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# 12formulas - Math/Stat 423/523 Chapter 12 Formulas Linear...

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Math/Stat 423/523 Chapter 12 Formulas Linear Model: i i 1 0 i x Y ε + β + β = where ε 's are iid N(mean=0,variance= σ 2 ). β 1 = average change in Y for every unit change in x μ y x* = β 0 + β 1 x * = average response at x * σ 2 y x* = variance of Y at x=x* -------------------------------------------------------------------------------------- Least-Squares Estimates: ( 29 ( 29 n x x n y x y x ˆ 2 i 2 i i i i i 1 - - = β x ˆ y ˆ 1 0 β - = β Fitted Value: i 1 0 i x ˆ ˆ β + β = Residual: i i i y e - = ( 29 = = = - = n 1 i 2 i n 1 i 2 i i e y SSE or i i 1 i 0 2 i y x ˆ y ˆ y SSE β - β - = . Estimate of σ 2 : 2 n SSE MSE ˆ 2 - = = σ . -------------------------------------------------------------------------------------- Numerical Diagnostics ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 n y x y x y y x x S n y y y y S or SST n x x x x S i i i i i i xy 2 i 2 i 2 i yy 2 i 2 i 2 i xx - = - - = -

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12formulas - Math/Stat 423/523 Chapter 12 Formulas Linear...

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