Lec12.MultiDiag - Click to edit Master subtitle style...

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Unformatted text preview: Click to edit Master subtitle style Multiple Regression Diagnostics KNNL Chapter 10 (10.1-10.3,10.5) Building the Regression Model II Lec12.MultiDiag.ssc Multicolinearity: KNNL Chapters 7.6, 10.5 Comments section also Adding or deleting a predictor variable changes the regression coefficients Estimated standard deviations of coefficients become large Coefficients may not be statistically significant Make sure to read alligator$Length 60 80 100 120 140 100 200 300 400 500 600 alligator$Weight Alligator Polynomial Model F-Statistic: Kutner et al. pg 73 anova(alligator2.lm, alligator3.lm, test = "F") Analysis of Variance Table Response: Weight Terms Resid.Df Resid.Dev 1 Length + Length^2 21 5267.637 2 Length + Length^2 + Length^3 20 2684.465 Test Df Sum of Sq F Value Pr(F) +I(Length^3) 1 2583.172 19.24534 0.0002847591 : hypothesis null Test 3 = anova(alligator3.lm, alligator4.lm, test = "F") Analysis of Variance Table Response: Weight Terms Resid. Df Resid. Dev 1 Length + Length^2 + Length^3 20 2684.465 2 Length + Length^2 + Length^3 + Length^4 19 2581.174 Test Df Sum of Sq F Value Pr(F) +I(Length^4) 1 103.2905 0.7603201 0.3941139 : hypothesis null Test 4 = ( 29 -- = = 2 1 2 2 2 2 ) ( exp ) 2 ( 1 ; n i i n x L x The Normal Likelihood Function O bj1 0 5 2 2 2 2 ) ( ) 2 ln( 2 ln - + =- i x n L The Negative Log Likelihood 2 ) ( ln -- =- i x L d d 2 2 2 ln n L d d =- Hessian Matrix Akaike Information Criteria (AIC) AIC = n*log(SSE) - n*log(n) + 2*p SBC = n*log(SSE) - n*log(n) + log(n)*p Kutner et al. Notation # Splus/R AIC # -2*log-likelihood + 2*npar # where npar includes coefficients and sigma2 sum(resid(alligator3.lm)^2) 2684.465 SSE = sum(resid(alligator3.lm)^2) p = length(coef(alligator3.lm)) lm1=lm(Weight~Length,data=alligator) text(1,AIC(lm1),1) lm1=lm(Weight~Length^2,data=alligator) text(1,AIC(lm1),2) lm1=lm(Weight~Length^3,data=alligator) text(1,AIC(lm1),3) lm1=lm(Weight~Length^4,data=alligator) text(1,AIC(lm1),4) One at a time 1 2 3 4 5 6 100 150 200 250 300 350 AIC 1 2 3 4 AIC Plot: Single Variable Models lm1=lm(Weight~Length+Length^2,data=alligator) AIC.p = rbind(AIC.p,c(3,AIC(lm1),12)) lm1=lm(Weight~Length+Length^3,data=alligator) AIC.p = rbind(AIC.p,c(3,AIC(lm1),13)) lm1=lm(Weight~Length+Length^4,data=alligator)...
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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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Lec12.MultiDiag - Click to edit Master subtitle style...

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