13formulas - Math/Stat 423/523 Chapter 13 Formulas Section 13.1 More on Residuals i th residual(random version is i i i Y ˆ Y E = • 29 29 29 29

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Unformatted text preview: Math/Stat 423/523 Chapter 13 Formulas Section 13.1 More on Residuals i th residual (random version) is i i i Y ˆ Y E- = • ( 29 ( 29 ( 29 ( 29 i i xx 2 i 2 i i E V variance , mean ( N ~ E S x x n 1 1 E V , E E = = --- σ = = where ( 29 ∑- = 2 i xx x x S • Standardized residual ( 29 xx 2 i i i * i S x x n 1 1 s yˆ y e---- = Diagnostic Plots 1. e i * (or e i ) versus x i (no pattern) 2. e i * (or e i ) versus y i (no pattern) 3. i i y versus yˆ (linear) 4. normal probability plot of e i * (or e i ) (linear)-------------------------------------------------------------------------------------- Section 13.2 Transformed Variables Definition • intrinsically linear models- function of x and y that can be transformed as y' = β + β 1 x' where y' = function of y and x' = function of x Examples of Intrinsically Linear Models Name Model Linearized Version Exponential x e y β α = x ) ln( ) y ln( β + α = Power β α = x y ) x log( ) log( ) y log( β + α = ) x log( y β + α = linear already Reciprocal x 1 y β + α = linear already For intrinsically linear models, compute the least-squares line for the transformed data ) y , x ( ),..., y , x ( ), y , x ( ' n '...
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This note was uploaded on 05/07/2008 for the course MATH 423 taught by Professor Pascual during the Spring '06 term at Washington State University .

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13formulas - Math/Stat 423/523 Chapter 13 Formulas Section 13.1 More on Residuals i th residual(random version is i i i Y ˆ Y E = • 29 29 29 29

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