Lec16.QuantQual - QuantitativeandQualitative Predictors...

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    Quantitative and Qualitative  Predictors KNNL 8.2 Interactions 8.3 Qualitative Predictors 8.4 Indicator Variables 8.5 Qualitative-Quantitative Interaction
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    Idealized Interactions Additive  Y=12+0.5X Y=22+0.5X Reinforcement Y=12+1.5X Y=22+0.5X Interference Y=12+0.7X Y=22+0.5X x y2 0 20 40 60 80 100 30 40 50 60 70 x 0 20 40 60 80 100 100 150 0 20 40 60 80 100
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    Surgical Data Surgical[1:5,]   BloodClot.Score Prognostic.Index Enzyme.Test Liver.Test Age  1             6.7               62          81       2.59  50 2             5.1               59          66       1.70  39 3             7.4               57          83       2.16  55 4             6.5               73          41       2.01  48 5             7.8               65         115       4.30  45   Gender AlcUse.Mod AlcUse.Hvy Survival.Time LogSurv.Time  1      0          1          0           695        6.544 2      0          0          0           403        5.999 3      0          0          0           710        6.565 4      0          0          0           349        5.854 5      0          0          1          2343        7.759
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    Enzyme.Test LogSurv.Time 20 40 60 80 100 120 5.5 6.0 6.5 7.0 7.5 Log(Surv Time) vs. Enzyme Test
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    How might alcohol influence  performance of the test? Y=B0+B1X  low alcohol Y=B2+B1X  high alcohol Y=B0+B1X+B2A  where A=0 if low and    A=1 if high This would be the additive model.
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    Alternatively Y=B0+B1X  low alcohol Y=B0+B2X  high alcohol Y=B0+B1X+B2XA  where A=0 if low   and    A=1 if high This would be the interaction model.
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    Log(Surv Time) vs. Enzyme Test Enzyme.Test LogSurv.Time 20 40 60 80 100 120 5.5 6.0 6.5 7.0 7.5 Low Use Moderate Use Heavy Use
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    Log(Surv Time) vs. Enzyme Test Enzyme.Test LogSurv.Time 20 40 60 80 100 120 5.5 6.0 6.5 7.0 7.5 Separate  Regressions
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    Alcohol Script Surg7a.glm = glm( LogSurv.Time ~ Enzyme.Test, data=Surgical) Surg7b.glm = glm( LogSurv.Time ~ Enzyme.Test + AlcUse.Mod +  AlcUse.Hvy, data=Surgical) Surg7c.glm = glm( LogSurv.Time ~ Enzyme.Test + AlcUse.Mod +  AlcUse.Hvy +   Enzyme.Test * AlcUse.Mod + Enzyme.Test *  AlcUse.Hvy , data=Surgical) anova(Surg7a.glm,Surg7b.glm,test="F")  Pr(F) = 0.007289761 anova(Surg7b.glm,Surg7c.glm,test="F")  Pr(F) = 0.7260922 AIC(Surg7a.glm)  103.5191 AIC(Surg7b.glm)   97.2979 AIC(Surg7c.glm)  100.6201
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Lec16.QuantQual - QuantitativeandQualitative Predictors...

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