FORMULAS-ch3-ml
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Last updated 12:14 PM on 8/1/26
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25 Terms
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Simple Linear Regression Model
Y = β₀ + β₁X + ε
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Fitted Regression Line
Ŷ = β̂₀ + β̂₁X
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Residual Formula
eᵢ = yᵢ − ŷᵢ
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Residual Sum of Squares
RSS = e₁² + e₂² + … + eₙ²
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Residual Sum of Squares (Expanded)
RSS = Σ(yᵢ − ŷᵢ)²
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Slope Estimate
β̂₁ = Σ(xᵢ − x̄)(yᵢ − ȳ) / Σ(xᵢ − x̄)²
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Intercept Estimate
β̂₀ = ȳ − β̂₁x̄
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Null Hypothesis
H₀ : β₁ = 0
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Alternative Hypothesis
Hₐ : β₁ ≠ 0
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t-Statistic
t = (β̂₁ − 0)/SE(β̂₁)
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Residual Standard Error
RSE = √(RSS/(n−2))
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R² Statistic
R² = 1 − RSS/TSS
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Total Sum of Squares
TSS = Σ(yᵢ − ȳ)²