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hw04a - STA 6207 Homework 4 Due An experiment was conducted...

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STA 6207 – Homework 4 Due 10/21/09 An experiment was conducted, measuring Luminance scores (Y) and quality grades in 5 varieties of Egyptian cotton. Dummy variables and interaction terms were created to allow separate regressions for each of the 5 varieties (Giza69,Giza67,Giza70,Giza68, and Menoufi). The logarithm of the quality grade was used in the linear regression: ε δ δ δ δ γ γ γ γ β β + + + + + + + + + + = 4 4 3 3 2 2 1 1 4 4 3 3 2 2 1 1 1 0 XZ XZ XZ XZ Z Z Z Z X Y Where: Y=Luminance score X=ln(quality grade) Z 1 =1 if Variety=Giza69, 0 otherwise Z 2 =1 if Variety=Giza67, 0 otherwise Z 3 =1 if Variety=Giza70, 0 otherwise Z 4 =1 if Variety=Giza68, 0 otherwise 1. Write out the model for each of the 5 varieties. 2. Fit the full model using SAS or R’s regression routine, as well as in matrix form. 3. Test whether the slopes relating ln(quality grade) to luminance are the same for each variety, using both matrix form (K’ β =m) and regression package (SS(Res Full ) and SS(Res Reduced )) at the α =0.05 significance level.
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