Scatterplots & Association

You’ll be able to

Identify explanatory and response variables and plot them correctly
Describe a scatterplot by direction, form, strength, and unusual features
Distinguish association from causation

Explanatory and response variables

With two quantitative variables, we often treat one as the explanatory variable (the presumed cause or predictor, plotted on the x-axis) and the other as the response variable (the outcome, plotted on the y-axis). Choosing which is which is a judgment about the question you are asking — we use hours studied to predict exam score, not the reverse.

Describing a scatterplot: DUFS

Describe a scatterplot with four features — Direction (positive: y rises as x rises; negative: y falls as x rises), Unusual features (outliers, distinct clusters), Form (linear or curved), and Strength (how tightly the points cluster around the pattern — strong, moderate, or weak). As always, describe it in context with the variable names.

Association is not causation

A scatterplot can show a strong association, but that alone never proves that one variable causes the other. A lurking variable may drive both. Ice cream sales and drowning deaths rise together, but neither causes the other — hot weather drives both. Only a well-designed experiment with randomization can establish causation.

Watch out

Even a perfectly straight, strong association is not proof of cause and effect. Observational data can reveal association only. Reserve the word "causes" for randomized experiments, and always ask what lurking variable might explain the link.

Worked example

A scatterplot of hours studied (x) versus exam score (y) for 30 students shows points rising steadily to the right, tightly clustered around a straight line, with one student who studied 8 hours but scored very low. Describe the association.

1.Direction: as hours studied increases, exam score increases, so the direction is positive.
2.Form: the points follow a straight-line pattern, so the form is linear.
3.Strength: the points cluster tightly around the line, so the association is strong.
4.Unusual feature: the student who studied 8 hours but scored very low is an outlier that departs from the pattern.

Answer: There is a strong, positive, linear association between hours studied and exam score, with one outlier (a student who studied a lot but scored low). More studying is associated with higher scores among these students.

Checkpoint

A researcher wants to use a car’s weight to predict its fuel economy (miles per gallon). Which variable should be on the x-axis?

Tip

Remember DUFS for scatterplots — Direction, Unusual features, Form, Strength — the two-variable cousin of SOCS. Every scatterplot description on the exam should touch all four, in context.

Checkpoint

Cities with more firefighters at a blaze tend to have more fire damage. A student concludes that firefighters cause damage. What is the best critique?

Answer the 2 checkpoints as you read.