Lesson 2: 3.2 Relationships Between Two Quantitative Variables

How do we decide which variable belongs on the x-axis and which belongs on the y-axis?

What are the four characteristics we must use to describe the "story" a scatterplot is telling? (Direction, Form, Strength, Outliers).

Explanatory variable

Response variable

Scatterplot

Direction (Positive/Negative association)

Form (Linear/Non-linear)

Strength

Outliers

HSS-ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

The SAT frequently asks students to identify the "best" description of a relationship shown in a scatterplot. Students must distinguish between "strong" and "weak" associations and recognize linear vs. exponential patterns.

This section transitions students from categorical tables to coordinate planes. The goal is for students to see data as a "cloud" of points and learn to describe that cloud using standard statistical language (DFSO: Direction, Form, Strength, Outliers).

The Problem: A researcher collects data on the body weight (in kg) and the brain weight (in g) of 15 different mammal species.

Task: Construct a scatterplot. Describe the relationship. Are there any species that don't seem to fit the general pattern?

Axis Swap: Students often put the variable they "like" more on the x-axis rather than identifying which variable predicts the other.

Vague Descriptions: Students often say a relationship is "good" or "increasing" instead of using precise terms like "strong, positive, and linear."

Support: Use a "Describing Relationships" graphic organizer (the DFSO checklist) to ensure they hit all four required descriptors every time.

Extension: Provide a scatterplot with a "hidden" variable (like gender or age) and have students use different colors or symbols to see if the relationship changes when the third variable is revealed.

Teacher assigns examples from the textbook and other resources.

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