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[Description] Model Predictivity - Calculate R², Adjusted R², and understand model fit quality
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Model Predictivity Worksheet
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Dataset: Birds Abundance Study
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Variables: ABUNDANCE (Y) vs ELEVATION (X)
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Source: ../Dataset/birds.txt
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Learning Objectives:
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1. Calculate SST (Total Sum of Squares)
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2. Calculate SSE (Error Sum of Squares) from residuals
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3. Calculate SSR (Regression Sum of Squares)
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4. Verify: SST = SSR + SSE
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5. Calculate R² = SSR/SST = 1 - SSE/SST
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6. Calculate Adjusted R² = 1 - (SSE/(n-p))/(SST/(n-1))
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7. Calculate RSE (Residual Standard Error) = sqrt(SSE/(n-p))
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Key Formulas:
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SST:Σ(Yᵢ - Ȳ)² = Total variation in Y
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Relation:
SST = SSR + SSE (Total = Explained + Residual)
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SSR:Σ(Ŷᵢ - Ȳ)² = Variation explained by model
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SSE:Σ(Yᵢ - Ŷᵢ)² = Residual variation
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R²:SSR/SST = 1 - SSE/SST
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Adj R²:1 - [(n-1)/(n-p)] × (1-R²)
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RSE:sqrt(SSE/(n-p)) = sqrt(MSE)
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Color Guide:
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Given Data (Input)
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Intermediate Calculations
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Final Results
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Correct Answer (✓)
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Incorrect Answer (✗)
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