Slope inference

Math

Definition

Statistical procedures for making inferences about the true slope of a population regression line based on sample data. This includes constructing confidence intervals for the slope and performing hypothesis tests to determine whether the slope is significantly different from zero.

Examples

  • Testing whether hours studied has a statistically significant linear relationship with exam scores
  • Constructing a 95% confidence interval for the slope of the regression line predicting income from education years
Key Fact

Test statistic: t = (b − β₀) / SE_b, with df = n − 2

Related Terms

Least-squares regression Confidence interval for slope T-test for slope Correlation

Study This Concept

Practice slope inference with free review games in these units:

AP Statistics Unit 9: Inference for Regression