Confidence interval for slope

Math

Definition

A confidence interval for slope estimates the range of plausible values for the true slope of a population regression line based on sample data. It uses the sample slope, standard error of the slope, and a t-critical value.

Examples

  • A 95% CI for slope of (0.3, 0.8) means we're 95% confident the true slope is between 0.3 and 0.8
  • If a CI for slope contains 0, there may be no linear relationship
  • Estimating how much each additional hour of study increases test scores
Key Fact

CI: b₁ ± t* · SE(b₁), where b₁ is the sample slope

Related Terms

Least-squares regression Slope inference T-test for slope Confidence intervals for proportions

Study This Concept

Practice confidence interval for slope with free review games in these units:

AP Statistics Unit 9: Inference for Regression