Describe correlation in bivariate data

Detailed Explanation: Describe correlation in bivariate data

Correlation describes how two quantitative variables tend to vary together. To describe correlation from a scatterplot, look at:

• Direction:
  • Positive: as one variable increases, the other tends to increase.
  • Negative: as one variable increases, the other tends to decrease.
  • Negligible: there is little clear trend.
• Strength: Decide whether the points follow the trend closely or are widely scattered.
• Form: Check whether the pattern is roughly linear or curved.
• Unusual points: Look for points that do not fit the overall pattern.

Worked example

A scatterplot compares hours studied with test score. The plotted points are approximately:

Here, the first coordinate represents hours studied and the second represents test score.

Step 1: Identify the direction.
Most points rise from left to right. Students who study more hours generally have higher scores. This is a positive association.

Step 2: Describe the strength.
The first six points are fairly close to an upward trend, so the association is fairly strong for those points. However, the point $(7,55)$ is far from the trend. It is an unusual point, which makes the overall association weaker.

Step 3: Describe the form.
The main pattern is approximately a straight-line pattern, so it is roughly linear.

Step 4: Write a complete conclusion.
A suitable description is:

The scatterplot shows a moderate positive linear association between hours studied and test score. Most students who study more hours tend to earn higher scores, but the point representing $7$ hours and a score of $55$ is unusual and weakens the association.

Remember that correlation describes an association, not cause and effect. This scatterplot does not prove that studying more hours causes higher scores; other factors could also be involved. Also, if a scatterplot has a clear curved pattern, do not describe it as a strong linear correlation.