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Statistics · AP · Exploring Two-Variable Data

What this topic is

In Statistics · AP, this CED topic focuses on: Analyzing Departures from Linearity. In plain terms, students should be able to explain the main idea in their own words and complete a straightforward practice item with justification.

This topic is assessed on the AP Exam.

Why it matters

• Two-variable exploration (scatterplots, correlation, regression) is core AP Stats.
• Students must interpret slope, intercept, and r/r² in context—not as bare numbers.
• Residual analysis shows whether a linear model is appropriate.
• Extrapolation and confusing association with causation are classic traps.

How you can support

• Ask: “Is the association positive or negative, and is linear reasonable?”
• Have them interpret slope in a full sentence with units.
• Celebrate a correct residual = observed − predicted check.
• Ask what r² means in plain words (percent of variation explained).
• Discuss one point that might be influential or an outlier.

What not to do

• Do not treat correlation as causation.
• Do not extrapolate far beyond the data without flagging risk.
• Do not confuse r with slope.
• Do not ignore a curved residual pattern that says “linear model is weak.”