← Statistics syllabus

United StatesStatistics

Unit 2: Exploring Two-Variable Data

9 dot points across 9 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we identify outliers and influential points, and how do transformations rescue a non-linear relationship?

Topic 2.9 Analyzing Departures from Linearity: identify outliers, high-leverage, and influential points in regression, and use transformations to model a non-linear relationship.
A focused answer to AP Statistics Topic 2.9, on regression outliers, high-leverage and influential points, and using transformations (logs and powers) to linearise a curved relationship, with a worked transformation example.
10 min answer →

What does the correlation coefficient r measure, and what are its limits?

Topic 2.5 Correlation: calculate and interpret the correlation coefficient r, understand its properties (range, unit-free, resistance), and recognize what it can and cannot tell you.
A focused answer to AP Statistics Topic 2.5, defining the correlation coefficient r, its range and properties (unit-free, symmetric, non-resistant), what it measures and misses, and the correlation-causation caution, with a worked interpretation.
9 min answer →

How do we ask whether two variables are related, and what does an association really mean?

Topic 2.1 Introducing Statistics - Are Variables Related?: identify questions about the association between two variables, distinguish association from causation, and recognize what two-variable data can answer.
A focused answer to AP Statistics Topic 2.1, on framing questions about the association between two variables, the difference between explanatory and response variables, why association is not causation, and what two-variable data can answer, with worked examples.
9 min answer →

What makes the least-squares line the best line, and what do its formulas and r-squared tell us?

Topic 2.8 Least Squares Regression: determine the least-squares regression line from summary statistics, and interpret the coefficient of determination r-squared and the standard deviation of the residuals.
A focused answer to AP Statistics Topic 2.8, on why the least-squares line minimizes squared residuals, computing it from means, standard deviations, and r, and interpreting r-squared and s, with full worked calculations.
10 min answer →

How does a linear regression model predict one variable from another, and how do we interpret its slope and intercept?

Topic 2.6 Linear Regression Models: write, interpret, and use a least-squares regression equation to predict a response, interpreting the slope and intercept in context, and recognizing the danger of extrapolation.
A focused answer to AP Statistics Topic 2.6, on the form of a regression equation, interpreting slope and intercept in context, making predictions, and the danger of extrapolation, with a worked prediction and interpretation.
10 min answer →

How do scatterplots display two quantitative variables, and how do we describe what we see?

Topic 2.4 Representing the Relationship Between Two Quantitative Variables: construct and describe scatterplots by direction, form, strength, and unusual features, in context.
A focused answer to AP Statistics Topic 2.4, on building scatterplots and describing them by direction, form, strength, and unusual features (the DUFS framework), in context, with a worked description.
9 min answer →

How do we display two categorical variables together, and what do two-way tables and segmented bar graphs reveal?

Topic 2.2 Representing Two Categorical Variables: construct and interpret two-way (contingency) tables and segmented or side-by-side bar graphs for two categorical variables.
A focused answer to AP Statistics Topic 2.2, on building and reading two-way tables and segmented or side-by-side bar graphs for two categorical variables, with marginal totals and a worked table.
9 min answer →

What is a residual, and how does a residual plot reveal whether a linear model fits?

Topic 2.7 Residuals: calculate and interpret residuals, construct and read residual plots, and use them to assess whether a linear model is appropriate.
A focused answer to AP Statistics Topic 2.7, defining the residual as observed minus predicted, interpreting positive and negative residuals, and using residual plots to judge whether a linear model is appropriate, with worked calculations.
9 min answer →

How do joint, marginal, and conditional proportions help us decide whether two categorical variables are associated?

Topic 2.3 Statistics for Two Categorical Variables: calculate joint, marginal, and conditional relative frequencies from a two-way table, and use conditional distributions to judge association.
A focused answer to AP Statistics Topic 2.3, on joint, marginal, and conditional relative frequencies from two-way tables, and using conditional distributions to assess association, with full worked proportion calculations.
10 min answer →