AP®︎ Statistics (pre-2026): Unit 2 Flashcards

Categorical variables place individuals into groups; quantitative variables record numerical amounts or measurements.

Graphs for two categorical variables that compare conditional proportions across groups.

A visible trend or structure in data that may reflect a real relationship or random variation.

Natural chance-based differences in data that can create misleading patterns.

Data on two variables for each individual, which may be categorical or quantitative.

A relationship between variables that can be positive, negative, or absent.

A proportion describing one variable within a specific category of another variable.

A cell count divided by the total number of observations in the entire table.

Counts show numbers in each cell; relative frequencies show proportions or percents instead.

Bars for one categorical variable are grouped by categories of a second variable for comparison.

Each bar represents one group and is divided into segments showing category proportions within that group.

A graph of rectangles whose areas represent joint relative frequencies for two categorical variables.

Compare conditional proportions across groups to judge whether two categorical variables are associated.

A table that displays counts or relative frequencies for all combinations of two categorical variables.

A row or column total divided by the grand total in a two-way table.

A cell count divided by its row or column total, showing a category's share within a given group.

Variables are associated when conditional relative frequencies differ across groups and independent when the conditional distributions are the same.

Data consisting of paired numerical measurements for two variables on each individual.

The explanatory variable goes on the horizontal axis and the response variable on the vertical axis.

Describe association by form, direction, strength, and unusual features, in context.

The overall shape of the association, usually linear or nonlinear.

The overall trend of the points, described as positive or negative.

How closely the points follow the overall pattern, such as strong, moderate, or weak.

Patterns that stand out, especially clusters or points far from the overall pattern.

A group of nearby points that may suggest a subgroup within the data.

A point with a response value far from what the overall pattern would predict.

The x-variable explains or predicts, and the y-variable records the resulting outcome.

An increasing pattern is positive, while a decreasing pattern is negative.

A straight-line pattern is linear, while a curved pattern is nonlinear.

A graph of paired quantitative data with one variable on each axis.

A number from -1 to 1 measuring the direction and strength of a linear relationship.

r = 1 is perfect positive linear association, r = -1 perfect negative, and r = 0 no linear association.

It has no units because it is based on standardized values, not original measurement scales.

r = (1/(n - 1)) times the sum of paired x and y z-score products.

Use statistical software or a graphing calculator to compute r from paired quantitative data.

It describes how closely points follow a straight-line pattern, not curved or other nonlinear patterns.

A value near 1 or -1 can occur even when a curved pattern makes a linear model inappropriate.

An association between two variables does not prove that one variable causes changes in the other.

Extreme points can strongly change the value because the calculation uses means and standard deviations.

The sign shows direction, and the size shows the strength of linear association.

An equation using one explanatory variable x to predict a response variable y.

The model's estimated y-value for a given explanatory-variable value x.

b is the change in predicted y per 1-unit x increase; a is predicted y when x = 0.

Use ŷ = a + bx to calculate the predicted response for a given x-value.

Predictions within observed x-values are safer; beyond them, predictions are extrapolations and less reliable.

Positive means the model underestimated; negative means the model overestimated the actual response.

The vertical distance from a data point to the regression line on a scatterplot.

The difference between an observed response and its predicted value, found by y minus y-hat.

A graph of residuals versus explanatory or predicted values used to assess model fit.

Random scatter supports a linear model, while curved patterns suggest a nonlinear relationship.

Residuals are observed minus predicted values; squaring prevents cancellation and emphasizes larger errors.

Predicted response equals y-hat = a + bx, with a as intercept and b as slope.

The predicted change in y for each 1-unit increase in x.

Compute slope with b = r(sy/sx), using correlation and the variables' standard deviations.

Compute intercept with a = y-bar - b x-bar.

The regression line always contains the point of the sample means.

The square of r; the proportion of y-variation explained by its linear relationship with x.

State the percent of variation in the response variable explained by the linear model with x.

The predicted y-value when x = 0, though it may lack meaning in context.

The line y-hat = a + bx that minimizes the sum of squared residuals and best fits the data.

A data point whose removal substantially changes the regression line or correlation.

A point far from the overall pattern vertically, with a large residual.

A point with an x-value much farther from the others than most observations.

Outliers are unusual in y with large residuals; high-leverage points are unusual in x.

A new data set created by applying a function to x, y, or both.

Applying transformations so a curved pattern becomes approximately linear for regression.

A nonlinear model of the form y-hat = ab^x, with constant multiplicative change.

A nonlinear model of the form y-hat = ax^b, relating variables by powers.

Take ln(y) so the model becomes linear: ln(y-hat) = ln(a) + x ln(b).

Take ln(x) and ln(y) so the model becomes linear: ln(y-hat) = ln(a) + b ln(x).

A better model has residuals that look more random and less curved after transformation.

A transformed model is stronger when its r-squared moves closer to 1.

Use the transformed line, then undo the transformation to predict on the original scale.

Outliers and high-leverage points are often influential because they can strongly change regression results.