Quantitative Aptitude · Correlation and Regression

Scatter Diagram Method of Correlation for CA Foundation

Updated 1 October 2026

A scatter diagram plots each pair of values (x, y) as a point on a graph. The pattern of points shows the direction and strength of correlation. Points rising left to right mean positive correlation, falling mean negative, a tight line means strong, and a shapeless cloud means no correlation.

Understand Scatter Diagram Method

Correlation tells you whether two variables move together. For example, as advertising spend rises, does sales also rise? A scatter diagram (also called a dot diagram) answers this with a picture.

You take paired data, such as (x, y) for each shop or each student. Put x on the horizontal axis and y on the vertical axis. Mark one dot for each pair. The full set of dots is the scatter diagram.

Now read the pattern. If dots drift upward from left to right, y tends to rise when x rises. This is positive correlation. If dots drift downward, y tends to fall when x rises. This is negative correlation. If dots show no direction, there is no correlation.

Strength depends on how closely the dots hug a line. Dots tightly packed around a straight line mean high correlation. Dots widely spread mean low correlation. If all dots lie exactly on one straight line, the correlation is perfect: r = +1 for a rising line and r = -1 for a falling line.

The method is visual only. It gives a rough idea, not an exact number. For a numerical value you need Karl Pearson's coefficient or Spearman's rank correlation.

Key formulas to remember

Perfect positive correlation: r = +1; All points lie on a straight line rising from left to right.
Perfect negative correlation: r = -1; All points lie on a straight line falling from left to right.
No correlation: r = 0; Points are scattered with no pattern. Strictly, r = 0 means no linear relationship.
Range of r: -1 ≤ r ≤ +1; Closer to ±1 means points are closer to a straight line.
Horizontal or vertical line of points: r undefined; If y does not change with x (or the reverse), one variable has zero variance, so r works out to 0 ÷ 0. It is undefined, and no linear correlation can be measured.

How to solve Scatter Diagram Method questions

Use this method for any question that gives a scatter diagram or describes one in words.

1Identify which variable is on the x-axis and which is on the y-axis.
2Look at the overall direction of the dots: rising left to right, falling, or no direction.
3Decide the sign: rising is positive, falling is negative, no direction means r is near 0.
4Judge the strength: dots tightly along a line mean r is close to ±1; widely spread means r is closer to 0.
5Check for a straight line. If dots lie exactly on a line, r is +1 or -1. If they follow a curve, linear correlation may be low.
6Match your conclusion to the options, rejecting any that contradict the sign or strength.
7If asked for an exact value, remember a scatter diagram cannot give it; the answer must be a range or a type.

Quickest way: Slope-and-spread check

When to use it: Use for any MCQ that shows a plot or describes one in words. It takes about 15 seconds.

Trace an imaginary line through the dots. Note whether it goes up, down or flat.
Up gives a positive r, down gives a negative r, flat gives r near 0.
Check the spread: tight means near ±1, loose means near 0.
Cross out options with the wrong sign first. Then pick by strength.
Skip if a curved pattern or unusual wording confuses you, since wrong answers cost 0.25.

Common mistakes in Scatter Diagram Method

Thinking a steep line means higher correlation than a gentle line.
Students confuse slope with strength.
Fix: Strength depends only on how closely the dots follow a line. Any rising or falling (non-horizontal, non-vertical) straight line of points, steep or gentle, gives r = +1 or -1. For a horizontal or vertical line of points, r is undefined because one variable has zero variance, so no linear correlation can be measured.
Saying a horizontal line of dots shows perfect correlation.
The dots lie on a line, so students assume r = 1.
Fix: If y stays constant as x changes, the standard deviation of y is zero, so r is undefined (0 ÷ 0) and no linear correlation can be measured. Perfect correlation needs a rising or falling line.
Treating a falling pattern as weak correlation.
Negative sign is mistaken for low value.
Fix: Sign shows direction, not strength. r = -0.9 is strong. Compare the size of r ignoring the sign.
Claiming the scatter diagram gives the exact value of r.
Students mix it up with Karl Pearson's method.
Fix: It only shows type and rough degree. Exact value needs a formula.
Assuming correlation means one variable causes the other.
A visible pattern feels like proof of cause.
Fix: Correlation shows association only. Both variables may be driven by a third factor.
Calling a curved pattern 'no correlation' without care.
Dots do not follow a straight line.
Fix: The relationship may be non-linear. Say the linear correlation is low or absent, as these topics deal with linear correlation.

Worked examples

Example 1

In a scatter diagram, all points lie exactly on a straight line that falls from left to right. The coefficient of correlation is: (a) +1 (b) -1 (c) 0 (d) -0.5

Show the solution

The points lie exactly on one straight line, so correlation is perfect.
The line falls from left to right, so the correlation is negative.
Perfect negative correlation means r = -1.
Options (a) is wrong in sign, (c) means no pattern and (d) would show scatter.

Answer: (b) -1

Example 2

A scatter diagram shows points rising from left to right but widely spread around the trend. The correlation is best described as: (a) high positive (b) high negative (c) low positive (d) zero

Show the solution

The points rise, so the sign is positive. This rules out (b).
The points are widely spread, so the strength is low. This rules out (a).
There is still a rising trend, so r is not exactly zero. This rules out (d).
The description is low positive correlation.

Answer: (c) low positive

Example 3

Which statement about the scatter diagram method is correct? (a) It gives the exact value of r (b) It is a visual method showing the nature of correlation (c) It proves cause and effect (d) It needs the calculation of standard deviations

Show the solution

The method is plotting dots only, so it cannot give an exact r. (a) is wrong.
Correlation does not prove causation. (c) is wrong.
No standard deviation is used in plotting. (d) is wrong.
It is a simple visual method that shows direction and rough strength, so (b) is correct.

Answer: (b) It is a visual method showing the nature of correlation

Exam tips

Read sign first, strength second. Most options differ in sign, so this eliminates two quickly.
Remember the statement forms: perfect positive means r = +1 and perfect negative means r = -1. These are asked directly.
Questions on merits and demerits are common. Merits: simple, no calculation, shows outliers and pattern. Demerits: no exact value, hard for large data, subjective.
If the question asks for an exact value of r from a plot, look for an option that says it cannot be found by this method.
Do not guess on confusing curve-based questions, as each wrong answer costs 0.25 marks.

Practice questions from Correlation and Regression

Scatter Diagram Method: frequently asked questions

What is the scatter diagram method of correlation?

It is a graphical method where paired values are plotted as dots on x and y axes. The pattern of the dots shows whether correlation is positive, negative or absent, and roughly how strong it is.

What are the merits and demerits of the scatter diagram method?

Merits: it is simple, needs no calculation, is not influenced by the size of extreme items, and gives a quick first idea of the relationship. Demerits: it gives no exact numerical value of r, and it is hard to use for very large or closely packed data.

How do I recognise perfect positive and perfect negative correlation?

If all points lie on a straight line rising from left to right, it is perfect positive, r = +1. If they lie on a straight line falling from left to right, it is perfect negative, r = -1.

What does a scatter diagram with no pattern mean?

It means there is no linear correlation, so r is close to 0. The two variables do not move together in a straight-line way.