A scatter plot shows two quantitative variables measured on the same individuals: each dot is one individual, placed at $(x, y)$. In this unit we learn to describe, measure and model the pattern those dots make.
Key idea
Put the explanatory variable (the one that may explain or predict) on the x-axis and the response variable on the y-axis. Describe a scatterplot by its direction (positive or negative), form (linear or curved), strength (how tightly the dots follow the form) and any unusual features (outliers, clusters).
Why it works
Direction, form and strength answer the questions we care about: Does y tend to go up or down as x grows? Would a straight line describe the pattern, or would a line miss a bend? How well could knowing x help you predict y? A loose cloud means x tells you little; a tight band means x tells you a lot.
Worked example: Describing a scatterplot
Describe the relationship between a used car's age and its price in the plot above.
- Direction: as age goes up, price goes down, so the association is negative.
- Form: the dots fall along a straight line, not a curve: linear.
- Strength: the dots stay very close to that line: strong.
- Unusual features: none stand out.
Answer: A strong, negative, linear association, with no outliers.
Worked example: Which variable goes where?
A study asks whether the amount of rain in spring helps predict the summer corn harvest. Which variable goes on the x-axis?
- Spring rain could influence the harvest, not the other way around.
- So rain is explanatory (x) and harvest is the response (y).
Answer: Spring rainfall on the x-axis; harvest on the y-axis.
Common mistake
Calling a curved pattern "no association" because it is not a line. The speed and fuel-economy plot shows a strong relationship; it is just not linear. Always describe the form before judging strength.
"Positive" and "negative" describe direction only. A negative association, such as car age and price, can be just as strong and useful as a positive one.