What you'll learn
Inference about the slope of a population regression line (~2–5%).
The idea
A sample regression line estimates the true slope β. We test whether there's a real linear relationship (β ≠ 0) and estimate β with an interval.
Procedures
- t-test for slope: H₀: β = 0 (no linear relationship) vs Hₐ. t = b / SE(b), df = n − 2. A small p-value → evidence of a linear relationship.
- Confidence interval: b ± t*·SE(b). Read b and SE(b) from computer output.
Conditions (LINER)
- Linear relationship (residual plot), Independent observations (10%), Normal residuals, Equal variance (residual spread constant), Random data.
Interpretation
Interval for the slope: 'We are C% confident the true slope is between … units of y per unit of x.' If the interval excludes 0, there's evidence of a relationship.
Exam tips
- Read b, SE(b), and df = n − 2 from regression output.
- Check LINER and interpret the slope in context.
Common mistakes
- Forgetting df = n − 2.
- Skipping the residual-plot/conditions check.