Lec13.MultiRemed - Multiple Regression Diagnostics and...

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Multiple Regression Diagnostics and Remedial Measures KNNL Chapter 10.1,10.5
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Overview of today’s lecture Checking for information contained in additional variables Identifying the symptoms of colinearity Weighted least squares
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Model Adequacy Are added variables needed? Added Variable Plots Marginal importance of a variable Nature of variable’s relationship
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Consider Liver Surgery Data Assume we have Prognostic.Index and Enzyme.Test already in the model Now we wish to examine what if anything Liver.Test will contribute Importance Relationship
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BloodClot.Score 20 40 60 80 100 1 2 3 4 5 6 4 6 8 10 20 40 60 80100 Prognostic.Index Enzyme.Test 1 2 3 5 Liver.Test 4 6 8 10 20 40 60 80 100 120 5.5 6.0 6.5 7.0 7.5 5.5 6.5 7.5 LogSurv.Time
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Liver Test 1 2 3 4 5 6 5.5 6.0 6.5 7.0 7.5 Log(Survival Time) i i X Y 1 1 0 β β+ =
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Liver Test 1 2 3 4 5 6 5.5 6.0 6.5 7.0 7.5 Log(Survival Time) i i X Y 1 1 0 β β+ =
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Residuals Residuals are what remain left after accounting for the two main predictor variables Prognostic.index and Enzyme.test ) ˆ ˆ ˆ ( ) , ( ˆ ) , | ( 3 3 2 2 0 3 2 3 2 i i i i i i i i i i X X Y X X Y Y X X Y e β + + - = - =
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Liver Test 1 2 3 4 5 6 -500 0 500 1000 Residuals i i i i X X X Y e 1 1 0 3 2 ) , | ( β β+ =
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Liver Test 1 2 3 4 5 6 -500 0 500 1000 Residuals i i i i X X X Y e 1 1 0 3 2 ) , | ( β β+ =
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Added-Variable Plots Kutner et al. suggest that this isn’t enough, that we need to account for the effect on both response and predictor The second set of starred regression ) ˆ ˆ ˆ ( ˆ ) , | ( 3 * 3 2 * 2 * 0 1 1 1 3 2 1 i i i i i i i i X X X X X X X X e β + + - = - =
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Liver Test Residuals -2 -1 0 1 2 3 -500 0 500 1000 Survival.Time Residuals ) , | ( ) , | ( 3 2 1 1 0 3 2 i i i i i i X X X e X X Y e β β+ =
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Liver Test Residuals -2 -1 0 1 2 3 -500 0 500 1000 Survival.Time Residuals ) , | ( ) , | ( 3 2 1 1 0 3 2 i i i i i i X X X e X X Y e β β+ =
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Three predictors included Surg4c.lm = lm(Survival.Time ~ Liver.Test +  Prognostic.Index + Enzyme.Test, data = Surgical) summary(Surg4c.lm) Coefficients:                      Value Std. Error   t value  Pr(>|t|)       (Intercept) -630.3873  103.1037    -6.1141    0.0000       Liver.Test  120.6833   24.5072     4.9244    0.0000 Prognostic.Index    6.9037    1.2815     5.3871    0.0000      Enzyme.Test    7.4328    1.1084     6.7057    0.0000
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AIC while dropping one term library(MASS) stepAIC(Surg4c.lm) Start:  AIC= 1153.89   Survival.Time ~ Liver.Test + Prognostic.Index +  Enzyme.Test                     Df Sum of Sq     RSS      AIC 
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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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Lec13.MultiRemed - Multiple Regression Diagnostics and...

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