Chapter 11--Regression and Correlation Methods

Let z0 be the fishers transform of 0 the test

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Unformatted text preview: e Fisher’s transform by zxy = 1 log 2 1 + rxy 1 − rxy . Let z0 be the Fisher’s transform of ρ0 . The test statistics is √ H0 λ = (zxy − z0 ) n − 3 ∼ N (0, 1) We reject H0 if |λ| > z1−α/2 and p − value = 2 × P (Z > λcomputed ). This test is approximate. For the birth weight data test H0 : ρ = 0.85 vs Ha : ρ = 0.85 Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression R-codes for testing H0 : ρ = ρ0 when ρ0 = 0 r<-cor(bw,estriol) n<-length(bw) alpha<-.05 rho_0=0.7 z<-(1/2)*log((1+r)/(1-r)) z_rho_0 <-(1/2)*log((1+rho_0)/(1-rho_0)) lambda=(z-z_rho_0)*sqrt(n-3) p_value <- 2*(1-pnorm(abs(lambda))) Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression A 100(1 − α)% Conﬁdence Interval for ρxy Based on Fisher’s transform, construct conﬁdence interval for zρ as 1 = (a, b ), say. zxy ± z1−α/2 √ n−3 Then re-transforming the end points e 2a − 1 e 2b − 1 , e 2a + 1 e 2b + 1 yields an approximate 100(1 − α)% conﬁdence interval for ρxy . Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression A 100(1 − α)% Conﬁdence Interval for ρxy : R-code and Example For the birth weight-estriol example, construct 95% Conﬁdence interval for ρ. R-codes r<-cor(bw,estriol) n<-length(bw) alpha<-.05 z<-(1/2)*log((1+r)/(1-r)) conf_z<- z + c(-1,1)*qnorm(1-alpha/2)/sqrt(n-3) conf_rho<- (exp(2*conf_z)-1)/(exp(2*conf_z)+1) Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Introduction In...
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This note was uploaded on 02/03/2014 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.

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