AP Statistics Unit 2: Exploring Two-Variable Data

Two-variable data asks whether one quantity tells you something about another. For two categorical variables you build a two-way table and compare conditional relative frequencies: if the distribution of one variable changes across the categories of the other, the variables are associated.

For two quantitative variables you start with a scatterplot and describe direction, form, strength and unusual points. When the form is linear, the correlation $r$ measures strength and the least-squares regression line $\hat{y} = a + bx$ gives predictions. Residuals, $y - \hat{y}$, tell you how far each point sits from the line, and a residual plot with no pattern supports a linear model.