formulas%20p3%20FINAL

formulas%20p3%20FINAL - Regression Linear Regression Model...

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Page 3 Regression Linear Regression Model Population Version: Mean: () x Y E x Y 1 0 ) ( β μ + = = Individual: i i i x y ε + + = 1 0 where i is ) , 0 ( σ N Sample Version: Mean: x b b y 1 0 ˆ + = Individual: i i i e x b b y + + = 1 0 Standard Error of the Sample Slope () = = 2 1 ) ( s.e. x x s S s b XX Confidence Interval for 1 ) ( s.e. 1 * 1 b t b ± df = n – 2 t -Test for 1 To test 0 : 1 0 = H ) ( s.e. 0 1 1 b b t = df = n – 2 or MSE MSREG F = df = 1, n – 2 Parameter Estimators () () () () () = = = 2 2 1 x x y x x x x y y x x S S b XX XY x b y b 1 0 = Confidence Interval for the Mean Response s.e.(fit) ˆ * t y ± df = n – 2 where XX S x x n s 2 ) ( 1 ) fit ( s.e. + = Residuals y y e ˆ = = observed y – predicted y Prediction Interval for an Individual Response s.e.(pred) ˆ * t y ± df = n – 2 where () 2 2 ) fit ( s.e. s.e.(pred) + = s Correlation and its square YY XX XY S S S r = SSTO SSREG SSTO SSE SSTO r = = 2 where () 2 = = y y S SSTO YY Standard Error of the Sample Intercept XX S x n s b 2 0 1 ) ( s.e. + = Confidence Interval for 0 ) ( s.e. 0 * 0 b t b ± df = n – 2 Estimate of
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This note was uploaded on 09/26/2008 for the course STAT 350 taught by Professor Gunderson during the Winter '08 term at University of Michigan.

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