Lec06.RegOrigin - Regression Through the Origin KNNL Ch. 4,...

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Unformatted text preview: Regression Through the Origin KNNL Ch. 4, Section 4.4 P 161-165 When appropriate? Theory or empirical evidence that: E{Y} is proportional to X. Intercept not significantly different from zero (p-value > 0.05). Equal variance, normality and independence assumptions: satisfied. Regression through the origin The model: Assumptions: Linearity of the relationship, with a line through the origin Errors are independent, have equal variance, and are normally distributed 1 i i i Y X = + Parameter estimates ( 29 ( 29 ( 29 2 1 2 1 1 1 1 1 2 1 1 1 Minimize Minimize 2 n i i i n i i i n i i n i i i i n i i i Y Y Q Y b X X Y dQ X Y b X b db X = = = = =- =- = -- = = --- = 2 1 ) ( ) )( ( : when Recall X X Y Y X X b b i i i Variance estimators ( 29 -- + + = -- + = - =--- = = + = = 2 2 ) ( 2 2 2 2 2 1 2 1 2 1 2 1 ) ( ) ( 1 1 } { ) ( ) ( 1 } { ) ( 1 } { 2 X X X X n MSE Y s X X X X n MSE Y s X X MSE b s n X b b Y MSE s X b b Y i h new h i h h i n i i i i i ( 29 + = = =-- = = = = 2 2 ) ( 2 2 2 2 2 1 2 1 2 1 2 1 ) ( ) ( 1 } { ) ( ) ( } { ) ( 1 } { 1 i h new h i h h i n i i i i i X X MSE Y s X X MSE Y s X MSE b s n X b Y MSE s X b Y Example: KNNL, p. 162 Charles Plumbing Supplies Company 12 warehouses Number of work units performed (X) and the total variable labor cost (Y, in $US) Assess adequacy of a simple linear regression model through the origin. Charles Plumbing Data Table 4.2 pg 163 Work Cost 20 114 196 921 115 560 50 245 122 575 100 475 33 138 154 727 80 375 147 670 182 828 160 762...
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This note was uploaded on 04/17/2010 for the course STSCI 3200 taught by Professor Sullivan during the Spring '10 term at Cornell University (Engineering School).

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Lec06.RegOrigin - Regression Through the Origin KNNL Ch. 4,...

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