AP®︎ Statistics (pre-2026): Unit 9 Flashcards

The strength and direction of a linear relationship between two quantitative variables.

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

A third variable related to both variables that can create or distort an observed association.

Unpredictable scatter around a line is random, while consistent departures indicate systematic bias.

The observed y-value minus the predicted y-value from the sample regression line.

The sample slope b estimates β, and across many samples b is centered at β.

It estimates σ by √[Σ(y−ŷ)²/(n−2)] because two regression parameters are estimated.

Check linearity, constant variance, independence, and approximately normal responses for each x-value.

The sample regression slope b from the least-squares regression line.

A zero slope suggests no linear association; a positive or negative slope suggests linear association.

With all else fixed, larger samples produce narrower confidence intervals for the slope.

Higher confidence levels produce wider intervals because they require larger critical values.

In repeated same-size random samples, about C% of intervals capture the true slope.

State that you are C% confident the population slope lies between the endpoints in context.

Support claims whose slope values fall inside the interval and question values outside it.

An interval of plausible values for the true population regression slope β, typically computed as b ± t*SEb.

Compute the confidence interval for the slope as b ± t*SEb, where t* is the critical value from the t distribution with n - 2 degrees of freedom.

The standard error of the slope, SEb, estimates the variability of the sample slope from sample to sample, and the margin of error is t*SEb.

A significance test using a t-distribution to evaluate a population regression slope.

Check linearity, equal variance, independence, and normality using residual plots and residual graphs.

Compute t = (b - β0) / SEb to compare the sample slope to the hypothesized slope.

Assuming conditions hold and H0 is true, the standardized slope statistic follows a t-distribution.

Reject H0 if p-value ≤ α; otherwise, fail to reject H0.

State whether there is convincing evidence that the true population slope differs from the null value.

Use β < β0 or β > β0 for directional claims, and β ≠ β0 for any difference.

It is the probability, assuming β equals the null value, of results this extreme.

For inference about the slope in simple linear regression, use df = n - 2 because both the intercept and slope are estimated.

State hypotheses for the population slope as H0: β = β0 and Ha: β < β0, β > β0, or β ≠ β0, depending on the claim.

Choose the method by identifying parameter type, number of samples, design, and variable type.

Estimate a plausible parameter range with an interval, or evaluate a claim with a test.

Use for one population proportion; z-interval estimates it, z-test compares it to a claimed value.

Use for one population mean; t-interval estimates it, t-test compares it to a claimed value.

Use for comparing two population proportions; z-interval estimates difference, z-test tests claimed difference.

Tests whether one categorical variable's distribution matches a claimed distribution.

Tests whether two categorical variables are associated in one population.

Tests whether categorical distributions are the same across multiple populations or treatments.

Use for slope inference in least-squares regression; interval estimates slope, test checks if slope equals zero.

Goodness of fit compares one distribution, independence checks association, homogeneity compares group distributions.

Use z procedures for categorical proportions and t procedures for quantitative means.

Use paired differences for linked data and two-sample methods for independent groups.

Use slope inference for two quantitative variables, often using regression computer output.