MATH 226 - 10.1.2007

# MATH 226 - 10.1.2007 - b j = ybar •j ybar •• a 1 =...

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MATH 226 – October 1, 2007 Factor Study o Factor A with levels 1 through I o Factor B with levels 1 through J Ybar ij if level i of factor A and level j of factor B is used Dipping 1 Spraying 2 Primer Type 1 ybar 11 ybar 12 = 5.3 Ybar 1• = 4.78 Primer Type 2 ybar 21 ybar 22 = 6.07 Ybar 2• = 5.68 Primer Type 3 ybar 31 ybar 32 = 5.17 ybar 3• = 4.50 ybar •1 = 4.47 ybar •2 = 5.51 ybar •• = 4.99 ybar 1• = (ybar 11 + ybar 12 )/2 ybar •j = Σ i=1 I ybar ij /I where • is a summation ybar •• = (1/IJ) Σ i=1 J Σ i=1 I ybar ij DEFINITION: In a two complete factorial design with factors A and B the fitted main effect of factor A at level i is a i = ybar i• - ybar •• with a fitted main effect of factor B at level j is
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Unformatted text preview: b j = ybar •j- ybar •• a 1 = 4.78 – 4.99 = 0.21 a 2 = 5.68 – 4.99 = 0.69 a 3 = 4.50 – 4.99 = -0.49 a i = ybar i•- ybar •• ybar ij ≈ ybar •• + a i + b j to finish the definition The fitted interaction between level i of Factor A and level j of factor B is ab ij = ybar ij – (ybar •• + a i + b j ) ybar ij ≈ ybar •• + a i + b j + ab ij R 2 = [Σ(y – ybar) 2 – Σ(yhat – y) 2 ]/ Σ(y – ybar) 2 y ij ≈ μ + α i + β j + αβ ij yhat ij = ybar •• + a i + b j + ab ij y ij ≈ μ + α i + β j yhat ij = ybar •• + a i + b j...
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