In-class exercises:
1.What does the R script do? Revise the code so that it does the same job without resorting to the use of a nested ‘for’ loop. DONE
#This R script draw two pictures----qnorm#
ci_norm <- function(n=100, nci=50, nRun=3, level=0.95, pause=0.05) {
ci <- NULL
z0 = qnorm(1 - (1 - level)/2)
for ( j in 1:nRun ) {
zbar <- colMeans(replicate(nci, rnorm(n)))
zl <- zbar - z0 * 1/sqrt(n); zu <- zbar + z0 * 1/sqrt(n)
plot(1, xlim = c(0.5, nci + 0.5), ylim = c(min(zl), max(zu)),
type = "n", xlab = "Sample ID", ylab = "Average")
abline(h = 0, lty = 2)
for( i in 1:nci ) {
arrows(i, zl[i], i, zu[i], length = 0.05, angle = 90,
code = 3,
col = ifelse(0 > zl[i] & 0 < zu[i], "gray", "red"))
points(i, zbar[i], pch = 19, col = "gray")
Sys.sleep(pause)
}
Sys.sleep(3)
}
}
##
ci_norm(n = 36, nci = 51, nRun = 2)
# Revise to while-loop, repeat loop
ci_norm <- function(n=100, nci=50, nRun=3, level=0.95, pause=0.05) {
ci <- NULL
z0 = qnorm(1 - (1 - level)/2)
j <- 1
while ( j <= nRun ) {
j <- j+1
zbar <- colMeans(replicate(nci, rnorm(n)))
zl <- zbar - z0 * 1/sqrt(n); zu <- zbar + z0 * 1/sqrt(n)
plot(1, xlim = c(0.5, nci + 0.5), ylim = c(min(zl), max(zu)),
type = "n", xlab = "Sample ID", ylab = "Average")
abline(h = 0, lty = 2)
i <- 1
repeat{
if( i > nci )break
i <- i+1
arrows(i, zl[i], i, zu[i], length = 0.05, angle = 90,
code = 3,
col = ifelse(0 > zl[i] & 0 < zu[i], "gray", "red"))
points(i, zbar[i], pch = 19, col = "gray")
}
}
}
##
ci_norm(n = 36, nci = 51, nRun = 2)
2.Use the read and math variables from the high schools data example for this problem. First firgure out what this R script does and then eliminate the for loop in the code segment. DONE
#open the data
dta <- read.table("C:/Users/boss/Desktop/data_management/hs0.txt", h=T)
# subset the race column"asian" as dta.asian
dta.asian <- subset(dta, race=="asian")
# define r0 as the correlation between math and socst column data in dta.asian
r0 <- cor(dta.asian$math, dta.asian$socst)
#define cnt as 0
cnt <- 0
#define nIter as 1001
nIter <- 1001
#use for loop to aggregate 1~nIter that define "new" as "read" column in dta.asian's simple sampling
#and then define "r" as "math" column in dta.asian's corelation, finally order that if (r0 <= r)*cnt, define it as cnt+1
for (i in 1:nIter) {
new <- sample(dta.asian$read)
r <- cor(new, dta.asian$math)
if ( r0 <= r ) cnt <- cnt+1
}
#
#aggregate cnt/nIter
cnt/nIter
#> [1] 0.03596404
#define "newread" as replicate "nIter" data for the sample "column "read" in dta.asian" times
newread <- replicate(nIter, sample(dta.asian$read))
#make "newread" as a data frame then unlist it
newread <- data.frame(unlist(newread))
#use function "with" to evaluate an R expression in an environment constructed from data, possibly modyfing the original data
with(newread, lapply(names(newread), function(x)
#lapply give the name to "newread" data, then aggregate the correlation between "math" column data in dta.asian, and use the named data as substitute
#eval() ensure R willl run it
cor(dta.asian$math, eval(substitute(tmp, list(tmp=as.name(x))))))
)
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#> [[353]]
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#> [[406]]
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#> [[441]]
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#> [[449]]
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#> [[450]]
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#> [[452]]
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#> [[453]]
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#> [[468]]
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#> [[472]]
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#> [[473]]
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#> [[475]]
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#> [[476]]
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#> [[478]]
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#> [[479]]
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#> [[481]]
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#> [[482]]
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#> [[483]]
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#> [[484]]
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#> [[485]]
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#> [[493]]
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#> [[494]]
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#> [[496]]
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#> [[497]]
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#> [[498]]
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#> [[499]]
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#> [[500]]
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#> [[508]]
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#> [[512]]
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#> [[513]]
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#> [[514]]
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#> [[515]]
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#> [[516]]
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#> [[517]]
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#> [[518]]
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#> [[519]]
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#> [[521]]
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#> [[522]]
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#> [[523]]
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#> [[524]]
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#> [[525]]
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#> [[526]]
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#> [[527]]
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#> [[528]]
#> [1] 0.02227855
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#> [[529]]
#> [1] 0.2957185
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#> [[530]]
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#> [[531]]
#> [1] 0.06742193
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#> [[532]]
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#> [[533]]
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#> [[534]]
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#> [[535]]
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#> [[536]]
#> [1] 0.2015623
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#> [[537]]
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#> [[538]]
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#> [[539]]
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#> [[540]]
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#> [[541]]
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#> [[542]]
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#> [[543]]
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#> [[544]]
#> [1] 0.02356836
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#> [[545]]
#> [1] 0.2454158
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#> [[546]]
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#> [[547]]
#> [1] 0.2776611
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#> [[548]]
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#> [[549]]
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#> [[550]]
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#> [[551]]
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#> [[552]]
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#> [[553]]
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#> [[554]]
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#> [[555]]
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#> [[556]]
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#> [[557]]
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#> [[558]]
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#> [[559]]
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#> [[560]]
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#> [[561]]
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#> [[562]]
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#> [[563]]
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#> [[564]]
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#> [[565]]
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#> [[566]]
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#> [[567]]
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#> [[568]]
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#> [[569]]
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#> [[570]]
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#> [[571]]
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#> [[572]]
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#> [[573]]
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#> [[574]]
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#> [[575]]
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#> [[576]]
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#> [[577]]
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#> [[578]]
#> [1] -0.1905403
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#> [[579]]
#> [1] 0.1615781
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#> [[580]]
#> [1] -0.2227855
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#> [[581]]
#> [1] 0.6014037
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#> [[582]]
#> [1] -0.0667184
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#> [[583]]
#> [1] 0.4517856
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#> [[584]]
#> [1] -0.1492663
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#> [[585]]
#> [1] 0.01840912
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#> [[586]]
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#> [[587]]
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#> [[588]]
#> [1] 0.2105909
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#> [[589]]
#> [1] 0.1873744
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#> [[590]]
#> [1] 0.2467057
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#> [[591]]
#> [1] 0.1525495
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#> [[592]]
#> [1] 0.08160985
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#> [[593]]
#> [1] 0.1048265
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#> [[594]]
#> [1] -0.05639991
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#> [[595]]
#> [1] -0.4485024
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#> [[596]]
#> [1] -0.1660338
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#> [[597]]
#> [1] 0.2196196
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#> [[598]]
#> [1] -0.02544445
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#> [[599]]
#> [1] -0.2292346
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#> [[600]]
#> [1] -0.4626904
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#> [[601]]
#> [1] 0.06613212
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#> [[602]]
#> [1] 0.4775818
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#> [[603]]
#> [1] 0.3782664
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#> [[604]]
#> [1] 0.3434415
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#> [[605]]
#> [1] 0.09063853
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#> [[606]]
#> [1] 0.3369924
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#> [[607]]
#> [1] -0.3130723
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#> [[608]]
#> [1] 0.1577087
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#> [[609]]
#> [1] -0.04092218
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#> [[610]]
#> [1] 0.1332023
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#> [[611]]
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#> [[612]]
#> [1] -0.1247599
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#> [[613]]
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#> [[614]]
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#> [[615]]
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#> [[616]]
#> [1] -0.08090632
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#> [[617]]
#> [1] 0.6826617
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#> [[618]]
#> [1] 0.2518649
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#> [[619]]
#> [1] 0.2028521
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#> [[620]]
#> [1] 0.6426776
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#> [[621]]
#> [1] 0.002931388
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#> [[622]]
#> [1] -0.137658
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#> [[623]]
#> [1] 0.05323401
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#> [[624]]
#> [1] 0.01324988
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#> [[625]]
#> [1] -0.2550308
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#> [[626]]
#> [1] 0.2596038
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#> [[627]]
#> [1] 0.02872761
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#> [[628]]
#> [1] -0.1221803
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#> [[629]]
#> [1] 0.09321815
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#> [[630]]
#> [1] 0.4066422
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#> [[631]]
#> [1] -0.2795372
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#> [[632]]
#> [1] 0.3898747
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#> [[633]]
#> [1] 0.3137758
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#> [[634]]
#> [1] -0.01254634
#>
#> [[635]]
#> [1] 0.5885055
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#> [[636]]
#> [1] -0.01641578
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#> [[637]]
#> [1] 0.0635525
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#> [[638]]
#> [1] -0.1441071
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#> [[639]]
#> [1] -0.1570052
#>
#> [[640]]
#> [1] 0.06484231
#>
#> [[641]]
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#> [[731]]
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#> [[733]]
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#> [[734]]
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#> [[736]]
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#> [[738]]
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#> [[739]]
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#> [[742]]
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#> [[743]]
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#> [[744]]
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#> [[746]]
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#> [[750]]
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#> [[755]]
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#> [[756]]
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#> [[758]]
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#> [[759]]
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#> [[764]]
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#> [[766]]
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#> [[769]]
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#> [[773]]
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#> [[775]]
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#> [[776]]
#> [1] 0.1022468
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#> [[777]]
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#> [[778]]
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#> [[779]]
#> [1] 0.4208301
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#> [[780]]
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#> [[782]]
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#> [[783]]
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#> [[784]]
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#> [[786]]
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#> [[787]]
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#> [[788]]
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#> [[789]]
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#> [[794]]
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#> [[795]]
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#> [[797]]
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#> [[799]]
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#> [[803]]
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#> [[805]]
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#> [[807]]
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#> [[808]]
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#> [[813]]
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#> [[814]]
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#> [[815]]
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#> [[821]]
#> [1] 0.07258118
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#> [[822]]
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#> [[824]]
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#> [[825]]
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#> [[826]]
#> [1] 0.0751608
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#> [[827]]
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#> [[828]]
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#> [[829]]
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#> [[830]]
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#> [[831]]
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#> [[834]]
#> [1] 0.1796355
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#> [[835]]
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#> [[836]]
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#> [[837]]
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#> [[839]]
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#> [[840]]
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#> [[841]]
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#> [1] 0.3473109
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#> [[843]]
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#> [[844]]
#> [1] -0.04608143
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#> [[845]]
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#> [[846]]
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#> [[847]]
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#> [[848]]
#> [1] 0.2995879
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#> [[849]]
#> [1] 0.5601297
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#> [1] 0.04936458
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#> [[851]]
#> [1] -0.4278655
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#> [[852]]
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#> [[853]]
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#> [[854]]
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#> [[855]]
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#> [[856]]
#> [1] 0.1654476
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#> [[857]]
#> [1] -0.5439484
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#> [[858]]
#> [1] 0.5278844
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#> [[859]]
#> [1] 0.1241736
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#> [[860]]
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#> [[861]]
#> [1] 0.1383615
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#> [[862]]
#> [1] -0.04737124
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#> [[863]]
#> [1] -0.1905403
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#> [[864]]
#> [1] 0.2093011
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#> [[865]]
#> [1] 0.2299381
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#> [[866]]
#> [1] 0.1770559
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#> [[867]]
#> [1] -0.226655
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#> [[868]]
#> [1] -0.2627697
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#> [[869]]
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#> [[872]]
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#> [[873]]
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#> [[874]]
#> [1] 0.05581364
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#> [[875]]
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#> [[876]]
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#> [[877]]
#> [1] 0.3434415
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#> [[878]]
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#> [[879]]
#> [1] -0.5542669
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#> [[880]]
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#> [[881]]
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#> [[882]]
#> [1] -0.1441071
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#> [[883]]
#> [1] 0.08289967
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#> [[884]]
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#> [[885]]
#> [1] 0.4195403
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#> [[886]]
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#> [[887]]
#> [1] -0.5916714
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#> [[888]]
#> [1] -0.4497922
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#> [[889]]
#> [1] 0.1138551
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#> [[890]]
#> [1] -0.04479162
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#> [[891]]
#> [1] -0.2253651
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#> [[892]]
#> [1] 0.06613212
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#> [[893]]
#> [1] 0.02227855
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#> [[894]]
#> [1] 0.5420724
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#> [[895]]
#> [1] 0.3627886
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#> [[896]]
#> [1] -0.1905403
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#> [[897]]
#> [1] 0.1099857
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#> [[898]]
#> [1] -0.6303658
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#> [[899]]
#> [1] -0.4123877
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#> [[900]]
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#> [[901]]
#> [1] 0.05710345
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#> [[902]]
#> [1] 0.01196006
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#> [[903]]
#> [1] 0.2363872
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#> [[904]]
#> [1] 0.2763713
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#> [[905]]
#> [1] -0.1944097
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#> [[906]]
#> [1] -0.4807477
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#> [[907]]
#> [1] 0.121594
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#> [[908]]
#> [1] -0.1208905
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#> [[909]]
#> [1] -0.3349991
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#> [[910]]
#> [1] 0.1628679
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#> [[911]]
#> [1] 0.4517856
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#> [[912]]
#> [1] 0.1293329
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#> [[913]]
#> [1] 0.1473902
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#> [[914]]
#> [1] -0.3504768
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#> [[915]]
#> [1] -0.07316746
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#> [[916]]
#> [1] -0.2563206
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#> [[917]]
#> [1] 0.008090632
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#> [[918]]
#> [1] -0.5826428
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#> [[919]]
#> [1] 0.001641578
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#> [[920]]
#> [1] 0.2144604
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#> [[921]]
#> [1] -0.4252858
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#> [[922]]
#> [1] -0.1299191
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#> [[923]]
#> [1] 0.1783457
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#> [[924]]
#> [1] -0.3981998
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#> [[925]]
#> [1] 0.09579777
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#> [[926]]
#> [1] 0.4814512
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#> [[927]]
#> [1] 0.1757661
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#> [[928]]
#> [1] -0.1273395
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#> [[929]]
#> [1] 0.3189351
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#> [[930]]
#> [1] -0.04221199
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#> [[931]]
#> [1] -0.2098874
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#> [[932]]
#> [1] 0.1319125
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#> [[933]]
#> [1] -0.02415464
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#> [[934]]
#> [1] -0.6045696
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#> [[935]]
#> [1] -0.05768972
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#> [[936]]
#> [1] 0.5136965
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#> [[937]]
#> [1] -0.1312089
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#> [[938]]
#> [1] 0.4917697
#>
#> [[939]]
#> [1] 0.3021675
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#> [[940]]
#> [1] 0.1448106
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#> [[941]]
#> [1] 0.3550498
#>
#> [[942]]
#> [1] 0.1809253
#>
#> [[943]]
#> [1] 0.4234097
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#> [[944]]
#> [1] -0.1002535
#>
#> [[945]]
#> [1] -0.1608746
#>
#> [[946]]
#> [1] -0.540079
#>
#> [[947]]
#> [1] 0.687821
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#> [[948]]
#> [1] 0.258314
#>
#> [[949]]
#> [1] 0.0158295
#>
#> [[950]]
#> [1] 0.3189351
#>
#> [[951]]
#> [1] 0.5562603
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#> [[952]]
#> [1] 0.1241736
#>
#> [[953]]
#> [1] 0.3189351
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#> [[954]]
#> [1] 0.1538393
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#> [[955]]
#> [1] -0.7142035
#>
#> [[956]]
#> [1] -0.5491077
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#> [[957]]
#> [1] 0.1228838
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#> [[958]]
#> [1] 0.1512596
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#> [[959]]
#> [1] -0.1531357
#>
#> [[960]]
#> [1] -0.2589002
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#> [[961]]
#> [1] -0.2047282
#>
#> [[962]]
#> [1] -0.08219613
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#> [[963]]
#> [1] 0.2247789
#>
#> [[964]]
#> [1] 0.3318332
#>
#> [[965]]
#> [1] -0.3827221
#>
#> [[966]]
#> [1] -0.5207318
#>
#> [[967]]
#> [1] 0.02872761
#>
#> [[968]]
#> [1] -0.46527
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#> [[969]]
#> [1] -0.04737124
#>
#> [[970]]
#> [1] -0.1157312
#>
#> [[971]]
#> [1] 0.7510217
#>
#> [[972]]
#> [1] 0.1925336
#>
#> [[973]]
#> [1] 0.6104323
#>
#> [[974]]
#> [1] 0.1319125
#>
#> [[975]]
#> [1] 0.3279637
#>
#> [[976]]
#> [1] 0.6452572
#>
#> [[977]]
#> [1] 0.4221199
#>
#> [[978]]
#> [1] 0.2286483
#>
#> [[979]]
#> [1] 0.196403
#>
#> [[980]]
#> [1] 0.009380443
#>
#> [[981]]
#> [1] -0.1479765
#>
#> [[982]]
#> [1] 0.05839326
#>
#> [[983]]
#> [1] 0.4698429
#>
#> [[984]]
#> [1] 0.05065439
#>
#> [[985]]
#> [1] 0.100957
#>
#> [[986]]
#> [1] -0.05768972
#>
#> [[987]]
#> [1] 0.08032004
#>
#> [[988]]
#> [1] -0.1956995
#>
#> [[989]]
#> [1] -0.1157312
#>
#> [[990]]
#> [1] 0.2995879
#>
#> [[991]]
#> [1] 0.05065439
#>
#> [[992]]
#> [1] -0.5104134
#>
#> [[993]]
#> [1] 0.05839326
#>
#> [[994]]
#> [1] -0.0551101
#>
#> [[995]]
#> [1] 0.4956392
#>
#> [[996]]
#> [1] 0.2157502
#>
#> [[997]]
#> [1] -0.2679289
#>
#> [[998]]
#> [1] -0.6497129
#>
#> [[999]]
#> [1] -0.3646647
#>
#> [[1000]]
#> [1] 0.4866105
#>
#> [[1001]]
#> [1] -0.233104
#do the pearcon's correlation to "asian" column's math and socst data in dta
cor.test(dta[dta$race=="asian", "math"], dta[dta$race=="asian", "socst"])
#>
#> Pearson's product-moment correlation
#>
#> data: dta[dta$race == "asian", "math"] and dta[dta$race == "asian", "socst"]
#> t = 1.9887, df = 9, p-value = 0.07796
#> alternative hypothesis: true correlation is not equal to 0
#> 95 percent confidence interval:
#> -0.07083501 0.86552255
#> sample estimates:
#> cor
#> 0.5525177# Revise~~
#use the while~
dta <- read.table("C:/Users/boss/Desktop/data_management/hs0.txt", h=T)
dta.asian <- subset(dta, race=="asian")
r0 <- cor(dta.asian$math, dta.asian$socst)
cnt <- 0
nIter <- 1001
i <- 1
while (i <= nIter) {
i <- i+1
new <- sample(dta.asian$read)
r <- cor(new, dta.asian$math)
if ( r0 <= r ) cnt <- cnt+1
}
#
cnt/nIter
#> [1] 0.04395604
newread <- replicate(nIter, sample(dta.asian$read))
newread <- data.frame(unlist(newread))
with(newread, lapply(names(newread), function(x)
cor(dta.asian$math, eval(substitute(tmp, list(tmp=as.name(x))))))
)
#> [[1]]
#> [1] 0.1847947
#>
#> [[2]]
#> [1] 0.4814512
#>
#> [[3]]
#> [1] 0.4904799
#>
#> [[4]]
#> [1] 0.1435208
#>
#> [[5]]
#> [1] -0.1737727
#>
#> [[6]]
#> [1] 0.1099857
#>
#> [[7]]
#> [1] 0.2815305
#>
#> [[8]]
#> [1] 0.1370717
#>
#> [[9]]
#> [1] 0.1538393
#>
#> [[10]]
#> [1] -0.4046489
#>
#> [[11]]
#> [1] 0.306037
#>
#> [[12]]
#> [1] -0.06929802
#>
#> [[13]]
#> [1] -0.1041229
#>
#> [[14]]
#> [1] -0.3272602
#>
#> [[15]]
#> [1] -0.4252858
#>
#> [[16]]
#> [1] 0.2841102
#>
#> [[17]]
#> [1] -0.1273395
#>
#> [[18]]
#> [1] -0.8277068
#>
#> [[19]]
#> [1] -0.2975946
#>
#> [[20]]
#> [1] 0.2557343
#>
#> [[21]]
#> [1] 0.1860845
#>
#> [[22]]
#> [1] -0.1208905
#>
#> [[23]]
#> [1] 0.2080113
#>
#> [[24]]
#> [1] 0.8284104
#>
#> [[25]]
#> [1] -0.2343938
#>
#> [[26]]
#> [1] 0.008090632
#>
#> [[27]]
#> [1] 0.1177246
#>
#> [[28]]
#> [1] -0.4614005
#>
#> [[29]]
#> [1] -0.1428172
#>
#> [[30]]
#> [1] -0.04866105
#>
#> [[31]]
#> [1] -0.3246806
#>
#> [[32]]
#> [1] -0.1441071
#>
#> [[33]]
#> [1] -0.7412895
#>
#> [[34]]
#> [1] -0.6651907
#>
#> [[35]]
#> [1] 0.4066422
#>
#> [[36]]
#> [1] -0.2292346
#>
#> [[37]]
#> [1] -0.1660338
#>
#> [[38]]
#> [1] 0.05065439
#>
#> [[39]]
#> [1] 0.2854
#>
#> [[40]]
#> [1] 0.5253048
#>
#> [[41]]
#> [1] 0.08547929
#>
#> [[42]]
#> [1] 0.3137758
#>
#> [[43]]
#> [1] 0.3589192
#>
#> [[44]]
#> [1] 0.2067215
#>
#> [[45]]
#> [1] -0.164744
#>
#> [[46]]
#> [1] -0.4781681
#>
#> [[47]]
#> [1] -0.006097288
#>
#> [[48]]
#> [1] -0.1828014
#>
#> [[49]]
#> [1] 0.1809253
#>
#> [[50]]
#> [1] 0.3344128
#>
#> [[51]]
#> [1] 0.07258118
#>
#> [[52]]
#> [1] -0.2705085
#>
#> [[53]]
#> [1] 0.189954
#>
#> [[54]]
#> [1] 0.4891901
#>
#> [[55]]
#> [1] 0.04291553
#>
#> [[56]]
#> [1] 0.2479955
#>
#> [[57]]
#> [1] -0.2382633
#>
#> [[58]]
#> [1] -0.1802218
#>
#> [[59]]
#> [1] -0.05639991
#>
#> [[60]]
#> [1] 0.3292536
#>
#> [[61]]
#> [1] -0.5968307
#>
#> [[62]]
#> [1] -0.2008587
#>
#> [[63]]
#> [1] 0.06226269
#>
#> [[64]]
#> [1] 0.1989826
#>
#> [[65]]
#> [1] -0.089935
#>
#> [[66]]
#> [1] 0.01324988
#>
#> [[67]]
#> [1] 0.00551101
#>
#> [[68]]
#> [1] -0.1312089
#>
#> [[69]]
#> [1] 0.06226269
#>
#> [[70]]
#> [1] -0.3246806
#>
#> [[71]]
#> [1] -0.5387892
#>
#> [[72]]
#> [1] -0.4820375
#>
#> [[73]]
#> [1] -0.307913
#>
#> [[74]]
#> [1] 0.2131706
#>
#> [[75]]
#> [1] -0.3375787
#>
#> [[76]]
#> [1] -0.2137568
#>
#> [[77]]
#> [1] -0.1402376
#>
#> [[78]]
#> [1] -0.02673426
#>
#> [[79]]
#> [1] -0.0551101
#>
#> [[80]]
#> [1] 0.1061163
#>
#> [[81]]
#> [1] 0.1835049
#>
#> [[82]]
#> [1] -0.3453176
#>
#> [[83]]
#> [1] 0.264763
#>
#> [[84]]
#> [1] -0.5387892
#>
#> [[85]]
#> [1] 0.5046678
#>
#> [[86]]
#> [1] 0.1757661
#>
#> [[87]]
#> [1] 0.1641578
#>
#> [[88]]
#> [1] 0.03388685
#>
#> [[89]]
#> [1] -0.0783267
#>
#> [[90]]
#> [1] -0.04221199
#>
#> [[91]]
#> [1] 0.08805891
#>
#> [[92]]
#> [1] -0.3466074
#>
#> [[93]]
#> [1] -0.1260497
#>
#> [[94]]
#> [1] 0.07129137
#>
#> [[95]]
#> [1] -0.369824
#>
#> [[96]]
#> [1] -0.4781681
#>
#> [[97]]
#> [1] -0.206018
#>
#> [[98]]
#> [1] 0.4440467
#>
#> [[99]]
#> [1] 0.3950339
#>
#> [[100]]
#> [1] 0.0158295
#>
#> [[101]]
#> [1] 0.1332023
#>
#> [[102]]
#> [1] 0.2273585
#>
#> [[103]]
#> [1] -0.3246806
#>
#> [[104]]
#> [1] -0.1157312
#>
#> [[105]]
#> [1] 0.5188558
#>
#> [[106]]
#> [1] -0.004807477
#>
#> [[107]]
#> [1] 0.2234891
#>
#> [[108]]
#> [1] -0.1815116
#>
#> [[109]]
#> [1] -0.0189954
#>
#> [[110]]
#> [1] 0.3111962
#>
#> [[111]]
#> [1] 0.2608936
#>
#> [[112]]
#> [1] -0.1453969
#>
#> [[113]]
#> [1] 0.2247789
#>
#> [[114]]
#> [1] 0.6168814
#>
#> [[115]]
#> [1] 0.06097288
#>
#> [[116]]
#> [1] 0.1357819
#>
#> [[117]]
#> [1] -0.09509424
#>
#> [[118]]
#> [1] -0.3672443
#>
#> [[119]]
#> [1] 0.01453969
#>
#> [[120]]
#> [1] 0.01196006
#>
#> [[121]]
#> [1] 0.1770559
#>
#> [[122]]
#> [1] 0.1925336
#>
#> [[123]]
#> [1] 0.04678496
#>
#> [[124]]
#> [1] -0.1608746
#>
#> [[125]]
#> [1] 0.03001742
#>
#> [[126]]
#> [1] -0.4665598
#>
#> [[127]]
#> [1] -0.4136775
#>
#> [[128]]
#> [1] -0.4046489
#>
#> [[129]]
#> [1] 0.1035366
#>
#> [[130]]
#> [1] 0.2273585
#>
#> [[131]]
#> [1] -0.117021
#>
#> [[132]]
#> [1] 0.4866105
#>
#> [[133]]
#> [1] 0.4001932
#>
#> [[134]]
#> [1] -0.1711931
#>
#> [[135]]
#> [1] -0.0783267
#>
#> [[136]]
#> [1] -0.3466074
#>
#> [[137]]
#> [1] 0.1499698
#>
#> [[138]]
#> [1] -0.1131516
#>
#> [[139]]
#> [1] -0.3466074
#>
#> [[140]]
#> [1] -0.1866708
#>
#> [[141]]
#> [1] 0.1241736
#>
#> [[142]]
#> [1] -0.3143621
#>
#> [[143]]
#> [1] 0.07258118
#>
#> [[144]]
#> [1] 0.08934872
#>
#> [[145]]
#> [1] -0.3233908
#>
#> [[146]]
#> [1] -0.2550308
#>
#> [[147]]
#> [1] -0.002227855
#>
#> [[148]]
#> [1] 0.2995879
#>
#> [[149]]
#> [1] -0.2253651
#>
#> [[150]]
#> [1] -0.3865915
#>
#> [[151]]
#> [1] 0.3640784
#>
#> [[152]]
#> [1] -0.03189351
#>
#> [[153]]
#> [1] 0.3202249
#>
#> [[154]]
#> [1] -0.03705275
#>
#> [[155]]
#> [1] -0.07187765
#>
#> [[156]]
#> [1] 0.1319125
#>
#> [[157]]
#> [1] -0.485907
#>
#> [[158]]
#> [1] -0.1002535
#>
#> [[159]]
#> [1] -0.3001742
#>
#> [[160]]
#> [1] -0.1015433
#>
#> [[161]]
#> [1] -0.5104134
#>
#> [[162]]
#> [1] 0.7161968
#>
#> [[163]]
#> [1] 0.5369131
#>
#> [[164]]
#> [1] 0.2699222
#>
#> [[165]]
#> [1] -0.1815116
#>
#> [[166]]
#> [1] -0.05639991
#>
#> [[167]]
#> [1] -0.2846964
#>
#> [[168]]
#> [1] 0.3344128
#>
#> [[169]]
#> [1] 0.1254634
#>
#> [[170]]
#> [1] 0.4246996
#>
#> [[171]]
#> [1] 0.0983774
#>
#> [[172]]
#> [1] -0.4730088
#>
#> [[173]]
#> [1] -0.09509424
#>
#> [[174]]
#> [1] 0.3421517
#>
#> [[175]]
#> [1] 0.2763713
#>
#> [[176]]
#> [1] -0.4072285
#>
#> [[177]]
#> [1] -0.1918301
#>
#> [[178]]
#> [1] -0.1879606
#>
#> [[179]]
#> [1] 0.2389668
#>
#> [[180]]
#> [1] 0.1112755
#>
#> [[181]]
#> [1] -0.2756678
#>
#> [[182]]
#> [1] 0.3021675
#>
#> [[183]]
#> [1] 0.08547929
#>
#> [[184]]
#> [1] -0.1673237
#>
#> [[185]]
#> [1] 0.5188558
#>
#> [[186]]
#> [1] -0.5890918
#>
#> [[187]]
#> [1] 0.5614195
#>
#> [[188]]
#> [1] 0.7587606
#>
#> [[189]]
#> [1] 0.2209094
#>
#> [[190]]
#> [1] -0.5839326
#>
#> [[191]]
#> [1] -0.4252858
#>
#> [[192]]
#> [1] 0.08289967
#>
#> [[193]]
#> [1] 0.196403
#>
#> [[194]]
#> [1] -0.2730881
#>
#> [[195]]
#> [1] -0.4794579
#>
#> [[196]]
#> [1] 0.237677
#>
#> [[197]]
#> [1] 0.01840912
#>
#> [[198]]
#> [1] 0.08547929
#>
#> [[199]]
#> [1] -0.3904609
#>
#> [[200]]
#> [1] -0.5581364
#>
#> [[201]]
#> [1] 0.05323401
#>
#> [[202]]
#> [1] 0.3473109
#>
#> [[203]]
#> [1] -0.5929613
#>
#> [[204]]
#> [1] -0.5749039
#>
#> [[205]]
#> [1] -0.4020692
#>
#> [[206]]
#> [1] -0.2305244
#>
#> [[207]]
#> [1] 0.1086959
#>
#> [[208]]
#> [1] 0.2828204
#>
#> [[209]]
#> [1] 0.4040626
#>
#> [[210]]
#> [1] 0.2183298
#>
#> [[211]]
#> [1] -0.2705085
#>
#> [[212]]
#> [1] -0.2705085
#>
#> [[213]]
#> [1] -0.3530564
#>
#> [[214]]
#> [1] 0.2737917
#>
#> [[215]]
#> [1] -0.4962254
#>
#> [[216]]
#> [1] -0.4459228
#>
#> [[217]]
#> [1] -0.1144414
#>
#> [[218]]
#> [1] -0.4123877
#>
#> [[219]]
#> [1] 0.2015623
#>
#> [[220]]
#> [1] -0.1931199
#>
#> [[221]]
#> [1] -0.0551101
#>
#> [[222]]
#> [1] -0.369824
#>
#> [[223]]
#> [1] -0.2963047
#>
#> [[224]]
#> [1] -0.2202059
#>
#> [[225]]
#> [1] 0.01196006
#>
#> [[226]]
#> [1] 0.1525495
#>
#> [[227]]
#> [1] 0.2105909
#>
#> [[228]]
#> [1] -0.5684549
#>
#> [[229]]
#> [1] -0.3182315
#>
#> [[230]]
#> [1] -0.03189351
#>
#> [[231]]
#> [1] -0.4588209
#>
#> [[232]]
#> [1] 0.1731864
#>
#> [[233]]
#> [1] -0.7748246
#>
#> [[234]]
#> [1] -0.2563206
#>
#> [[235]]
#> [1] -0.369824
#>
#> [[236]]
#> [1] -0.2382633
#>
#> [[237]]
#> [1] -0.1892504
#>
#> [[238]]
#> [1] -0.2692187
#>
#> [[239]]
#> [1] 0.592375
#>
#> [[240]]
#> [1] -0.7915921
#>
#> [[241]]
#> [1] 0.4724226
#>
#> [[242]]
#> [1] -0.1595848
#>
#> [[243]]
#> [1] 0.09321815
#>
#> [[244]]
#> [1] -0.1699033
#>
#> [[245]]
#> [1] 0.2815305
#>
#> [[246]]
#> [1] -0.1234701
#>
#> [[247]]
#> [1] 0.09063853
#>
#> [[248]]
#> [1] 0.5085373
#>
#> [[249]]
#> [1] 0.07903023
#>
#> [[250]]
#> [1] -0.08219613
#>
#> [[251]]
#> [1] 0.05968307
#>
#> [[252]]
#> [1] -0.1208905
#>
#> [[253]]
#> [1] -0.1505561
#>
#> [[254]]
#> [1] 0.1641578
#>
#> [[255]]
#> [1] -0.1415274
#>
#> [[256]]
#> [1] 0.6658942
#>
#> [[257]]
#> [1] -0.4252858
#>
#> [[258]]
#> [1] 0.2144604
#>
#> [[259]]
#> [1] -0.7915921
#>
#> [[260]]
#> [1] -0.1247599
#>
#> [[261]]
#> [1] 0.04936458
#>
#> [[262]]
#> [1] -0.349187
#>
#> [[263]]
#> [1] -0.1466867
#>
#> [[264]]
#> [1] 0.2557343
#>
#> [[265]]
#> [1] 0.428569
#>
#> [[266]]
#> [1] -0.07316746
#>
#> [[267]]
#> [1] 0.08032004
#>
#> [[268]]
#> [1] -0.2189161
#>
#> [[269]]
#> [1] 0.1383615
#>
#> [[270]]
#> [1] 0.08805891
#>
#> [[271]]
#> [1] 0.4891901
#>
#> [[272]]
#> [1] -0.2460021
#>
#> [[273]]
#> [1] -0.5349198
#>
#> [[274]]
#> [1] 0.04162572
#>
#> [[275]]
#> [1] -0.1905403
#>
#> [[276]]
#> [1] 0.1035366
#>
#> [[277]]
#> [1] 0.2634732
#>
#> [[278]]
#> [1] 0.06613212
#>
#> [[279]]
#> [1] -0.05639991
#>
#> [[280]]
#> [1] 0.2479955
#>
#> [[281]]
#> [1] 0.3279637
#>
#> [[282]]
#> [1] 0.2157502
#>
#> [[283]]
#> [1] -0.1183108
#>
#> [[284]]
#> [1] 0.3563396
#>
#> [[285]]
#> [1] 0.3240943
#>
#> [[286]]
#> [1] 0.142231
#>
#> [[287]]
#> [1] 0.2957185
#>
#> [[288]]
#> [1] 0.2350974
#>
#> [[289]]
#> [1] -0.2292346
#>
#> [[290]]
#> [1] -0.2382633
#>
#> [[291]]
#> [1] 0.1589985
#>
#> [[292]]
#> [1] -0.2872761
#>
#> [[293]]
#> [1] -0.07058783
#>
#> [[294]]
#> [1] 0.455655
#>
#> [[295]]
#> [1] -0.2227855
#>
#> [[296]]
#> [1] 0.05968307
#>
#> [[297]]
#> [1] 0.3614988
#>
#> [[298]]
#> [1] 0.1022468
#>
#> [[299]]
#> [1] -0.1247599
#>
#> [[300]]
#> [1] 0.05323401
#>
#> [[301]]
#> [1] -0.185381
#>
#> [[302]]
#> [1] 0.1564189
#>
#> [[303]]
#> [1] -0.2782474
#>
#> [[304]]
#> [1] 0.1718966
#>
#> [[305]]
#> [1] -0.3711138
#>
#> [[306]]
#> [1] 0.2557343
#>
#> [[307]]
#> [1] -0.3853017
#>
#> [[308]]
#> [1] 0.5794769
#>
#> [[309]]
#> [1] 0.1744762
#>
#> [[310]]
#> [1] -0.09122481
#>
#> [[311]]
#> [1] 0.142231
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#> [[529]]
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#> [[530]]
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#> [[531]]
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#> [[532]]
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#> [[535]]
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#> [[538]]
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#> [[541]]
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#> [[549]]
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#> [[556]]
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#> [[560]]
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#> [[561]]
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#> [[562]]
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#> [[563]]
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#> [[564]]
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#> [[565]]
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#> [[566]]
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#> [[569]]
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#> [[574]]
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#> [[575]]
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#> [[577]]
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#> [[578]]
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#> [[579]]
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#> [[580]]
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#> [[581]]
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#> [[582]]
#> [1] 0.5627093
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#> [[583]]
#> [1] 0.7858466
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#> [[584]]
#> [1] 0.07258118
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#> [[585]]
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#> [[586]]
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#> [[587]]
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#> [[588]]
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#> [[589]]
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#> [[590]]
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#> [[591]]
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#> [[593]]
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#> [[597]]
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#> [[598]]
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#> [[599]]
#> [1] 0.4259894
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#> [[600]]
#> [1] 0.3266739
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#> [[601]]
#> [1] 0.04807477
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#> [[602]]
#> [1] 0.6736331
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#> [[603]]
#> [1] 0.2673426
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#> [[604]]
#> [1] 0.6259101
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#> [[605]]
#> [1] -0.137658
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#> [[606]]
#> [1] 0.02614799
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#> [[607]]
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#> [[608]]
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#> [[609]]
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#> [[611]]
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#> [[613]]
#> [1] 0.2931388
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#> [[614]]
#> [1] 0.03646647
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#> [[615]]
#> [1] 0.3189351
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#> [[616]]
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#> [[617]]
#> [1] -0.4265756
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#> [[618]]
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#> [[619]]
#> [1] 0.4040626
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#> [[620]]
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#> [[621]]
#> [1] -0.0551101
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#> [[622]]
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#> [[623]]
#> [1] -0.3736934
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#> [[624]]
#> [1] -0.06800821
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#> [[625]]
#> [1] 0.01453969
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#> [[626]]
#> [1] -0.05897954
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#> [[627]]
#> [1] 0.4027728
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#> [[628]]
#> [1] -0.1389478
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#> [[629]]
#> [1] 0.3950339
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#> [[630]]
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#> [[631]]
#> [1] 0.04420534
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#> [[632]]
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#> [[633]]
#> [1] -0.4227062
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#> [[634]]
#> [1] -0.1931199
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#> [[635]]
#> [1] 0.5369131
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#> [[636]]
#> [1] 0.3228045
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#> [[637]]
#> [1] -0.05897954
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#> [[638]]
#> [1] 0.09192834
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#> [[639]]
#> [1] -0.01512596
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#> [[640]]
#> [1] 0.2492853
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#> [[641]]
#> [1] 0.4840309
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#> [[642]]
#> [1] -0.04608143
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#> [[643]]
#> [1] -0.1892504
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#> [[644]]
#> [1] 0.1138551
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#> [[645]]
#> [1] 0.2725019
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#> [[646]]
#> [1] 0.1822151
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#> [[647]]
#> [1] -0.417547
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#> [[648]]
#> [1] -0.08219613
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#> [[649]]
#> [1] 0.1757661
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#> [[650]]
#> [1] 0.2621834
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#> [[651]]
#> [1] 0.3550498
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#> [[652]]
#> [1] 0.3524701
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#> [[653]]
#> [1] -0.2640595
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#> [[654]]
#> [1] 0.09579777
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#> [[655]]
#> [1] 0.1654476
#>
#> [[656]]
#> [1] 0.1667374
#>
#> [[657]]
#> [1] 0.3640784
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#> [[658]]
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#> [1] 0.3176453
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#> [1] 0.4272792
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#> [[664]]
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#> [[665]]
#> [1] -0.2498716
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#> [[666]]
#> [1] 0.1473902
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#> [1] 0.3034573
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#> [[668]]
#> [1] -0.1673237
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#> [[669]]
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#> [1] 0.2467057
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#> [[677]]
#> [1] 0.3847154
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#> [[679]]
#> [1] -0.1273395
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#> [[681]]
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#> [[687]]
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#> [[696]]
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#> [1] -0.274378
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#> [[700]]
#> [1] 0.100957
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#> [[701]]
#> [1] 0.2363872
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#> [[702]]
#> [1] 0.1370717
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#> [[703]]
#> [1] 0.08805891
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#> [[704]]
#> [1] 0.3344128
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#> [[705]]
#> [1] -0.629076
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#> [[706]]
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#> [[707]]
#> [1] 0.2982981
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#> [[708]]
#> [1] 0.5201456
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#> [[709]]
#> [1] 0.1589985
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#> [[710]]
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#> [[711]]
#> [1] 0.03259704
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#> [[712]]
#> [1] 0.4092218
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#> [[713]]
#> [1] -0.4846171
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#> [[714]]
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#> [[715]]
#> [1] 0.1228838
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#> [[717]]
#> [1] 0.2247789
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#> [1] -0.02673426
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#> [1] 0.05968307
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#> [[721]]
#> [1] -0.0435018
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#> [[722]]
#> [1] -0.4639802
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#> [[723]]
#> [1] 0.04678496
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#> [[724]]
#> [1] -0.3298398
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#> [[725]]
#> [1] -0.4136775
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#> [[726]]
#> [1] -0.07703689
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#> [[727]]
#> [1] 0.1448106
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#> [[728]]
#> [1] 0.6336489
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#> [[729]]
#> [1] 0.5149863
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#> [[730]]
#> [1] 0.333123
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#> [[731]]
#> [1] -0.4291553
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#> [[732]]
#> [1] 0.3524701
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#> [[733]]
#> [1] -0.1453969
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#> [[734]]
#> [1] 0.339572
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#> [[735]]
#> [1] 0.3150656
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#> [[736]]
#> [1] -0.1737727
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#> [[737]]
#> [1] 0.1577087
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#> [[738]]
#> [1] -0.1350784
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#> [[739]]
#> [1] 0.03001742
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#> [[740]]
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#> [[741]]
#> [1] -0.08864519
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#> [[742]]
#> [1] 0.3679479
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#> [[743]]
#> [1] 0.3460211
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#> [[744]]
#> [1] -0.2369734
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#> [[745]]
#> [1] 0.03001742
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#> [[746]]
#> [1] -0.3749832
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#> [[747]]
#> [1] 0.08418948
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#> [[748]]
#> [1] 0.1835049
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#> [[749]]
#> [1] -0.5516873
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#> [[750]]
#> [1] 0.2737917
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#> [[751]]
#> [1] 0.4698429
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#> [[752]]
#> [1] -0.4214164
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#> [[753]]
#> [1] -0.07703689
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#> [[754]]
#> [1] 0.1125653
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#> [[755]]
#> [1] 0.03388685
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#> [[756]]
#> [1] 0.1190144
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#> [[757]]
#> [1] 0.4904799
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#> [[758]]
#> [1] -0.1737727
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#> [[759]]
#> [1] -0.2524512
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#> [[760]]
#> [1] -0.7000156
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#> [[761]]
#> [1] -0.004807477
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#> [[762]]
#> [1] 0.1615781
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#> [[763]]
#> [1] -0.5516873
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#> [[764]]
#> [1] 0.5794769
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#> [[765]]
#> [1] 0.2544445
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#> [[766]]
#> [1] -0.7541876
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#> [[767]]
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#> [[768]]
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#> [[769]]
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#> [[770]]
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#> [[771]]
#> [1] 0.1151449
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#> [[772]]
#> [1] 0.3150656
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#> [[773]]
#> [1] -0.164744
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#> [[774]]
#> [1] 0.001641578
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#> [[775]]
#> [1] 0.4517856
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#> [[776]]
#> [1] -0.07445727
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#> [[777]]
#> [1] 0.3073268
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#> [[778]]
#> [1] -0.3775628
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#> [[779]]
#> [1] 0.07387099
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#> [[780]]
#> [1] 0.05323401
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#> [[781]]
#> [1] 0.4737124
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#> [[782]]
#> [1] -0.1969893
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#> [[783]]
#> [1] -0.4278655
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#> [[784]]
#> [1] 0.2247789
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#> [[785]]
#> [1] -0.06542859
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#> [[786]]
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#> [[787]]
#> [1] 0.4130913
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#> [[788]]
#> [1] -0.26019
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#> [[789]]
#> [1] 0.3240943
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#> [[790]]
#> [1] 0.4466263
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#> [[791]]
#> [1] 0.03517666
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#> [[792]]
#> [1] -0.2963047
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#> [[793]]
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#> [[794]]
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#> [[795]]
#> [1] -0.4098081
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#> [[796]]
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#> [[797]]
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#> [[798]]
#> [1] 0.1061163
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#> [[799]]
#> [1] -0.2279448
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#> [[800]]
#> [1] 0.1641578
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#> [[801]]
#> [1] 0.07258118
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#> [[802]]
#> [1] 0.2866898
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#> [[803]]
#> [1] 0.3511803
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#> [[804]]
#> [1] 0.3150656
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#> [[805]]
#> [1] -0.2576104
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#> [[806]]
#> [1] 0.0867691
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#> [[807]]
#> [1] -0.1737727
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#> [[808]]
#> [1] -0.2189161
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#> [[809]]
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#> [[810]]
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#> [[811]]
#> [1] -0.4085183
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#> [[812]]
#> [1] -0.04995086
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#> [[813]]
#> [1] 0.4930595
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#> [[814]]
#> [1] 0.2144604
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#> [[815]]
#> [1] -0.01770559
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#> [[816]]
#> [1] -0.3517666
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#> [[817]]
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#> [[818]]
#> [1] 0.4582346
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#> [[819]]
#> [1] -0.1776421
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#> [[820]]
#> [1] 0.0158295
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#> [[821]]
#> [1] 0.0519442
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#> [[822]]
#> [1] 0.1306227
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#> [[823]]
#> [1] 0.05839326
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#> [[824]]
#> [1] 0.3627886
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#> [[825]]
#> [1] -0.2550308
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#> [[826]]
#> [1] -0.1686135
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#> [[827]]
#> [1] 0.1564189
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#> [[828]]
#> [1] 0.7768179
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#> [[829]]
#> [1] -0.3646647
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#> [[830]]
#> [1] 0.4659735
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#> [[831]]
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#> [[832]]
#> [1] 0.1267532
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#> [[833]]
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#> [[834]]
#> [1] 0.0751608
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#> [[835]]
#> [1] 0.2608936
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#> [[836]]
#> [1] -0.09122481
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#> [[837]]
#> [1] -0.04479162
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#> [[838]]
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#> [[839]]
#> [1] -0.2111772
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#> [[840]]
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#> [[841]]
#> [1] 0.09708759
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#> [[842]]
#> [1] -0.7761144
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#> [[843]]
#> [1] -0.1389478
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#> [[844]]
#> [1] -0.08348594
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#> [[845]]
#> [1] 0.03130723
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#> [[846]]
#> [1] -0.6703499
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#> [[847]]
#> [1] 0.1061163
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#> [[848]]
#> [1] -0.206018
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#> [[849]]
#> [1] 0.08547929
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#> [[850]]
#> [1] -0.2846964
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#> [[851]]
#> [1] -0.09896367
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#> [[852]]
#> [1] -0.1415274
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#> [[853]]
#> [1] -0.5117032
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#> [[854]]
#> [1] 0.08547929
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#> [[855]]
#> [1] -0.110572
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#> [[856]]
#> [1] 0.3421517
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#> [[857]]
#> [1] 0.1551291
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#> [[858]]
#> [1] 0.05323401
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#> [[859]]
#> [1] -0.06800821
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#> [[860]]
#> [1] 0.3215147
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#> [[861]]
#> [1] 0.524015
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#> [[862]]
#> [1] 0.02614799
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#> [[863]]
#> [1] -0.2963047
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#> [[864]]
#> [1] -0.2756678
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#> [[865]]
#> [1] 0.05452383
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#> [[866]]
#> [1] -0.06026935
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#> [[867]]
#> [1] -0.8186782
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#> [[868]]
#> [1] 0.3795562
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#> [[869]]
#> [1] -0.2202059
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#> [[870]]
#> [1] 0.5369131
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#> [[871]]
#> [1] -0.1363682
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#> [[872]]
#> [1] 0.14868
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#> [[873]]
#> [1] 0.4879003
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#> [[874]]
#> [1] 0.100957
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#> [[875]]
#> [1] -0.2460021
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#> [[876]]
#> [1] 0.3679479
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#> [[877]]
#> [1] -0.1531357
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#> [[878]]
#> [1] -0.2150467
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#> [[879]]
#> [1] -0.2047282
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#> [[880]]
#> [1] 0.1757661
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#> [[881]]
#> [1] 0.07129137
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#> [[882]]
#> [1] -0.002227855
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#> [[883]]
#> [1] -0.5284707
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#> [[884]]
#> [1] -0.1131516
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#> [[885]]
#> [1] 0.2209094
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#> [[886]]
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#> [[887]]
#> [1] -0.08219613
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#> [[888]]
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#> [[889]]
#> [1] -0.009966721
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#> [[890]]
#> [1] -0.2318142
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#> [[891]]
#> [1] 0.196403
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#> [[892]]
#> [1] -0.2911455
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#> [[893]]
#> [1] 0.1086959
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#> [[894]]
#> [1] -0.1234701
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#> [[895]]
#> [1] -0.2576104
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#> [[896]]
#> [1] 0.407932
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#> [[897]]
#> [1] -0.5749039
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#> [[898]]
#> [1] 0.5730278
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#> [[899]]
#> [1] -0.1969893
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#> [[900]]
#> [1] 0.0751608
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#> [[901]]
#> [1] -0.1686135
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#> [[902]]
#> [1] 0.5639991
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#> [[903]]
#> [1] 0.571738
#>
#> [[904]]
#> [1] 0.1976928
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#> [[905]]
#> [1] -0.2150467
#>
#> [[906]]
#> [1] 0.3460211
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#> [[907]]
#> [1] -0.2963047
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#> [[908]]
#> [1] -0.2240753
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#> [[909]]
#> [1] -0.253741
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#> [[910]]
#> [1] -0.3646647
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#> [[911]]
#> [1] 0.3215147
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#> [[912]]
#> [1] -0.4820375
#>
#> [[913]]
#> [1] 0.1048265
#>
#> [[914]]
#> [1] -0.1208905
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#> [[915]]
#> [1] 0.0519442
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#> [[916]]
#> [1] -0.2253651
#>
#> [[917]]
#> [1] -0.4871968
#>
#> [[918]]
#> [1] -0.1041229
#>
#> [[919]]
#> [1] 0.3369924
#>
#> [[920]]
#> [1] 0.3150656
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#> [[921]]
#> [1] 0.4427569
#>
#> [[922]]
#> [1] 0.4530754
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#> [[923]]
#> [1] -0.007387099
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#> [[924]]
#> [1] 0.4750022
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#> [[925]]
#> [1] 0.01969893
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#> [[926]]
#> [1] -0.3427379
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#> [[927]]
#> [1] -0.6497129
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#> [[928]]
#> [1] -0.1673237
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#> [[929]]
#> [1] -0.2408429
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#> [[930]]
#> [1] 0.3421517
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#> [[931]]
#> [1] -0.2782474
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#> [[932]]
#> [1] -0.2163365
#>
#> [[933]]
#> [1] 0.3614988
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#> [[934]]
#> [1] 0.4234097
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#> [[935]]
#> [1] 0.03904609
#>
#> [[936]]
#> [1] -0.8792993
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#> [[937]]
#> [1] 0.5485214
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#> [[938]]
#> [1] -0.04737124
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#> [[939]]
#> [1] -0.2988844
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#> [[940]]
#> [1] -0.2369734
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#> [[941]]
#> [1] -0.2137568
#>
#> [[942]]
#> [1] 0.1228838
#>
#> [[943]]
#> [1] -0.5736141
#>
#> [[944]]
#> [1] -0.1995689
#>
#> [[945]]
#> [1] -0.06413878
#>
#> [[946]]
#> [1] 0.5910852
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#> [[947]]
#> [1] -0.5632956
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#> [[948]]
#> [1] -0.4459228
#>
#> [[949]]
#> [1] -0.2963047
#>
#> [[950]]
#> [1] 0.04033591
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#> [[951]]
#> [1] -0.3543462
#>
#> [[952]]
#> [1] -0.2305244
#>
#> [[953]]
#> [1] -0.1247599
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#> [[954]]
#> [1] 0.3614988
#>
#> [[955]]
#> [1] 0.1706068
#>
#> [[956]]
#> [1] 0.1461004
#>
#> [[957]]
#> [1] 0.1099857
#>
#> [[958]]
#> [1] 0.1332023
#>
#> [[959]]
#> [1] 0.08934872
#>
#> [[960]]
#> [1] 0.14868
#>
#> [[961]]
#> [1] 0.6775025
#>
#> [[962]]
#> [1] 0.3305434
#>
#> [[963]]
#> [1] 0.1706068
#>
#> [[964]]
#> [1] 0.3305434
#>
#> [[965]]
#> [1] 0.3692377
#>
#> [[966]]
#> [1] 0.6014037
#>
#> [[967]]
#> [1] 0.07000156
#>
#> [[968]]
#> [1] 0.2957185
#>
#> [[969]]
#> [1] 0.4621041
#>
#> [[970]]
#> [1] -0.212467
#>
#> [[971]]
#> [1] -0.1441071
#>
#> [[972]]
#> [1] 0.1357819
#>
#> [[973]]
#> [1] -0.01125653
#>
#> [[974]]
#> [1] -0.2950149
#>
#> [[975]]
#> [1] -0.02802407
#>
#> [[976]]
#> [1] -0.4665598
#>
#> [[977]]
#> [1] 0.1061163
#>
#> [[978]]
#> [1] 0.1112755
#>
#> [[979]]
#> [1] -0.6458435
#>
#> [[980]]
#> [1] 0.4105116
#>
#> [[981]]
#> [1] 0.128043
#>
#> [[982]]
#> [1] 0.1344921
#>
#> [[983]]
#> [1] 0.2789509
#>
#> [[984]]
#> [1] 0.3150656
#>
#> [[985]]
#> [1] 0.3344128
#>
#> [[986]]
#> [1] 0.196403
#>
#> [[987]]
#> [1] 0.2299381
#>
#> [[988]]
#> [1] 0.004221199
#>
#> [[989]]
#> [1] -0.4807477
#>
#> [[990]]
#> [1] 0.3447313
#>
#> [[991]]
#> [1] -0.0009380443
#>
#> [[992]]
#> [1] 0.09708759
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#> [[993]]
#> [1] -0.5542669
#>
#> [[994]]
#> [1] -0.3569259
#>
#> [[995]]
#> [1] 0.5575501
#>
#> [[996]]
#> [1] 0.2570241
#>
#> [[997]]
#> [1] -0.4330247
#>
#> [[998]]
#> [1] -0.3478972
#>
#> [[999]]
#> [1] 0.2299381
#>
#> [[1000]]
#> [1] 0.08032004
#>
#> [[1001]]
#> [1] 0.2841102
cor.test(dta[dta$race=="asian", "math"], dta[dta$race=="asian", "socst"])
#>
#> Pearson's product-moment correlation
#>
#> data: dta[dta$race == "asian", "math"] and dta[dta$race == "asian", "socst"]
#> t = 1.9887, df = 9, p-value = 0.07796
#> alternative hypothesis: true correlation is not equal to 0
#> 95 percent confidence interval:
#> -0.07083501 0.86552255
#> sample estimates:
#> cor
#> 0.55251773.An example of obtaining (nonparametric) bootstrap estimates of coefficients for a multiple linear regression model for the anorexia{MASS} data set is presented in the following script . Figure out how it works and improve the code. DONE~I guess…
#open data#
data(anorexia, package="MASS")
#define dta as data#
dta <- anorexia
#see the summary of data#
summary(dta)
#> Treat Prewt Postwt
#> CBT :29 Min. :70.00 Min. : 71.30
#> Cont:26 1st Qu.:79.60 1st Qu.: 79.33
#> FT :17 Median :82.30 Median : 84.05
#> Mean :82.41 Mean : 85.17
#> 3rd Qu.:86.00 3rd Qu.: 91.55
#> Max. :94.90 Max. :103.60
#see how long the data of any dimention#
dim(dta)
#> [1] 72 3
#see the row names of the data#
row.names(dta)
#> [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15"
#> [16] "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" "30"
#> [31] "31" "32" "33" "34" "35" "36" "37" "38" "39" "40" "41" "42" "43" "44" "45"
#> [46] "46" "47" "48" "49" "50" "51" "52" "53" "54" "55" "56" "57" "58" "59" "60"
#> [61] "61" "62" "63" "64" "65" "66" "67" "68" "69" "70" "71" "72"
#define "anrx_lm " as a Regression equation with Postwt ~ Prewt + Treat#
anrx_lm <- lm(Postwt ~ Prewt + Treat, data=dta)
#see the result of anrx_lm #
summary(anrx_lm)
#>
#> Call:
#> lm(formula = Postwt ~ Prewt + Treat, data = dta)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -14.1083 -4.2773 -0.5484 5.4838 15.2922
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 49.7711 13.3910 3.717 0.00041 ***
#> Prewt 0.4345 0.1612 2.695 0.00885 **
#> TreatCont -4.0971 1.8935 -2.164 0.03400 *
#> TreatFT 4.5631 2.1333 2.139 0.03604 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 6.978 on 68 degrees of freedom
#> Multiple R-squared: 0.2777, Adjusted R-squared: 0.2458
#> F-statistic: 8.713 on 3 and 68 DF, p-value: 5.719e-05
#do the coefficent of anrx_lm#
coef(anrx_lm)
#> (Intercept) Prewt TreatCont TreatFT
#> 49.7711090 0.4344612 -4.0970655 4.5630627
#do the bootstrap and matrixof the data#
bootstrap_function <- function(string_formula, nc, model_data, ndraws) {
coeff_mtx <- matrix(0, nrow = ndraws, ncol = nc)
for (i in 1:ndraws) {
bootstrap_ids <- sample(seq(nrow(model_data)), nrow(model_data), replace = TRUE)
bootstrap_data <- model_data[bootstrap_ids,]
bootstrap_model <- lm(as.formula(string_formula), bootstrap_data)
coeff_mtx[i,] <- bootstrap_model$coefficients
if (i == 1) {
print(bootstrap_model$coefficients)
}
}
return(coeff_mtx)
}
##
bootstrap_estimates <- bootstrap_function("Postwt ~ Prewt + Treat", nc=4, dta, 500)
#> (Intercept) Prewt TreatCont TreatFT
#> 59.1174458 0.3128159 -4.0222982 8.1316941
##
bootstrap_CIs <- matrix(0, nrow = 4, ncol = 2)
for (i in 1:4) {
bootstrap_CIs[i,1] <- quantile(bootstrap_estimates[,i], 0.025)
bootstrap_CIs[i,2] <- quantile(bootstrap_estimates[,i], 0.975)
}
##
print(bootstrap_CIs)
#> [,1] [,2]
#> [1,] 18.79460713 77.3689262
#> [2,] 0.11155887 0.8119030
#> [3,] -7.45249107 -0.6329951
#> [4,] -0.06543772 8.7001310
##
confint(anrx_lm)
#> 2.5 % 97.5 %
#> (Intercept) 23.0498681 76.4923499
#> Prewt 0.1128268 0.7560955
#> TreatCont -7.8754712 -0.3186599
#> TreatFT 0.3060571 8.8200682
#I add this to knit#
par(mar = rep(2, 4))
#do 4 histogram#
par(mfrow=c(2,2))
hist(bootstrap_estimates[,1])
hist(bootstrap_estimates[,2])
hist(bootstrap_estimates[,3])
hist(bootstrap_estimates[,4])
4.What does the R script do? Replace the “while” loop in the code with a different iteration control structure. DONE~
#it does the Brownian motion in 512 times
#
#
Brownian <- function(n = 11, pause = 0.05, nIter = 512, ...) {
x = rnorm(n)
y = rnorm(n)
i = 1
repeat {
plot(x, y, ...)
text(x, y, cex = 0.5)
x = x + rnorm(n)
y = y + rnorm(n)
Sys.sleep(pause)
i = i + 1
if(i >= nIter) break
}
}
###
## test it
Brownian(xlim = c(-20, 20), ylim = c(-20, 20),
pch = 21, cex = 2, col = "cyan", bg = "lavender") 
5.Here is an example of simulation using R. Figure out how it works and improve the code. DONE…I guess
#
#
#
simSexHeight <- function(n) {
# it define m as a matrix, with uniform distribution and random normal distribution, 2 column
m <- matrix(c(runif(n), rnorm(n)), ncol=2)
#it define draw as a "mr" function, and if mr < 0.505, then sex = 1, cm = 170+7*mr
# if not, sex = 0, cm = 160+5*mr
draw <- function(mr) { # mr = one row of m
if (mr[1] < 0.505) {
sex <- 1
cm <- 170 + 7*mr[2]
} else {
sex <- 0
cm <- 160 + 5*mr[2]
}
#return it
return(c(sex, cm))
}
# define person as do the transpose with "m" and "draw", and report with 1 vector
person <- t(apply(m, 1, draw))
#turn person to a data.frame
person <- as.data.frame(person)
#define the column "person" report "M" of "F"
person[, 1] <- ifelse(person[, 1]==1, "M", "F")
#and define the "person" names as "Gender" then "Height"
names(person) <- c("Gender", "Height")
#retun it
return(person)
}
###
simSexHeight(10)
#> Gender Height
#> 1 F 157.3075
#> 2 F 161.3748
#> 3 F 165.7450
#> 4 F 163.2426
#> 5 F 147.7559
#> 6 M 162.3518
#> 7 M 164.2871
#> 8 M 181.5974
#> 9 F 158.8925
#> 10 M 166.8779
#don't know how to improve it...Exercises:
1.Download the data set consisting 9 different measurements on 1,597 faculty, including their salaries, gender, ranks, and etc, recorded over several years by executing the first few lines of the salary script.
Note that there are different numbers of observations per faculty.
Generate a plot (see below for example) the distributions of faculty’s salaries in their final years next to that for all years by rank (Assist, Assoc, Full).
You will need to do a bit of programming for data manipulation to get the salary for the final year for each faculty. unfinish
##
fL <- "http://faculty.washington.edu/kenrice/rintro/salary.txt"
dta <- read.table(fL, header=TRUE)
##
str(dta)
#> 'data.frame': 19792 obs. of 11 variables:
#> $ case : int 1 2 3 4 5 6 7 8 9 10 ...
#> $ id : int 1 2 2 4 6 6 6 6 6 7 ...
#> $ gender : chr "F" "M" "M" "M" ...
#> $ deg : chr "Other" "Other" "Other" "PhD" ...
#> $ yrdeg : int 92 91 91 96 66 66 66 66 66 70 ...
#> $ field : chr "Other" "Other" "Other" "Other" ...
#> $ startyr: int 95 94 94 95 91 91 91 91 91 71 ...
#> $ year : int 95 94 95 95 91 92 93 94 95 76 ...
#> $ rank : chr "Assist" "Assist" "Assist" "Assist" ...
#> $ admin : int 0 0 0 0 1 1 0 0 0 0 ...
#> $ salary : num 6684 4743 4881 NA 11182 ...
##
dim(dta)
#> [1] 19792 11
##
names(dta)
#> [1] "case" "id" "gender" "deg" "yrdeg" "field" "startyr"
#> [8] "year" "rank" "admin" "salary"2.The riffle function carries out the task of interlacing two lists of numbers, starting with the longer list, without repeating.
The same objective could have been achieved with the script here. Revise the orginal riffle function with the approach taken in the latter. unfinish
#
# riffle
# interlace two lists of numbers, starting with the longer list,
# without repeating
#
riffle <- function(x, y) {
z <- NULL
count <- 1
for (i in 1:max(length(x), length(y))) {
if (i <= length(x)) {
z[count] <- x[i]
count <- count + 1
}
if (i <= length(y)) {
z[count] <- y[i]
count <- count + 1
}
}
return(z)
}
###
##
# test it
riffle(1:10, 50:55)
#> [1] 1 50 2 51 3 52 4 53 5 54 6 55 7 8 9 10
###
#
#
#
x <- 1:10
y <- 50:55
dl <- length(x) - length(y)
y[(length(y)+1):(length(y)+dl)] <- rep(NA, dl)
c(na.omit(as.numeric(t(cbind(x,y)))))
#> [1] 1 50 2 51 3 52 4 53 5 54 6 55 7 8 9 10
###3.The script produces the color strip below:
Draw the color squares below by revising and vectorizing the code given. (Hint: ?rect) DONE~
#
#plot a color strip
my_cl <- c("yellow", "forestgreen", "dodgerblue", "violet", "purple", "indianred","orange")
a <- length(my_cl) - 1
plot.new()
plot.window(xlim = c(0, a), ylim = c(0, a), asp = 1)
for(i in 1:a){for(j in 1:a){ rect(i-1, j-1, i, j, col = my_cl[(i+ a+1 -j) %% (a+1)+1])}}
4.Simulate sequences of 100 coin tosses and look for the length of the longest streak (run) in each sequence.
Investigate the relationship between the probability of heads (or tails) and the maximum run length. (Hint: ?rle). DONE~
library("tidyverse")
#> -- Attaching packages ------------------------------------------------------------------------------------------------------------------------------------------- tidyverse 1.3.0 --
#> √ ggplot2 3.3.0 √ purrr 0.3.4
#> √ tibble 3.0.1 √ dplyr 0.8.5
#> √ tidyr 1.0.2 √ stringr 1.4.0
#> √ readr 1.3.1 √ forcats 0.5.0
#> -- Conflicts ---------------------------------------------------------------------------------------------------------------------------------------------- tidyverse_conflicts() --
#> x dplyr::filter() masks stats::filter()
#> x dplyr::lag() masks stats::lag()
coin <- function(p = .5, n = 100){ifelse(runif(n) < p, 'H', 'T')}
sapply(seq(0, 1, by = .1), function(p)c(p, max(rle(coin(p))[[1]]))) %>%
t() %>% as.data.frame()
#> V1 V2
#> 1 0.0 100
#> 2 0.1 37
#> 3 0.2 9
#> 4 0.3 6
#> 5 0.4 6
#> 6 0.5 6
#> 7 0.6 7
#> 8 0.7 16
#> 9 0.8 23
#> 10 0.9 30
#> 11 1.0 1005.Use the geometrical properties of the following plot to write an R function to estimate the value of π (i.e., the area of a unit circle) through Monte Carlo simulation. DONE~~
library("plotrix")
set.seed(1234)
plot(1, 1, xlim=c(0, 1), ylim=c(0, 1), type="n", axes=T, asp=1, xlab="", ylab="", main=expression(paste("Monte Carlo for ", pi)))
pi.simulation <- function(samplesize) {
c <- rep(0, samplesize)
numberInCircle <- 0
lines(x=c(0,1,1,0,0), y=c(0,0,1,1,0))
for (i in 1:samplesize) {
x <- runif(2)
if (sqrt((x[1])^2 + (x[2])^2) <= 1) {
numberInCircle <- numberInCircle + 1
points(x[1], x[2], col="green", pch=".")
}
else {
points(x[1], x[2], col="red", pch=".")
}
c[i] <- (numberInCircle / i) * 4
}
return(c)
}
size <- 10000
pi.sim <- pi.simulation(size)