karl Pearson's coefficient is needed.