AP Statistics Chapter 15 Notes. Inference for a Regression Line Goal: To determine if there is a relationship between two quantitative variables. Goal:

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Presentation transcript:

AP Statistics Chapter 15 Notes

Inference for a Regression Line Goal: To determine if there is a relationship between two quantitative variables. Goal: To determine if there is a relationship between two quantitative variables. i.e. What is the slope of the regression line? i.e. What is the slope of the regression line? From sample…a and b are statistics From sample…a and b are statistics True regression line…α and β are parameters. True regression line…α and β are parameters.

Conditions 1. Observations are independent. 1. Observations are independent. 2. True relationship is linear. 2. True relationship is linear. 3. σ is constant. 3. σ is constant. Check residual plot…make sure there is no pattern and the magnitude of the residuals is stable. Check residual plot…make sure there is no pattern and the magnitude of the residuals is stable. 4. Response varies Normally about the true regression line. 4. Response varies Normally about the true regression line. Make histogram or stemplot of residuals. Make histogram or stemplot of residuals.

Confidence Interval (estimate β) b ± t* SE b (df = n – 2) b ± t* SE b (df = n – 2) Significance Test Significance Test H o : β = 0t = b/SE b H o : β = 0t = b/SE b H a : β ≠ > < 0