Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- Bivariate quantitative data are ordered pairs (x, y) of two quantitative variables measured on the same individuals.
- A scatterplot shows one dot per individual. Do not join the dots.
- The explanatory variable (used to explain or predict) goes on the x-axis. The response variable (being predicted) goes on the y-axis.
- Label both axes with the variable name and units. Use equal steps; an axis need not start at zero.
Key relationships
| Feature | What it describes | Words to use |
|---|---|---|
| Form | the shape of the pattern | linear; non-linear (curved) |
| Direction | what y tends to do as x increases | positive (tends to increase); negative (tends to decrease) |
| Strength | how closely the points follow the pattern | strong; moderate; weak |
| Unusual features | anything that breaks the pattern | unusual points; clusters; gaps |
A model sentence: “There is a strong, negative, non-linear association between age and price of these cars: older cars tend to cost less, and there are no unusual points.”
Assumptions and conventions
- Both variables are quantitative and paired by individual.
- “Explanatory” means “used to predict”, not “causes”.
- If neither variable naturally explains the other, either axis choice is fine.
- A scatterplot can support or challenge a claim. An association alone does not show cause and effect.
Mistakes to avoid
- Swapping the axes: the variable you want to predict goes on the y-axis.
- “Linear because I can draw a line through it”: look for a constant rate of change.
- “Steep, so strong”: steepness and strength are different ideas.
- “Always” instead of “tends to”: associations are tendencies.
- No context: name both variables and say what the direction means.
- Missing unusual features: mention any outlier or cluster, with a possible reason.
- Joining the dots or unequal scale steps.
Quick self-check
- A café owner wants to predict daily soup sales from the outside temperature. Which variable goes on the y-axis? (Daily soup sales: it is the response)
- Points lie very close to a straight line that falls gently. Is the association weak because the slope is small? (No. Close points mean strong; it is a strong, negative, linear association)
- Response values run from 12 to 57. Is a y-axis from 0 to 60 in steps of 10 acceptable? (Yes: equal steps covering all values)
- A scatterplot shows two separate groups of points with a gap between them. What is this feature called? (Clusters)
Next: practice questions.