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[Description] Outliers and Influence Diagnostics
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Outliers and Influence Diagnostics Worksheet
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Dataset:birds.txt (6 observations selected)
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X variable:LNSURF (log of lake surface area)
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Y variable:ABUNDANCE (bird species abundance)
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Learning Objectives:
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1. Understand leverage (hᵢᵢ) and its meaning in regression
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2. Calculate studentized residuals to identify outliers
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3. Compute Cook's Distance to measure influence
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4. Distinguish between outliers and influential points
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Key Formulas:
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Leverage:hᵢᵢ = 1/n + (xᵢ - x̄)² / SSₓ
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Studentized Residual:rᵢ = eᵢ / (s × √(1 - hᵢᵢ))
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Cook's Distance:Dᵢ = eᵢ² × hᵢᵢ / (p × MSE × (1-hᵢᵢ)²)
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Thresholds:
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Leverage: hᵢᵢ > 2p/n is high leverage
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Studentized: |rᵢ| > 2 suggests outlier
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Cook's: Dᵢ > 1 (or > 4/n) suggests influential
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Color Guide:
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Given Data (Input)
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Intermediate Calculations
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Your Answer (Enter here)
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Correct Answer (✓)
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Incorrect Answer (✗)
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