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- #R-code STAT2008 assignment 2
- #u6405056 and u6380618
- setwd("/Users/amyyu/Desktop/stat2008 rstudio")
- Visits <- read.csv("Visits.csv", header = T)
- Visits
- attach(Visits)
- summary(Visits)
- #Question A
- res.y <- (Visits$nondocco + Visits$doctorco)
- res.y
- summary(res.y)
- hist(res.y)
- boxplot(res.y)
- #sex
- plot(res.y ~ factor(Visits$sex), col="cyan2")
- #age
- hist(Visits$age)
- boxplot(Visits$age, xlab="Visits$age", ylab="Age")
- plot(res.y ~ Visits$age)
- plot(res.y ~ factor(Visits$age), col="cyan2")
- #income
- hist(Visits$income)
- boxplot(Visits$income, xlab="Visits$income", ylab="Income")
- plot(res.y ~ Visits$income)
- #insurance
- #estimates for beta
- plot(res.y ~ factor(Visits$insurance), col="cyan2")
- #illness
- hist(Visits$illness)
- boxplot(Visits$illness, xlab="Visits$illness", ylab="Illness")
- plot(res.y ~ Visits$illness)
- #actdays
- hist(Visits$actdays)
- boxplot(Visits$actdays, xlab="Visits$actdays", ylab="Actdays")
- plot(res.y ~ Visits$actdays)
- #hscore
- hist(Visits$hscore)
- boxplot(Visits$hscore, xlab="Visits$hscore", ylab="Hscore")
- plot(res.y ~ Visits$hscore)
- #chcond
- plot(res.y ~ factor(Visits$chcond), col="cyan2")
- #hospadmi
- hist(Visits$hospadmi)
- boxplot(Visits$hospadmi, xlab="Visits$hospadmi", ylab="Hospadmi")
- plot(res.y ~ Visits$hospadmi)
- #hospdays
- hist(Visits$hospdays)
- boxplot(Visits$hospdays, xlab="Visits$hospdays", ylab="Hospdays")
- plot(res.y ~ Visits$hospdays)
- #prescrib
- hist(Visits$prescrib)
- boxplot(Visits$prescrib, xlab="Visits$prescrib", ylab="Prescrib")
- plot(res.y ~ Visits$prescrib)
- #nonpresc
- hist(Visits$nonpresc)
- boxplot(Visits$nonpresc, xlab="Visits$nonpresc", ylab="Nonpresc")
- plot(res.y ~ Visits$nonpresc)
- #Question B
- Visits.lm <- lm(res.y ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- plot(Visits.lm, which = 1)
- summary(Visits.lm)
- anova(Visits.lm)
- #Question C
- #log(y+1)
- Visits.lmt1 <- lm(log(res.y+1) ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- plot(Visits.lmt1, which = 1, sub="Transformation: log(y+1)")
- summary(Visits.lmt1)
- anova(Visits.lmt1)
- #sqrt(y)
- Visits.lmt2 <- lm(sqrt(res.y) ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- plot(Visits.lmt2, which = 1, sub="Transformation: sqrt(y)")
- summary(Visits.lmt2)
- anova(Visits.lmt2)
- #y^(1/4)
- Visits.lmt3 <- lm((res.y)^(1/4) ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- plot(Visits.lmt3, which = 1, sub="Transformation: y^(1/4)")
- summary(Visits.lmt3)
- anova(Visits.lmt3)
- #sqrt(y+1)
- Visits.lmt4 <- lm(sqrt(res.y+1) ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- plot(Visits.lmt4, which = 1, sub="Transformation: sqrt(y+1)")
- summary(Visits.lmt4)
- anova(Visits.lmt4)
- #log(y+2)
- Visits.lmt5 <- lm(log(res.y+2) ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- plot(Visits.lmt5, which = 1, sub="Transformation: log(y+2)")
- summary(Visits.lmt5)
- anova(Visits.lmt5)
- #Question D
- require(MASS)
- Visits.lmt6 <- lm((res.y+1) ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- plot(Visits.lmt6, which = 1)
- boxcox(Visits.lmt6, plotit=T, lambda=seq(-6.5, 0, by=0.1))
- boxcox(Visits.lmt6, plotit=T, lambda=seq(-4, -2.5, by=0.1))
- y.bc <- (res.y+1)^(-3.2)
- summary(y.bc)
- Visits.lmboxcox <- lm(y.bc ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- summary(Visits.lmboxcox)
- anova(Visits.lmboxcox)
- plot(Visits.lmboxcox, which = 1)
- lines(lowess(Visits.lmboxcox$fit, Visits.lmboxcox$res), lwd=2, col="red")
- #Question E
- d <- residuals(lm(res.y ~ factor(sex)+age+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc))
- g <- residuals(lm(income ~ factor(sex)+age+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc))
- plot(g, d,xlab="income residuals",
- ylab="res.y residuals",
- main="Added Variable Plot: Income",
- pch=16, cex.lab=1.5)
- lines(lowess(g, d), lwd=2, col="red")
- abline(lm(d~g), lwd=2, col="cyan4")
- d1 <- residuals(lm(res.y ~ factor(sex)+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc))
- g1 <- residuals(lm(age ~ factor(sex)+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc))
- plot(g1, d1,xlab="age residuals",
- ylab="res.y residuals",
- main="Added Variable Plot: Age",
- pch=16, cex.lab=1.5)
- lines(lowess(g1, d1), lwd=2, col="red")
- abline(lm(d1~g1), lwd=2, col="cyan4")
- #Question F
- choose(4,2)
- #6
- #m=6, 0.05/6 = 0.008 bonferroni
- insurance <- relevel(factor(insurance), ref="freepor")
- mod.1 <- lm(res.y ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- confint(mod.1, level=(1-0.008))
- int.1 <- confint(mod.1, level=(1-0.008))[5:7,]
- int.1
- insurance <- relevel(factor(insurance), ref="freerepa")
- mod.2 <- lm(res.y ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- #m=6, 0.05/6 = 0.008
- confint(mod.2, level=(1-0.008))
- int.2 <- confint(mod.2, level=(1-0.008))[6:7,]
- int.2
- insurance <- relevel(factor(insurance), ref="levyplus")
- mod.3 <- lm(res.y ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- #m=6, 0.05/6 = 0.008
- confint(mod.3, level=(1-0.008))
- int.3 <- confint(mod.3, level=(1-0.008))[7,]
- int.3
- pw.comps1 <- rbind(int.1, int.2, int.3)
- row.names(pw.comps1) <- c("freepor to freerpa", "freepor to levyplus", "freepor to medlevy",
- "freerpa to levyplus", "freerpa to medlevy",
- "levyplus to medlevy")
- pw.comps1
- #Question G
- choose(3,2)
- #3
- #m=3, bonferroni correction 0.05/3 = 1/60
- chcond <- relevel(factor(chcond), ref="la")
- mod.1 <- lm(res.y ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- confint(mod.1, level=(1-(1/60)))
- int.1 <- confint(mod.1, level=(1-1/60))[11:12,]
- int.1
- chcond <- relevel(factor(chcond), ref="nla")
- mod.2 <- lm(res.y ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- confint(mod.2, level=(1-(1/60)))
- int.2 <- confint(mod.2, level=(1-1/60))[12,]
- int.2
- pw.comps2 <- rbind(int.1, int.2)
- row.names(pw.comps2) <- c("la to nla", "la to np",
- "nla to np")
- pw.comps2
- #Question H
- #hypothesis test 1, beta insurance = age = sex = income = nonpresc = 0
- mod.l1 <- lm(res.y ~ illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc+income+age+factor(sex)+factor(insurance))
- anova(mod.l1)
- #hypothesis test 2, beta insurance = age = sex = 0
- mod.l2 <- lm(res.y ~ income+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc+age+factor(sex)+factor(insurance))
- anova(mod.l2)
- #hypothesis test 3, beta insurance = 0
- mod.l3 <- lm(res.y ~ factor(sex)+age+income+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc+factor(insurance))
- anova(mod.l3)
- Visits.lmfinal <- lm(res.y ~ factor(sex)+age+income+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib+nonpresc)
- anova(Visits.lmfinal)
- #Question I
- Visits.lmallinteractions <- lm(res.y ~ factor(sex)+factor(sex)*age+factor(sex)*income+factor(sex)*illness+factor(sex)*actdays+factor(sex)*hscore+factor(sex)*factor(chcond)+factor(sex)*hospadmi+factor(sex)*hospdays+factor(sex)*prescrib+factor(sex)*nonpresc)
- anova(Visits.lmfinal, Visits.lmallinteractions)
- anova(Visits.lmallinteractions)
- #testing the order by chcond last
- Visits.lmorder <- lm(res.y ~ factor(sex)+factor(sex)*age+factor(sex)*income+factor(sex)*illness+factor(sex)*actdays+factor(sex)*hscore+factor(chcond)+factor(sex)*hospadmi+factor(sex)*hospdays+factor(sex)*prescrib+factor(sex)*nonpresc+factor(sex):factor(chcond))
- anova(Visits.lmorder)
- #Question J
- plot(fitted(Visits.lmfinal), rstandard(Visits.lmfinal), xlab="Fitted Values", ylab="Internally Studentized Residuals")
- title(main="Internally Studentised Residuals vs Fitted Values", sub="Visits.lmfinal")
- lines(lowess(fitted(Visits.lmfinal), rstandard(Visits.lmfinal)), lwd=2, col="red")
- plot(Visits.lmfinal, which = 2)
- plot(Visits.lmfinal, which = 4)
- sort(cooks.distance(Visits.lmfinal), decreasing=TRUE)[1:7]
- sort(abs(rstandard(Visits.lmfinal)), decreasing=TRUE)[1:7]
- sort(hatvalues(Visits.lmfinal), decreasing=TRUE)[1:7]
- dfbetas(Visits.lmfinal)[c(948,965,739,913),]
- dffits(Visits.lmfinal)[c(948,965,739,913)]
- covratio(Visits.lmfinal)[c(948,965,739,913)]
- #Question K
- summary(Visits.lmfinal)
- Visits.lminsurance <- lm(res.y ~ factor(sex)+age+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib)
- #age
- plot(age,res.y,type="n", main="Response vs Age")
- x <- seq(0,12, by = 0.01)
- d0 <- ifelse(sex == "0", 1, 0)
- d1 <- ifelse(sex == "1", 1, 0)
- points((age[d1==0]), (res.y[d1==0]),
- col="cyan2", pch=16)
- points((age[d1==1]), (res.y[d1==1]),
- col="orange", pch=17)
- lines(x, predict(Visits.lminsurance, newdata=data.frame(age=x, insurance="freepor", sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="red")
- pr <- predict(Visits.lminsurance, newdata=data.frame(age=x, insurance="freepor", sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="red")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- lines(x, predict(Visits.lminsurance, newdata=data.frame(age=x, insurance="freerepa", sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="purple")
- pr <- predict(Visits.lminsurance, newdata=data.frame(age=x, insurance="freerepa", sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="purple")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- lines(x, predict(Visits.lminsurance, newdata=data.frame(age=x, insurance="levyplus", sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="green")
- pr <- predict(Visits.lminsurance, newdata=data.frame(age=x, insurance="levyplus", sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="green")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- lines(x, predict(Visits.lminsurance, newdata=data.frame(age=x, insurance="medlevy", sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="yellow")
- pr <- predict(Visits.lminsurance, newdata=data.frame(age=x, insurance="medlevy", sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="yellow")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- legend("topleft", legend=c("freepor", "freerepa", "levyplus", "medlevy"),
- col=c("red", "purple", "green", "yellow"), lty=1, lwd=2, cex = 0.75)
- #hscore
- plot(hscore,res.y,type ="n", main="Response vs Hscore")
- x <- seq(0,12, by = 0.01)
- d0 <- ifelse(sex == "0", 1, 0)
- d1 <- ifelse(sex == "1", 1, 0)
- points((hscore[d1==0]), (res.y[d1==0]),
- col="cyan2", pch=16)
- points((hscore[d1==1]), (res.y[d1==1]),
- col="orange", pch=17)
- lines(x, predict(Visits.lminsurance, newdata=data.frame(hscore=x, insurance="freepor", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="red")
- pr <- predict(Visits.lminsurance, newdata=data.frame(hscore=x, insurance="freepor", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="red")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- lines(x, predict(Visits.lminsurance, newdata=data.frame(hscore=x, insurance="freerepa", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="purple")
- pr <- predict(Visits.lminsurance, newdata=data.frame(hscore=x, insurance="freerepa", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="purple")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- lines(x, predict(Visits.lminsurance, newdata=data.frame(hscore=x, insurance="levyplus", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="green")
- pr <- predict(Visits.lminsurance, newdata=data.frame(hscore=x, insurance="levyplus", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="green")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- lines(x, predict(Visits.lminsurance, newdata=data.frame(hscore=x, insurance="medlevy", age=mean(age), sex="1",illness=mean(illness), actdays=mean(actdays), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="yellow")
- pr <- predict(Visits.lminsurance, newdata=data.frame(hscore=x, insurance="medlevy", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="yellow")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- legend("topleft", legend=c("freepor", "freerepa", "levyplus", "medlevy"),
- col=c("red", "purple", "green", "yellow"), lty=1, lwd=2, cex = 0.75)
- #income
- Visits.lmincome <- lm(res.y ~ factor(sex)+age+income+factor(insurance)+illness+actdays+hscore+factor(chcond)+hospadmi+hospdays+prescrib)
- plot(income,res.y,type="n", main="Response vs Income")
- x <- seq(0,12, by = 0.01)
- d0 <- ifelse(sex == "0", 1, 0)
- d1 <- ifelse(sex == "1", 1, 0)
- points((income[d1==0]), (res.y[d1==0]),
- col="cyan2", pch=16)
- points((income[d1==1]), (res.y[d1==1]),
- col="orange", pch=17)
- lines(x, predict(Visits.lmincome, newdata=data.frame(income=x, insurance="freepor", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="red")
- pr <- predict(Visits.lmincome, newdata=data.frame(income=x, insurance="freepor", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="red")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- lines(x, predict(Visits.lmincome, newdata=data.frame(income=x, insurance="freerepa", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="purple")
- pr <- predict(Visits.lmincome, newdata=data.frame(income=x, insurance="freerepa", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="purple")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- lines(x, predict(Visits.lmincome, newdata=data.frame(income=x, insurance="levyplus", age=mean(age), sex="1",illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="green")
- pr <- predict(Visits.lmincome, newdata=data.frame(income=x, insurance="levyplus", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="green")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- lines(x, predict(Visits.lmincome, newdata=data.frame(income=x, insurance="medlevy", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib))), lwd=2, col="yellow")
- pr <- predict(Visits.lmincome, newdata=data.frame(income=x, insurance="medlevy", age=mean(age), sex="1", illness=mean(illness), actdays=mean(actdays), hscore=mean(hscore), chcond="np", hospadmi=mean(hospadmi), hospdays=mean(hospdays), prescrib=mean(prescrib)), interval="confidence")
- lines(x, pr[,"fit"], lwd=2, col="yellow")
- lines(x, pr[,"lwr"], lty=2)
- lines(x, pr[,"upr"], lty=2)
- legend("topleft", legend=c("freepor", "freerepa", "levyplus", "medlevy"),
- col=c("red", "purple", "green", "yellow"), lty=1, lwd=2, cex = 0.75)
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