Math
Confidence interval for slope.
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
Real-world.
- 1 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
- 2 If a CI for slope contains 0, there may be no linear relationship
- 3 Estimating how much each additional hour of study increases test scores
Key Fact
CI: b₁ ± t* · SE(b₁), where b₁ is the sample slope