Statistics / Unit 4: Two-Variable Data
4.1 Scatterplots and Association
Notes
Two-variable data record two quantitative variables for each individual. The explanatory variable ($x$) is used to explain or predict the response variable ($y$).
- A scatterplot plots each individual as a point $(x, y)$.
- Describe a scatterplot by direction (positive or negative), form (linear or curved), strength (how tightly the points follow the form) and unusual points.
- Positive association: as $x$ increases, $y$ tends to increase. Negative: as $x$ increases, $y$ tends to decrease.
- Example: Hours studied (explanatory) and exam score (response) usually show a positive association.
Practice
A researcher wants to predict a student's exam score from the hours the student studied. The explanatory variable is:
The explanatory variable is the one used to predict or explain the response.
A scatterplot of points rising from left to right, all close to a straight line, shows:
Rising means positive. Points close to a line mean strong.
Which situation describes a negative association?
In a negative association, as one variable increases the other decreases.
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