WPA9

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Question 1 : Using a loop, print the integers from 1 to 50. (Hint, use the print() function).

one.to.fifty <- rep(NA, 50)

for(i in 1:50){
  one.to.fifty[i] <- i
}

print(one.to.fifty)

##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
## [24] 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
## [47] 47 48 49 50

Question 2. Using a loop, add all the integers between 0 and 1000.

current.sum <- 0
for(i in 1:1000) {
current.sum <- current.sum + i
}
current.sum

## [1] 500500

Now, add all the EVEN integers between 0 and 1000 (hint: use seq())

even.integers <- seq(0,1000,2)
current.sum.2 <- 0
for (i in even.integers) {
  current.sum.2 <- current.sum.2 + i
}
current.sum.2

## [1] 250500

Now, repeat A and B WITHOUT using a loop.

#A:
sum(1:1000)

## [1] 500500

#B:
sum(seq(0,1000, 2))

## [1] 250500

Question 3 : Here is a dataframe of survey data containing 5 questions I collected from 6 participants:

survey <- data.frame(
                     "participant" = c(1, 2, 3, 4, 5, 6),
                     "q1" = c(5, 3, 2, 7, 11, 0),
                     "q2" = c(4, 2, 2, 5, -10, 99),
                     "q3" = c(-4, -3, 4, 2, 9, 10),
                     "q4" = c(-30, 5, 2, 23, 4, 2),
                     "q5" = c(88, 4, -20, 2, 4, 2)
                     )

The response to each question should be an integer between 1 and 5. Obviously, we have some bad values in the dataframe. Let’s fix them. Using a loop, create a new dataframe called survey.clean where all the invalid values (those that are not integers between 1 and 5) are set to NA.

#Create a new object called survey.clean by assigning the original dataset to survey.clean.
survey.clean <- survey

#Set the loop index to i and set the loop index.values to the vector of data columns.
for (i in 2:ncol(survey.clean)){
  #In the loop code, assign the ith column of data to a new vector called data.temp.
data.temp <- survey.clean[, i]
#Convert all invalid values in data.temp to NA (hint: use )
data.temp[(data.temp %in% 1:5 == F)] <- NA
#Assign data.temp back to the ith column of survey.clean.
survey.clean[, i]<- data.temp
#Close the loop and let it run!
}
survey.clean

##   participant q1 q2 q3 q4 q5
## 1           1  5  4 NA NA NA
## 2           2  3  2 NA  5  4
## 3           3  2  2  4  2 NA
## 4           4 NA  5  2 NA  2
## 5           5 NA NA NA  4  4
## 6           6 NA NA NA  2  2

Now, again using a loop, add a new column to the dataframe called “invalid.answers” that indicates, for each participant, how many bad answers they gave.

Hint: Use the following steps

#Assign the new vector invalid.answers to the dataframe containing all NA values.
survey.clean$invalid.answers <- rep(NA, 6)
#Create a loop over the rows of the dataframe.
for (i in nrow(survey.clean)){
#Assign the data for the ith row to a new vector called part.i
part.i <- survey.clean[i, ]
#Calculate how many of the values in part.i are NA (use is.na())
number.na <- sum(is.na(part.i [1:6]))
#Assign the result to the ith row in invalid.answers
survey.clean$invalid.answers<- number.na

}
survey.clean

##   participant q1 q2 q3 q4 q5 invalid.answers
## 1           1  5  4 NA NA NA               3
## 2           2  3  2 NA  5  4               3
## 3           3  2  2  4  2 NA               3
## 4           4 NA  5  2 NA  2               3
## 5           5 NA NA NA  4  4               3
## 6           6 NA NA NA  2  2               3

Question 4

Standardizing a variable means subtracting the mean, and then dividing by the standard deviation. Let’s use a loop to standardize the numeric columns in the pirates dataset. You can access this dataset in the yarrr package, or by downloading it from http://nathanieldphillips.com/wp-content/uploads/2016/01/pirates.txt

pirates <- read.table ("http://nathanieldphillips.com/wp-content/uploads/2016/01/pirates.txt",
           header= TRUE)

Create a function called standardize.me() that takes a numeric vector as an argument, and returns the standardized version of the vector (hint: Look at the answers to WPA8!)

standardize.me <- function(x) {
  
  output <- (x - mean(x)) / sd(x)
  
  return(output)
  
}

Assign all the numeric columns of the original pirates dataset to a new dataset called pirates.z

pirates.z <- pirates[ , c(4,6,7,8,11,12,13)]

Using a loop and your new function, standardize all the variables pirates.z dataset

for(i in pirates.z){
  standard.pirates <- standardize.me(i)
}
standard.pirates

##    [1] -0.95912647  0.60280977  1.09091484  1.09091484 -0.95912647
##    [6]  1.18853585 -0.95912647 -0.76388444  0.99329382 -0.95912647
##   [11]  1.77426194 -0.95912647  1.09091484 -0.66626342  1.18853585
##   [16]  0.99329382  0.70043078 -0.95912647 -0.86150545 -0.86150545
##   [21] -0.95912647 -0.95912647  0.40756774 -0.86150545 -0.76388444
##   [26]  1.28615687  1.57901991  1.28615687  1.77426194  1.09091484
##   [31] -0.95912647 -0.86150545 -0.95912647 -0.76388444  1.57901991
##   [36] -0.27577937  0.01708368  1.18853585 -0.95912647 -0.95912647
##   [41]  0.30994672 -0.95912647  0.50518875  1.48139890 -0.95912647
##   [46]  0.21232571  2.06712499 -0.95912647 -0.95912647 -0.95912647
##   [51] -0.95912647 -0.95912647  0.60280977  1.38377788  1.38377788
##   [56]  0.89567281 -0.95912647  1.38377788 -0.95912647 -0.95912647
##   [61] -0.76388444 -0.95912647 -0.95912647  0.79805179 -0.86150545
##   [66] -0.95912647 -0.76388444  1.09091484 -0.95912647  0.11470469
##   [71]  0.30994672 -0.95912647  1.77426194 -0.86150545 -0.95912647
##   [76] -0.86150545 -0.86150545  0.89567281  0.30994672  0.70043078
##   [81] -0.08053734  1.28615687  1.28615687  0.99329382 -0.86150545
##   [86] -0.95912647  0.99329382  0.79805179 -0.86150545 -0.95912647
##   [91] -0.95912647 -0.17815835  0.79805179 -0.95912647  0.50518875
##   [96]  0.70043078 -0.86150545  1.77426194  0.99329382  2.35998803
##  [101] -0.86150545 -0.76388444  0.79805179 -0.95912647  1.18853585
##  [106]  0.99329382 -0.95912647  0.01708368  2.26236701 -0.95912647
##  [111]  1.38377788 -0.86150545  1.18853585 -0.08053734 -0.95912647
##  [116]  1.77426194 -0.86150545  1.96950397  0.11470469 -0.86150545
##  [121]  1.18853585  0.11470469 -0.95912647  1.28615687  0.60280977
##  [126] -0.95912647 -0.95912647  0.79805179  1.48139890 -0.95912647
##  [131] -0.86150545 -0.95912647 -0.95912647  1.67664093 -0.95912647
##  [136] -0.95912647  1.28615687 -0.95912647  1.09091484 -0.86150545
##  [141] -0.95912647 -0.95912647 -0.86150545 -0.86150545 -0.76388444
##  [146] -0.95912647 -0.95912647  0.50518875 -0.95912647  0.11470469
##  [151]  0.99329382  1.38377788 -0.95912647 -0.86150545  0.40756774
##  [156] -0.95912647  0.40756774  1.18853585 -0.86150545  1.09091484
##  [161]  0.01708368 -0.95912647 -0.95912647  1.87188296  0.01708368
##  [166] -0.86150545 -0.08053734 -0.95912647 -0.95912647  0.70043078
##  [171] -0.76388444  0.40756774 -0.95912647  1.87188296 -0.86150545
##  [176] -0.86150545 -0.86150545  0.79805179 -0.76388444  0.40756774
##  [181] -0.86150545 -0.86150545  0.01708368  0.21232571  1.28615687
##  [186]  1.18853585 -0.95912647  1.38377788 -0.95912647 -0.27577937
##  [191]  1.18853585  1.67664093  0.50518875 -0.86150545 -0.95912647
##  [196]  0.60280977 -0.76388444 -0.95912647  0.89567281  1.18853585
##  [201] -0.95912647 -0.95912647  0.60280977 -0.95912647 -0.95912647
##  [206] -0.86150545  0.70043078  1.96950397 -0.95912647  1.09091484
##  [211] -0.95912647 -0.95912647 -0.95912647 -0.37340038 -0.95912647
##  [216] -0.95912647  0.89567281  1.18853585 -0.95912647 -0.95912647
##  [221]  0.70043078 -0.76388444  0.99329382 -0.95912647  0.79805179
##  [226] -0.66626342  1.38377788  1.67664093 -0.27577937  0.40756774
##  [231] -0.95912647  1.09091484 -0.86150545  0.89567281  0.50518875
##  [236] -0.86150545 -0.95912647  2.26236701 -0.95912647  0.99329382
##  [241]  0.50518875 -0.95912647 -0.95912647  0.79805179  0.99329382
##  [246] -0.95912647 -0.95912647 -0.95912647  1.77426194 -0.95912647
##  [251]  0.79805179  1.57901991 -0.95912647  1.77426194 -0.95912647
##  [256] -0.95912647  1.28615687 -0.95912647 -0.95912647  1.67664093
##  [261]  0.30994672  1.38377788  0.79805179  1.38377788  0.89567281
##  [266] -0.95912647  0.60280977 -0.95912647  1.28615687 -0.27577937
##  [271] -0.76388444  0.50518875 -0.86150545  0.89567281  1.18853585
##  [276]  1.48139890 -0.95912647  1.57901991  1.48139890  1.09091484
##  [281] -0.95912647 -0.86150545 -0.95912647 -0.95912647  1.67664093
##  [286] -0.86150545  1.87188296  1.18853585  1.18853585 -0.95912647
##  [291]  0.11470469 -0.86150545  0.60280977  0.11470469 -0.95912647
##  [296]  1.18853585 -0.95912647  0.30994672  0.11470469  1.87188296
##  [301]  0.60280977  1.57901991 -0.95912647 -0.95912647  0.11470469
##  [306]  1.48139890  0.99329382  0.30994672  1.48139890  1.48139890
##  [311] -0.95912647 -0.95912647 -0.95912647  1.09091484 -0.95912647
##  [316] -0.86150545 -0.76388444  2.06712499 -0.86150545 -0.86150545
##  [321] -0.95912647  1.09091484 -0.76388444 -0.95912647  0.89567281
##  [326]  2.75047209  0.89567281  1.67664093  0.60280977  1.09091484
##  [331] -0.95912647  0.21232571  0.89567281  1.67664093 -0.86150545
##  [336] -0.95912647  1.09091484 -0.37340038  0.30994672 -0.86150545
##  [341]  0.60280977  1.38377788 -0.95912647 -0.95912647  0.70043078
##  [346]  0.40756774 -0.86150545  1.18853585  1.67664093  1.67664093
##  [351] -0.86150545 -0.86150545  0.99329382 -0.95912647  0.40756774
##  [356] -0.86150545  0.70043078  0.30994672 -0.95912647  0.99329382
##  [361] -0.95912647  1.57901991 -0.86150545  1.09091484  0.21232571
##  [366]  0.79805179  1.48139890  1.18853585 -0.17815835 -0.95912647
##  [371] -0.86150545 -0.95912647 -0.95912647 -0.95912647 -0.95912647
##  [376]  0.40756774 -0.86150545 -0.86150545 -0.95912647 -0.95912647
##  [381]  1.96950397 -0.95912647  1.18853585  1.48139890 -0.95912647
##  [386]  0.50518875 -0.95912647  1.28615687  1.57901991  1.48139890
##  [391]  0.70043078  1.28615687  0.79805179 -0.86150545  0.01708368
##  [396]  1.48139890  0.50518875  1.77426194  0.79805179  0.79805179
##  [401] -0.95912647  1.48139890  1.09091484 -0.95912647  0.11470469
##  [406]  0.89567281  0.89567281 -0.76388444 -0.95912647 -0.76388444
##  [411] -0.47102140 -0.08053734 -0.86150545 -0.76388444  1.28615687
##  [416] -0.86150545  1.67664093 -0.86150545  2.26236701 -0.95912647
##  [421] -0.95912647  0.40756774 -0.86150545 -0.95912647 -0.76388444
##  [426] -0.95912647 -0.95912647 -0.17815835  1.28615687 -0.95912647
##  [431]  0.70043078 -0.66626342 -0.86150545  0.89567281 -0.95912647
##  [436] -0.27577937  0.70043078 -0.95912647 -0.86150545 -0.37340038
##  [441]  1.77426194 -0.95912647 -0.95912647  0.79805179  1.77426194
##  [446] -0.95912647 -0.95912647 -0.17815835  1.28615687 -0.95912647
##  [451] -0.95912647 -0.76388444  1.48139890 -0.76388444  1.09091484
##  [456]  0.99329382  1.57901991  0.30994672 -0.95912647  0.50518875
##  [461]  1.28615687 -0.08053734 -0.95912647  1.18853585  0.11470469
##  [466] -0.95912647  0.99329382 -0.95912647 -0.86150545  1.67664093
##  [471] -0.95912647 -0.95912647 -0.95912647  0.79805179 -0.76388444
##  [476]  0.50518875  0.89567281  0.99329382 -0.95912647  0.01708368
##  [481]  0.60280977 -0.95912647  0.40756774  1.87188296 -0.76388444
##  [486]  0.79805179  1.28615687 -0.95912647  1.38377788 -0.86150545
##  [491] -0.95912647 -0.95912647 -0.95912647  0.70043078  1.96950397
##  [496] -0.95912647 -0.95912647  0.50518875  0.89567281 -0.95912647
##  [501]  0.89567281  1.09091484  1.09091484 -0.95912647 -0.37340038
##  [506] -0.95912647  0.99329382  0.60280977  1.09091484 -0.95912647
##  [511]  1.09091484  0.50518875  2.06712499 -0.76388444  1.28615687
##  [516] -0.95912647 -0.95912647  0.70043078  0.89567281 -0.86150545
##  [521] -0.86150545 -0.95912647 -0.95912647  0.30994672 -0.17815835
##  [526]  0.30994672 -0.95912647  0.60280977  0.89567281 -0.95912647
##  [531]  0.60280977  0.50518875 -0.86150545  0.30994672 -0.95912647
##  [536]  0.60280977  0.21232571  1.48139890 -0.86150545 -0.95912647
##  [541] -0.86150545  1.38377788  0.99329382  1.48139890 -0.95912647
##  [546] -0.95912647  0.60280977 -0.95912647 -0.76388444 -0.95912647
##  [551]  1.18853585  1.38377788  0.60280977 -0.86150545  1.67664093
##  [556]  0.79805179  2.16474600  1.09091484  0.30994672  0.50518875
##  [561] -0.95912647  0.60280977 -0.86150545 -0.95912647  0.70043078
##  [566]  1.48139890 -0.86150545 -0.76388444 -0.95912647  2.16474600
##  [571]  0.21232571  0.11470469  1.48139890 -0.95912647 -0.37340038
##  [576]  0.79805179  1.57901991  1.09091484 -0.95912647  1.09091484
##  [581] -0.95912647  0.40756774  0.60280977 -0.95912647  0.89567281
##  [586]  0.99329382 -0.86150545  0.79805179  0.30994672 -0.95912647
##  [591] -0.95912647  1.18853585 -0.95912647 -0.17815835  1.96950397
##  [596] -0.86150545  1.38377788 -0.86150545  0.30994672  1.09091484
##  [601]  0.89567281 -0.47102140  0.79805179  0.30994672  1.18853585
##  [606]  1.67664093 -0.95912647 -0.95912647 -0.95912647  1.18853585
##  [611]  0.60280977  1.96950397  1.57901991 -0.86150545 -0.95912647
##  [616] -0.86150545 -0.95912647  1.57901991  0.60280977 -0.95912647
##  [621] -0.47102140 -0.95912647 -0.86150545 -0.95912647  1.87188296
##  [626] -0.95912647  1.67664093 -0.95912647 -0.95912647 -0.76388444
##  [631]  0.40756774  0.11470469  0.79805179  0.99329382  0.21232571
##  [636]  0.30994672 -0.95912647 -0.95912647 -0.95912647  1.48139890
##  [641] -0.95912647 -0.95912647 -0.95912647  1.87188296 -0.86150545
##  [646] -0.86150545  0.89567281  0.11470469  0.79805179 -0.86150545
##  [651]  0.79805179 -0.95912647  0.70043078 -0.95912647 -0.95912647
##  [656]  0.70043078  0.99329382 -0.95912647 -0.76388444  0.89567281
##  [661] -0.95912647 -0.66626342  0.30994672 -0.95912647 -0.86150545
##  [666]  2.06712499 -0.95912647  1.48139890  0.70043078  0.70043078
##  [671] -0.95912647 -0.95912647  0.40756774  0.50518875 -0.86150545
##  [676] -0.95912647  1.67664093 -0.17815835  0.21232571 -0.95912647
##  [681] -0.86150545 -0.86150545 -0.86150545 -0.95912647 -0.86150545
##  [686] -0.37340038  1.57901991  0.79805179 -0.95912647  1.18853585
##  [691]  0.50518875  0.11470469  0.40756774 -0.95912647  0.89567281
##  [696] -0.95912647 -0.95912647  0.70043078 -0.95912647  0.60280977
##  [701] -0.95912647  1.87188296 -0.95912647 -0.95912647 -0.95912647
##  [706] -0.95912647  1.77426194 -0.95912647 -0.76388444  1.28615687
##  [711]  0.60280977  0.89567281 -0.76388444  0.70043078 -0.95912647
##  [716]  0.89567281 -0.86150545  0.79805179 -0.86150545 -0.95912647
##  [721]  0.89567281 -0.86150545 -0.95912647 -0.86150545 -0.95912647
##  [726] -0.95912647  1.09091484 -0.95912647 -0.95912647  1.28615687
##  [731]  0.50518875 -0.95912647 -0.95912647 -0.95912647 -0.95912647
##  [736]  1.28615687  0.79805179 -0.95912647  0.30994672 -0.95912647
##  [741] -0.95912647 -0.08053734 -0.86150545 -0.95912647 -0.86150545
##  [746] -0.95912647  0.79805179  0.40756774 -0.86150545  1.18853585
##  [751]  0.99329382  0.79805179 -0.27577937 -0.95912647  1.96950397
##  [756] -0.95912647 -0.95912647 -0.76388444 -0.86150545 -0.95912647
##  [761] -0.95912647 -0.95912647  0.50518875  1.57901991 -0.76388444
##  [766] -0.95912647 -0.86150545 -0.27577937 -0.95912647 -0.95912647
##  [771]  0.11470469 -0.95912647  1.67664093  0.40756774 -0.95912647
##  [776]  1.18853585  1.18853585  0.70043078  1.09091484  1.38377788
##  [781]  1.09091484  1.67664093 -0.95912647  0.50518875 -0.86150545
##  [786] -0.76388444  0.79805179  0.89567281 -0.95912647  1.38377788
##  [791]  1.18853585  0.89567281 -0.95912647  0.89567281 -0.76388444
##  [796] -0.95912647 -0.95912647 -0.86150545 -0.95912647 -0.95912647
##  [801]  1.18853585  1.18853585  0.40756774 -0.95912647 -0.95912647
##  [806] -0.95912647 -0.95912647  0.79805179  0.79805179 -0.17815835
##  [811] -0.95912647 -0.86150545 -0.95912647 -0.86150545 -0.95912647
##  [816] -0.86150545 -0.95912647 -0.95912647 -0.95912647 -0.86150545
##  [821] -0.86150545  1.87188296  0.50518875 -0.86150545 -0.95912647
##  [826] -0.86150545 -0.95912647 -0.76388444 -0.95912647  1.18853585
##  [831]  0.89567281  1.28615687  0.01708368 -0.95912647  0.30994672
##  [836] -0.95912647 -0.95912647 -0.86150545  1.09091484 -0.95912647
##  [841] -0.86150545  0.50518875 -0.95912647 -0.86150545  0.89567281
##  [846]  0.99329382 -0.95912647  0.60280977  1.18853585 -0.95912647
##  [851] -0.86150545 -0.95912647  0.99329382 -0.95912647  0.89567281
##  [856] -0.76388444 -0.95912647 -0.66626342  0.89567281  1.96950397
##  [861]  1.77426194  0.30994672 -0.86150545 -0.86150545  0.99329382
##  [866] -0.95912647  1.28615687  0.79805179 -0.86150545 -0.95912647
##  [871] -0.95912647  0.40756774 -0.95912647 -0.95912647 -0.95912647
##  [876] -0.95912647 -0.08053734 -0.95912647  1.28615687 -0.95912647
##  [881]  0.40756774 -0.95912647  0.60280977  0.99329382  1.09091484
##  [886] -0.86150545 -0.95912647 -0.95912647  0.89567281 -0.95912647
##  [891]  1.57901991  0.60280977 -0.66626342  1.67664093 -0.95912647
##  [896]  1.28615687  0.40756774 -0.95912647  0.79805179  0.70043078
##  [901] -0.95912647 -0.95912647 -0.95912647  1.09091484  1.18853585
##  [906] -0.95912647 -0.95912647  1.48139890 -0.95912647  1.38377788
##  [911]  0.21232571 -0.95912647  0.11470469  0.21232571  0.70043078
##  [916] -0.86150545 -0.86150545  1.48139890 -0.86150545 -0.95912647
##  [921]  0.60280977 -0.86150545  0.50518875 -0.08053734  0.40756774
##  [926]  0.11470469 -0.76388444 -0.86150545 -0.95912647 -0.95912647
##  [931] -0.95912647 -0.95912647  1.18853585 -0.95912647  0.89567281
##  [936]  0.40756774 -0.76388444 -0.95912647  0.30994672 -0.86150545
##  [941] -0.95912647 -0.95912647 -0.95912647 -0.95912647 -0.95912647
##  [946] -0.76388444  1.77426194  0.79805179  0.11470469  0.79805179
##  [951]  1.28615687 -0.95912647 -0.95912647  0.60280977  0.21232571
##  [956] -0.76388444 -0.95912647  0.70043078  0.70043078 -0.86150545
##  [961] -0.95912647  1.18853585 -0.08053734  1.09091484 -0.95912647
##  [966]  0.60280977 -0.95912647 -0.76388444  0.40756774  1.67664093
##  [971] -0.86150545 -0.86150545  1.48139890  0.99329382  1.28615687
##  [976]  1.48139890  0.89567281  0.40756774 -0.95912647 -0.95912647
##  [981]  1.38377788 -0.95912647 -0.86150545 -0.95912647  1.28615687
##  [986] -0.08053734 -0.95912647 -0.86150545 -0.86150545  0.79805179
##  [991] -0.95912647 -0.86150545 -0.95912647  0.30994672 -0.95912647
##  [996] -0.95912647 -0.95912647 -0.95912647 -0.95912647 -0.95912647

What should the mean and standard deviation of all your new standardized variables be? Test your prediction by running a loop

for(i in pirates.z) {
  mean.p. <- mean(standard.pirates)
  sd.p. <- sd(standard.pirates)
}
sd.p.

## [1] 1

mean.p. 

## [1] 7.438765e-17

standard.pirates

##    [1] -0.95912647  0.60280977  1.09091484  1.09091484 -0.95912647
##    [6]  1.18853585 -0.95912647 -0.76388444  0.99329382 -0.95912647
##   [11]  1.77426194 -0.95912647  1.09091484 -0.66626342  1.18853585
##   [16]  0.99329382  0.70043078 -0.95912647 -0.86150545 -0.86150545
##   [21] -0.95912647 -0.95912647  0.40756774 -0.86150545 -0.76388444
##   [26]  1.28615687  1.57901991  1.28615687  1.77426194  1.09091484
##   [31] -0.95912647 -0.86150545 -0.95912647 -0.76388444  1.57901991
##   [36] -0.27577937  0.01708368  1.18853585 -0.95912647 -0.95912647
##   [41]  0.30994672 -0.95912647  0.50518875  1.48139890 -0.95912647
##   [46]  0.21232571  2.06712499 -0.95912647 -0.95912647 -0.95912647
##   [51] -0.95912647 -0.95912647  0.60280977  1.38377788  1.38377788
##   [56]  0.89567281 -0.95912647  1.38377788 -0.95912647 -0.95912647
##   [61] -0.76388444 -0.95912647 -0.95912647  0.79805179 -0.86150545
##   [66] -0.95912647 -0.76388444  1.09091484 -0.95912647  0.11470469
##   [71]  0.30994672 -0.95912647  1.77426194 -0.86150545 -0.95912647
##   [76] -0.86150545 -0.86150545  0.89567281  0.30994672  0.70043078
##   [81] -0.08053734  1.28615687  1.28615687  0.99329382 -0.86150545
##   [86] -0.95912647  0.99329382  0.79805179 -0.86150545 -0.95912647
##   [91] -0.95912647 -0.17815835  0.79805179 -0.95912647  0.50518875
##   [96]  0.70043078 -0.86150545  1.77426194  0.99329382  2.35998803
##  [101] -0.86150545 -0.76388444  0.79805179 -0.95912647  1.18853585
##  [106]  0.99329382 -0.95912647  0.01708368  2.26236701 -0.95912647
##  [111]  1.38377788 -0.86150545  1.18853585 -0.08053734 -0.95912647
##  [116]  1.77426194 -0.86150545  1.96950397  0.11470469 -0.86150545
##  [121]  1.18853585  0.11470469 -0.95912647  1.28615687  0.60280977
##  [126] -0.95912647 -0.95912647  0.79805179  1.48139890 -0.95912647
##  [131] -0.86150545 -0.95912647 -0.95912647  1.67664093 -0.95912647
##  [136] -0.95912647  1.28615687 -0.95912647  1.09091484 -0.86150545
##  [141] -0.95912647 -0.95912647 -0.86150545 -0.86150545 -0.76388444
##  [146] -0.95912647 -0.95912647  0.50518875 -0.95912647  0.11470469
##  [151]  0.99329382  1.38377788 -0.95912647 -0.86150545  0.40756774
##  [156] -0.95912647  0.40756774  1.18853585 -0.86150545  1.09091484
##  [161]  0.01708368 -0.95912647 -0.95912647  1.87188296  0.01708368
##  [166] -0.86150545 -0.08053734 -0.95912647 -0.95912647  0.70043078
##  [171] -0.76388444  0.40756774 -0.95912647  1.87188296 -0.86150545
##  [176] -0.86150545 -0.86150545  0.79805179 -0.76388444  0.40756774
##  [181] -0.86150545 -0.86150545  0.01708368  0.21232571  1.28615687
##  [186]  1.18853585 -0.95912647  1.38377788 -0.95912647 -0.27577937
##  [191]  1.18853585  1.67664093  0.50518875 -0.86150545 -0.95912647
##  [196]  0.60280977 -0.76388444 -0.95912647  0.89567281  1.18853585
##  [201] -0.95912647 -0.95912647  0.60280977 -0.95912647 -0.95912647
##  [206] -0.86150545  0.70043078  1.96950397 -0.95912647  1.09091484
##  [211] -0.95912647 -0.95912647 -0.95912647 -0.37340038 -0.95912647
##  [216] -0.95912647  0.89567281  1.18853585 -0.95912647 -0.95912647
##  [221]  0.70043078 -0.76388444  0.99329382 -0.95912647  0.79805179
##  [226] -0.66626342  1.38377788  1.67664093 -0.27577937  0.40756774
##  [231] -0.95912647  1.09091484 -0.86150545  0.89567281  0.50518875
##  [236] -0.86150545 -0.95912647  2.26236701 -0.95912647  0.99329382
##  [241]  0.50518875 -0.95912647 -0.95912647  0.79805179  0.99329382
##  [246] -0.95912647 -0.95912647 -0.95912647  1.77426194 -0.95912647
##  [251]  0.79805179  1.57901991 -0.95912647  1.77426194 -0.95912647
##  [256] -0.95912647  1.28615687 -0.95912647 -0.95912647  1.67664093
##  [261]  0.30994672  1.38377788  0.79805179  1.38377788  0.89567281
##  [266] -0.95912647  0.60280977 -0.95912647  1.28615687 -0.27577937
##  [271] -0.76388444  0.50518875 -0.86150545  0.89567281  1.18853585
##  [276]  1.48139890 -0.95912647  1.57901991  1.48139890  1.09091484
##  [281] -0.95912647 -0.86150545 -0.95912647 -0.95912647  1.67664093
##  [286] -0.86150545  1.87188296  1.18853585  1.18853585 -0.95912647
##  [291]  0.11470469 -0.86150545  0.60280977  0.11470469 -0.95912647
##  [296]  1.18853585 -0.95912647  0.30994672  0.11470469  1.87188296
##  [301]  0.60280977  1.57901991 -0.95912647 -0.95912647  0.11470469
##  [306]  1.48139890  0.99329382  0.30994672  1.48139890  1.48139890
##  [311] -0.95912647 -0.95912647 -0.95912647  1.09091484 -0.95912647
##  [316] -0.86150545 -0.76388444  2.06712499 -0.86150545 -0.86150545
##  [321] -0.95912647  1.09091484 -0.76388444 -0.95912647  0.89567281
##  [326]  2.75047209  0.89567281  1.67664093  0.60280977  1.09091484
##  [331] -0.95912647  0.21232571  0.89567281  1.67664093 -0.86150545
##  [336] -0.95912647  1.09091484 -0.37340038  0.30994672 -0.86150545
##  [341]  0.60280977  1.38377788 -0.95912647 -0.95912647  0.70043078
##  [346]  0.40756774 -0.86150545  1.18853585  1.67664093  1.67664093
##  [351] -0.86150545 -0.86150545  0.99329382 -0.95912647  0.40756774
##  [356] -0.86150545  0.70043078  0.30994672 -0.95912647  0.99329382
##  [361] -0.95912647  1.57901991 -0.86150545  1.09091484  0.21232571
##  [366]  0.79805179  1.48139890  1.18853585 -0.17815835 -0.95912647
##  [371] -0.86150545 -0.95912647 -0.95912647 -0.95912647 -0.95912647
##  [376]  0.40756774 -0.86150545 -0.86150545 -0.95912647 -0.95912647
##  [381]  1.96950397 -0.95912647  1.18853585  1.48139890 -0.95912647
##  [386]  0.50518875 -0.95912647  1.28615687  1.57901991  1.48139890
##  [391]  0.70043078  1.28615687  0.79805179 -0.86150545  0.01708368
##  [396]  1.48139890  0.50518875  1.77426194  0.79805179  0.79805179
##  [401] -0.95912647  1.48139890  1.09091484 -0.95912647  0.11470469
##  [406]  0.89567281  0.89567281 -0.76388444 -0.95912647 -0.76388444
##  [411] -0.47102140 -0.08053734 -0.86150545 -0.76388444  1.28615687
##  [416] -0.86150545  1.67664093 -0.86150545  2.26236701 -0.95912647
##  [421] -0.95912647  0.40756774 -0.86150545 -0.95912647 -0.76388444
##  [426] -0.95912647 -0.95912647 -0.17815835  1.28615687 -0.95912647
##  [431]  0.70043078 -0.66626342 -0.86150545  0.89567281 -0.95912647
##  [436] -0.27577937  0.70043078 -0.95912647 -0.86150545 -0.37340038
##  [441]  1.77426194 -0.95912647 -0.95912647  0.79805179  1.77426194
##  [446] -0.95912647 -0.95912647 -0.17815835  1.28615687 -0.95912647
##  [451] -0.95912647 -0.76388444  1.48139890 -0.76388444  1.09091484
##  [456]  0.99329382  1.57901991  0.30994672 -0.95912647  0.50518875
##  [461]  1.28615687 -0.08053734 -0.95912647  1.18853585  0.11470469
##  [466] -0.95912647  0.99329382 -0.95912647 -0.86150545  1.67664093
##  [471] -0.95912647 -0.95912647 -0.95912647  0.79805179 -0.76388444
##  [476]  0.50518875  0.89567281  0.99329382 -0.95912647  0.01708368
##  [481]  0.60280977 -0.95912647  0.40756774  1.87188296 -0.76388444
##  [486]  0.79805179  1.28615687 -0.95912647  1.38377788 -0.86150545
##  [491] -0.95912647 -0.95912647 -0.95912647  0.70043078  1.96950397
##  [496] -0.95912647 -0.95912647  0.50518875  0.89567281 -0.95912647
##  [501]  0.89567281  1.09091484  1.09091484 -0.95912647 -0.37340038
##  [506] -0.95912647  0.99329382  0.60280977  1.09091484 -0.95912647
##  [511]  1.09091484  0.50518875  2.06712499 -0.76388444  1.28615687
##  [516] -0.95912647 -0.95912647  0.70043078  0.89567281 -0.86150545
##  [521] -0.86150545 -0.95912647 -0.95912647  0.30994672 -0.17815835
##  [526]  0.30994672 -0.95912647  0.60280977  0.89567281 -0.95912647
##  [531]  0.60280977  0.50518875 -0.86150545  0.30994672 -0.95912647
##  [536]  0.60280977  0.21232571  1.48139890 -0.86150545 -0.95912647
##  [541] -0.86150545  1.38377788  0.99329382  1.48139890 -0.95912647
##  [546] -0.95912647  0.60280977 -0.95912647 -0.76388444 -0.95912647
##  [551]  1.18853585  1.38377788  0.60280977 -0.86150545  1.67664093
##  [556]  0.79805179  2.16474600  1.09091484  0.30994672  0.50518875
##  [561] -0.95912647  0.60280977 -0.86150545 -0.95912647  0.70043078
##  [566]  1.48139890 -0.86150545 -0.76388444 -0.95912647  2.16474600
##  [571]  0.21232571  0.11470469  1.48139890 -0.95912647 -0.37340038
##  [576]  0.79805179  1.57901991  1.09091484 -0.95912647  1.09091484
##  [581] -0.95912647  0.40756774  0.60280977 -0.95912647  0.89567281
##  [586]  0.99329382 -0.86150545  0.79805179  0.30994672 -0.95912647
##  [591] -0.95912647  1.18853585 -0.95912647 -0.17815835  1.96950397
##  [596] -0.86150545  1.38377788 -0.86150545  0.30994672  1.09091484
##  [601]  0.89567281 -0.47102140  0.79805179  0.30994672  1.18853585
##  [606]  1.67664093 -0.95912647 -0.95912647 -0.95912647  1.18853585
##  [611]  0.60280977  1.96950397  1.57901991 -0.86150545 -0.95912647
##  [616] -0.86150545 -0.95912647  1.57901991  0.60280977 -0.95912647
##  [621] -0.47102140 -0.95912647 -0.86150545 -0.95912647  1.87188296
##  [626] -0.95912647  1.67664093 -0.95912647 -0.95912647 -0.76388444
##  [631]  0.40756774  0.11470469  0.79805179  0.99329382  0.21232571
##  [636]  0.30994672 -0.95912647 -0.95912647 -0.95912647  1.48139890
##  [641] -0.95912647 -0.95912647 -0.95912647  1.87188296 -0.86150545
##  [646] -0.86150545  0.89567281  0.11470469  0.79805179 -0.86150545
##  [651]  0.79805179 -0.95912647  0.70043078 -0.95912647 -0.95912647
##  [656]  0.70043078  0.99329382 -0.95912647 -0.76388444  0.89567281
##  [661] -0.95912647 -0.66626342  0.30994672 -0.95912647 -0.86150545
##  [666]  2.06712499 -0.95912647  1.48139890  0.70043078  0.70043078
##  [671] -0.95912647 -0.95912647  0.40756774  0.50518875 -0.86150545
##  [676] -0.95912647  1.67664093 -0.17815835  0.21232571 -0.95912647
##  [681] -0.86150545 -0.86150545 -0.86150545 -0.95912647 -0.86150545
##  [686] -0.37340038  1.57901991  0.79805179 -0.95912647  1.18853585
##  [691]  0.50518875  0.11470469  0.40756774 -0.95912647  0.89567281
##  [696] -0.95912647 -0.95912647  0.70043078 -0.95912647  0.60280977
##  [701] -0.95912647  1.87188296 -0.95912647 -0.95912647 -0.95912647
##  [706] -0.95912647  1.77426194 -0.95912647 -0.76388444  1.28615687
##  [711]  0.60280977  0.89567281 -0.76388444  0.70043078 -0.95912647
##  [716]  0.89567281 -0.86150545  0.79805179 -0.86150545 -0.95912647
##  [721]  0.89567281 -0.86150545 -0.95912647 -0.86150545 -0.95912647
##  [726] -0.95912647  1.09091484 -0.95912647 -0.95912647  1.28615687
##  [731]  0.50518875 -0.95912647 -0.95912647 -0.95912647 -0.95912647
##  [736]  1.28615687  0.79805179 -0.95912647  0.30994672 -0.95912647
##  [741] -0.95912647 -0.08053734 -0.86150545 -0.95912647 -0.86150545
##  [746] -0.95912647  0.79805179  0.40756774 -0.86150545  1.18853585
##  [751]  0.99329382  0.79805179 -0.27577937 -0.95912647  1.96950397
##  [756] -0.95912647 -0.95912647 -0.76388444 -0.86150545 -0.95912647
##  [761] -0.95912647 -0.95912647  0.50518875  1.57901991 -0.76388444
##  [766] -0.95912647 -0.86150545 -0.27577937 -0.95912647 -0.95912647
##  [771]  0.11470469 -0.95912647  1.67664093  0.40756774 -0.95912647
##  [776]  1.18853585  1.18853585  0.70043078  1.09091484  1.38377788
##  [781]  1.09091484  1.67664093 -0.95912647  0.50518875 -0.86150545
##  [786] -0.76388444  0.79805179  0.89567281 -0.95912647  1.38377788
##  [791]  1.18853585  0.89567281 -0.95912647  0.89567281 -0.76388444
##  [796] -0.95912647 -0.95912647 -0.86150545 -0.95912647 -0.95912647
##  [801]  1.18853585  1.18853585  0.40756774 -0.95912647 -0.95912647
##  [806] -0.95912647 -0.95912647  0.79805179  0.79805179 -0.17815835
##  [811] -0.95912647 -0.86150545 -0.95912647 -0.86150545 -0.95912647
##  [816] -0.86150545 -0.95912647 -0.95912647 -0.95912647 -0.86150545
##  [821] -0.86150545  1.87188296  0.50518875 -0.86150545 -0.95912647
##  [826] -0.86150545 -0.95912647 -0.76388444 -0.95912647  1.18853585
##  [831]  0.89567281  1.28615687  0.01708368 -0.95912647  0.30994672
##  [836] -0.95912647 -0.95912647 -0.86150545  1.09091484 -0.95912647
##  [841] -0.86150545  0.50518875 -0.95912647 -0.86150545  0.89567281
##  [846]  0.99329382 -0.95912647  0.60280977  1.18853585 -0.95912647
##  [851] -0.86150545 -0.95912647  0.99329382 -0.95912647  0.89567281
##  [856] -0.76388444 -0.95912647 -0.66626342  0.89567281  1.96950397
##  [861]  1.77426194  0.30994672 -0.86150545 -0.86150545  0.99329382
##  [866] -0.95912647  1.28615687  0.79805179 -0.86150545 -0.95912647
##  [871] -0.95912647  0.40756774 -0.95912647 -0.95912647 -0.95912647
##  [876] -0.95912647 -0.08053734 -0.95912647  1.28615687 -0.95912647
##  [881]  0.40756774 -0.95912647  0.60280977  0.99329382  1.09091484
##  [886] -0.86150545 -0.95912647 -0.95912647  0.89567281 -0.95912647
##  [891]  1.57901991  0.60280977 -0.66626342  1.67664093 -0.95912647
##  [896]  1.28615687  0.40756774 -0.95912647  0.79805179  0.70043078
##  [901] -0.95912647 -0.95912647 -0.95912647  1.09091484  1.18853585
##  [906] -0.95912647 -0.95912647  1.48139890 -0.95912647  1.38377788
##  [911]  0.21232571 -0.95912647  0.11470469  0.21232571  0.70043078
##  [916] -0.86150545 -0.86150545  1.48139890 -0.86150545 -0.95912647
##  [921]  0.60280977 -0.86150545  0.50518875 -0.08053734  0.40756774
##  [926]  0.11470469 -0.76388444 -0.86150545 -0.95912647 -0.95912647
##  [931] -0.95912647 -0.95912647  1.18853585 -0.95912647  0.89567281
##  [936]  0.40756774 -0.76388444 -0.95912647  0.30994672 -0.86150545
##  [941] -0.95912647 -0.95912647 -0.95912647 -0.95912647 -0.95912647
##  [946] -0.76388444  1.77426194  0.79805179  0.11470469  0.79805179
##  [951]  1.28615687 -0.95912647 -0.95912647  0.60280977  0.21232571
##  [956] -0.76388444 -0.95912647  0.70043078  0.70043078 -0.86150545
##  [961] -0.95912647  1.18853585 -0.08053734  1.09091484 -0.95912647
##  [966]  0.60280977 -0.95912647 -0.76388444  0.40756774  1.67664093
##  [971] -0.86150545 -0.86150545  1.48139890  0.99329382  1.28615687
##  [976]  1.48139890  0.89567281  0.40756774 -0.95912647 -0.95912647
##  [981]  1.38377788 -0.95912647 -0.86150545 -0.95912647  1.28615687
##  [986] -0.08053734 -0.95912647 -0.86150545 -0.86150545  0.79805179
##  [991] -0.95912647 -0.86150545 -0.95912647  0.30994672 -0.95912647
##  [996] -0.95912647 -0.95912647 -0.95912647 -0.95912647 -0.95912647