# Coursework MA321-7-SP: Initial Task - R Code to Get Started
# Version:January 2025
rm(list=ls())
# --- Setup ---
# Set your working directory to the folder where your data is stored
# Example: setwd("path/to/your/directory")
# If you're using a University lab computer, ensure you save your work on your network drive
# or back it up using cloud storage (e.g., Apple iCloud, Google Drive) or a USB stick.
# Always keep multiple backups of your work to prevent data loss.
# --- Load Data ---
# Copy the file "gene-expression-invasive-vs-noninvasive-cancer.csv" from Moodle to your working directory
InitialData <- read.csv(file = "C:/AS/gene-expression-invasive-vs-noninvasive-cancer.csv")
# --- Check the Data ---
# Use the following commands to understand the structure and dimensions of the dataset
str(InitialData)
## 'data.frame': 78 obs. of 4773 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ J00129 : num -0.448 -0.48 -0.568 -0.819 -0.112 -0.391 -0.624 -0.528 -0.811 -0.839 ...
## $ Contig29982_RC: num -0.296 -0.512 -0.411 -0.267 -0.67 -0.31 -0.12 -0.447 -0.536 2 ...
## $ Contig42854 : num -0.1 -0.031 -0.398 0.023 0.421 -0.06 -0.236 -0.254 -0.211 0.147 ...
## $ Contig42014_RC: num -0.177 -0.075 0.116 -0.23 -0.19 -0.164 -0.175 0.017 -0.201 -0.325 ...
## $ Contig27915_RC: num -0.107 -0.104 -0.092 0.198 0.032 -0.173 0.253 0.654 0.287 -0.303 ...
## $ Contig20156_RC: num -0.11 -0.234 -0.166 -0.51 0.281 -0.034 -0.125 0.364 -0.08 -0.061 ...
## $ Contig50634_RC: num -0.095 -0.225 0.036 0.529 0.31 -0.091 -0.127 0.068 -0.15 0.097 ...
## $ Contig42615_RC: num -0.076 -0.094 0.397 0.354 0.056 0.036 -0.02 0.181 0.045 0.006 ...
## $ Contig56678_RC: num -0.134 0.115 -0.194 -0.261 0.116 0.346 0.047 -1.14 -0.11 0.176 ...
## $ Contig48659_RC: num -0.14 0.019 -0.128 0.012 0.074 0.007 -0.15 -0.111 -0.072 -0.084 ...
## $ Contig49388_RC: num 0.006 0.15 0.139 -0.26 0.041 0.251 0.266 -0.153 0.471 0.114 ...
## $ Contig1970_RC : num 0.111 0.038 -0.033 -0.069 0.067 0.229 0.246 -0.415 -0.096 -0.081 ...
## $ Contig26343_RC: num -0.236 0.092 0.039 -0.115 0.279 0.297 0.142 0.111 0.047 -0.071 ...
## $ Contig53047_RC: num -0.866 -1.035 -1.114 -1.021 -1.006 ...
## $ Contig43945_RC: num 0.126 -0.062 0.011 -0.999 0.211 -0.1 -0.194 -0.053 0.096 -0.121 ...
## $ Contig19551 : num -0.692 -0.21 -0.462 0.273 0.242 -0.883 0.206 0.174 -0.355 0.23 ...
## $ Contig10437_RC: num 0.132 -0.139 -0.185 0.159 0.276 -0.146 -0.301 -0.075 0.253 0.022 ...
## $ Contig47230_RC: num 0.095 0.068 -0.168 -0.398 -0.604 0.382 -0.549 -0.635 0.856 0.515 ...
## $ Contig20749_RC: num 0.252 0.268 -0.289 -0.734 0.08 0.403 -0.012 -0.586 0.105 0.138 ...
## $ AL157502 : num 0.139 -0.179 -0.378 -0.427 0.372 -0.014 -0.022 -0.821 -0.294 -0.165 ...
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## $ AF114264 : num 0.096 0.051 -0.164 -0.047 0.245 -0.165 -0.072 -0.427 -0.249 -0.372 ...
## $ Contig40673_RC: num 0.305 -0.056 -0.124 -0.02 -0.19 0.016 -0.246 0.181 1.48 -0.199 ...
## $ Contig17345_RC: num 0.055 -0.031 -0.031 0.251 -0.06 -0.104 -0.254 0.408 -0.003 0.002 ...
## $ AB033034 : num -0.137 -0.05 -0.188 0.153 0.181 -0.231 -0.032 -0.024 -0.305 -0.249 ...
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## $ AB033043 : num 0.108 0.105 0.079 -0.223 0.109 0.201 0.361 -0.224 0.02 0.188 ...
## $ AB033049 : num 0.329 0.049 0.177 -0.307 0.3 0.046 -0.139 0.036 -0.154 0.069 ...
## $ Contig55834_RC: num 0.078 0.175 -0.375 0.017 0.255 0.035 -0.044 -0.379 -0.302 0.071 ...
## $ Contig67229_RC: num -0.098 -0.107 0.612 -0.107 0.143 0.065 0.061 0.358 0.016 0.025 ...
## $ Contig3396_RC : num -0.097 -0.068 0.071 -0.113 -0.021 0.4 0.031 -0.043 -0.004 -0.199 ...
## $ AB033050 : num -0.019 0.104 0.023 0.582 0.128 0.216 0.091 -0.186 -0.156 0.032 ...
## $ AB033055 : num 0.208 0.003 -0.051 0.024 0.161 -0.073 -0.167 -0.28 -0.071 -0.099 ...
## $ AF009314 : num -0.021 0.025 -0.279 -0.226 0.09 0.026 0.121 -0.541 -0.106 0.041 ...
## $ AB033062 : num 0.113 -0.166 -0.153 -0.695 0.101 -0.037 0.366 0.139 -0.05 -0.202 ...
## $ AB033066 : num 0.178 0.065 -0.077 0.176 -0.089 0.018 -0.144 -0.077 -0.157 0.008 ...
## $ Contig46243_RC: num -0.081 0.015 -0.262 -0.209 0.366 0.292 -0.058 -0.017 -0.082 0.113 ...
## $ Contig26077_RC: num 0.272 0.197 -0.218 -0.038 -0.254 0.107 0.14 -0.4 0.26 0.219 ...
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## $ AB033073 : num -0.152 0.018 -0.028 -0.167 0.307 0.157 0.261 -0.297 0.129 0.282 ...
## $ AF018081 : num -0.063 -0.212 -0.129 -0.347 0.133 -0.128 0.05 -0.389 -0.116 0.145 ...
## $ AB033079 : num -0.009 0.07 -0.159 0.004 0.018 -0.26 0.069 -0.18 -0.378 -0.092 ...
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## $ AB033092 : num 0.015 -0.064 -0.312 -0.08 0.138 -0.071 0.012 0.025 -0.333 -0.013 ...
## $ NM_003004 : num -0.47 -0.576 -0.064 -0.104 0.134 -0.09 -0.072 0.854 -0.068 -0.049 ...
## $ Contig57877_RC: num 0.212 -0.053 -0.088 -0.356 0.007 -0.12 -0.14 -0.368 -0.277 -0.401 ...
## $ NM_003010 : num -0.211 -0.331 -0.355 -0.064 0.395 0.227 0.118 -0.106 -0.089 0.261 ...
## $ NM_003012 : num 0.238 -0.26 0.141 -0.306 -0.098 -0.114 -0.026 0.263 -0.095 -0.222 ...
## $ NM_003014 : num 0.039 -0.039 0.112 -0.273 -0.051 -0.047 0.317 -0.54 0.029 -0.16 ...
## $ Contig43806_RC: num -0.734 -0.661 -0.632 -0.944 -0.94 -0.58 -0.494 -0.924 -0.616 -0.7 ...
## $ Contig29226_RC: num 0.045 -0.135 -0.041 -0.54 0.185 -0.033 -0.064 0.084 0.048 -0.04 ...
## $ NM_003020 : num -0.103 -0.255 -0.034 -0.548 -0.067 -0.237 -0.002 -0.351 -0.362 -0.164 ...
## $ NM_003022 : num 0.292 0.092 -0.049 0.318 -0.051 0.259 -0.002 -0.284 -0.158 0.125 ...
## $ Contig54847_RC: num 0.181 -0.208 -0.178 -0.692 0.129 0.198 0.436 -0.838 -0.029 0.166 ...
## $ Contig33260_RC: num 0.056 0.297 -0.342 0.007 0.175 0.168 0.41 -0.089 -0.035 -0.006 ...
## $ NM_002300 : num -0.434 -0.316 -0.525 0.033 -0.178 -0.023 -0.149 0.245 -0.131 -0.457 ...
## $ Contig14658_RC: num 0.043 0.087 -0.036 -0.115 0.208 0.058 0.331 -0.161 0.599 0.23 ...
## $ NM_003033 : num 0.236 0.031 0.34 0.023 -0.247 0.123 -0.309 -0.077 -0.119 -0.23 ...
## $ NM_003034 : num 0.096 -0.09 -0.047 -0.011 -0.406 -0.244 -0.218 -0.081 -0.016 -0.593 ...
## $ NM_002306 : num -0.271 0.066 0.092 -0.185 -0.01 0.025 0.094 0.152 0.156 0.185 ...
## $ NM_003035 : num -0.385 -0.08 0.053 -0.032 -0.071 -0.184 -0.534 0.581 -0.283 -0.253 ...
## $ NM_002308 : num -0.237 -0.269 0.203 0.312 0.088 -0.399 -0.076 0.425 -0.054 0.116 ...
## $ NM_003038 : num 0.131 0.275 0.065 0.043 -0.171 0.192 -0.046 0.086 0.384 0.015 ...
## $ NM_002313 : num -0.047 -0.036 0.109 0.516 -0.197 0.063 0.026 -0.108 -0.185 0.143 ...
## $ Contig54839_RC: num 0.13 -0.101 0.224 -0.149 0.01 -0.05 -0.104 0.083 0.156 0.028 ...
## $ NM_002318 : num -0.386 0.189 -0.122 -0.75 0.039 -0.236 0.343 -0.285 0.148 -0.205 ...
## $ NM_003051 : num 0.299 -0.173 0.193 -0.02 -0.155 0.005 -0.375 -0.3 -0.363 0.064 ...
## $ NM_003056 : num 0.116 -0.073 0.03 -0.041 -0.164 -0.049 0.113 0.167 0.035 -0.314 ...
## $ Contig66143_RC: num -0.294 0.55 0.642 -0.087 -0.381 -0.417 -0.137 -0.081 -0.27 -0.859 ...
## $ Contig51809_RC: num 0.169 -0.086 0.129 -0.3 -0.054 -0.104 0.076 0.176 0.184 -0.298 ...
## $ NM_002332 : num 0.025 -0.141 -0.113 -0.389 0.257 0.047 0.341 -0.346 0.221 0.215 ...
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## [list output truncated]
# Output Example:
# 'data.frame': 78 obs. of 4773 variables
# $ X : int 1 2 3 4 5 6 7 8 9 10 ...
# $ J00129 : num -0.448 -0.48 -0.568 -0.819 ...
# $ Contig29982_RC: num -0.296 -0.512 -0.411 -0.267 ...
# $ Contig42854 : num -0.1 -0.031 -0.398 0.023 ...
dim(InitialData) # Returns dataset dimensions (rows and columns)
## [1] 78 4773
# Example Output:
# [1] 78 4773
dimnames(InitialData)[[2]][4770:4773] # View the names of the last columns
## [1] "NM_000895" "NM_000898" "AF067420" "Class"
# Example Output:
# [1] "NM_000895" "NM_000898" "AF067420" "Class"
# Summary of the dataset:
# - 78 rows (patients)
# - 4773 columns: 4772 columns represent gene expression measurements,
# and column 4773 contains the "Class" variable (values: 1 or 2).
# Check the distribution of the "Class" variable
table(InitialData[, 'Class'])
##
## 1 2
## 34 44
# Example Output:
# Class
# 1 2
# 34 44
# --- Randomization Setup ---
# The script assigns a subset of variables to each registration number.
# In the file 'subsets.csv', each registration number is associated with 10 columns (variables).
# Load the file 'subsets.csv', which contains the registration numbers and their associated variable subsets.
subsets <- read.csv("C:/AS/subsets.csv")
# Specify your registration number to identify your subset of variables.
# Replace 2401468 with your personal registration number.
my_registration_number <- 2404410
# Find the index of the row corresponding to your registration number.
idx <- which(subsets$RegId == my_registration_number)
print(idx) # Print the index to confirm that the registration number was found.
## [1] 46
# For example, [1] 1 indicates that the corresponding row is the first row in the dataset.
# Extract the subset of variables (excluding the first column "RegId") for your registration number.
# The result is a vector of 10 variables associated with your registration number.
my_subset <- unlist(c(subsets[idx, -1]))
print(my_subset) # Print your subset of variables.
## Var1 Var2 Var3 Var4 Var5 Var6 Var7 Var8 Var9 Var10
## 367 3195 2626 1415 4517 4391 2426 2142 4541 4493
# Example output:
# Var1 Var2 Var3 Var4 Var5 Var6 Var7 Var8 Var9 Var10
# 417 3124 2492 4590 107 1557 4554 3610 4657 2428
# Assume that InitialData is a preloaded dataset containing the original variables.
Class <- InitialData$Class # Extract the "Class" column, which represents the labels or targets.
# Select only the columns (variables) specified in the subset (my_subset).
X <- InitialData[, my_subset]
# Combine the "Class" column with the selected variables to create the final dataset.
My_DataSet <- cbind(Class, X)
# The dataset 'My_DataSet' contains:
# - The "Class" column as the first column.
# - The 10 variables associated with your registration number.
print(My_DataSet)
## Class AL133047 AL049397 NM_006644 Contig43859_RC AL050370 Contig43678_RC
## 1 2 -0.039 -0.408 -0.017 -0.020 0.036 -0.192
## 2 2 -0.022 -0.153 0.117 0.062 -0.177 -0.278
## 3 2 -0.115 -0.145 -0.186 -0.040 0.184 -0.159
## 4 2 -0.153 -0.088 -0.102 -0.216 0.162 -0.007
## 5 2 0.120 0.167 0.137 0.442 0.179 -0.286
## 6 2 0.100 -0.227 -0.560 0.047 0.402 -0.066
## 7 2 0.211 -0.090 0.173 0.345 -0.058 0.431
## 8 2 -0.335 0.283 -0.175 -0.283 -0.536 0.020
## 9 2 -0.132 -0.175 -0.375 0.159 0.272 0.473
## 10 2 0.122 0.005 -0.179 0.134 0.033 -0.193
## 11 2 -0.060 -0.076 -0.052 0.130 -0.208 -0.001
## 12 2 -0.092 0.241 -0.136 0.203 -0.335 -0.255
## 13 2 -0.120 -0.150 -0.580 -0.264 -0.303 0.016
## 14 2 -0.045 -0.001 -0.404 0.189 0.013 0.186
## 15 2 -0.136 0.264 0.507 -0.005 -0.138 0.051
## 16 2 -0.085 -0.025 -0.222 -0.054 -0.274 0.010
## 17 2 0.121 -0.120 -0.251 0.108 0.219 0.058
## 18 2 0.192 0.094 0.191 0.136 0.111 -0.148
## 19 2 0.115 0.007 -0.062 0.248 0.267 -0.209
## 20 2 -0.147 0.153 0.042 -0.122 -0.647 0.452
## 21 2 0.070 -0.126 -0.056 0.190 0.028 0.006
## 22 2 0.287 0.122 0.120 0.182 -0.071 0.188
## 23 2 0.208 -0.251 -0.089 -0.045 -0.033 -0.435
## 24 2 0.054 0.090 -0.094 -0.157 -0.375 -0.562
## 25 2 -0.074 -0.243 0.024 -0.128 0.142 -0.288
## 26 2 0.322 0.040 0.009 0.239 -0.054 -0.084
## 27 2 0.243 -0.136 -0.089 0.050 0.056 -0.111
## 28 2 0.277 -0.235 0.072 -0.053 -0.358 -0.165
## 29 2 0.028 -0.192 -0.279 0.042 -0.255 0.211
## 30 2 0.134 -0.138 -0.149 0.097 -0.125 0.071
## 31 2 -0.052 -0.026 -0.236 0.239 -0.034 -0.183
## 32 2 -0.053 -0.006 -0.035 -0.055 -0.206 -0.057
## 33 2 0.002 -0.283 -0.097 0.026 0.135 0.146
## 34 2 -0.363 -0.466 0.101 -0.278 -0.469 -0.271
## 35 2 -0.106 -0.011 -0.153 0.121 -0.430 0.003
## 36 2 0.152 -0.026 -0.147 0.332 -0.236 0.124
## 37 2 -0.221 -0.668 -0.455 -0.316 -0.335 -0.046
## 38 2 -0.058 -0.006 0.230 -0.071 0.207 -0.064
## 39 2 0.088 -0.041 0.222 0.407 0.207 0.329
## 40 2 -0.110 -0.007 -0.180 -0.181 -0.176 -0.075
## 41 2 -0.176 -0.309 -0.039 0.026 0.049 0.232
## 42 2 0.254 -0.160 -0.198 0.344 -0.164 0.203
## 43 2 -0.056 -0.135 0.010 -0.052 -0.131 0.252
## 44 2 -0.122 0.208 0.006 0.069 -0.604 -0.174
## 45 1 -0.042 -0.306 -0.314 -0.255 -0.111 -0.015
## 46 1 0.099 -0.012 0.106 0.272 -0.158 0.116
## 47 1 -0.098 -0.131 -0.110 0.041 0.507 0.185
## 48 1 -0.227 0.383 0.218 -0.166 -0.501 0.020
## 49 1 -0.030 -0.103 0.203 -0.233 -0.345 -0.237
## 50 1 -0.052 0.151 0.137 -0.044 -0.176 -0.038
## 51 1 0.002 -0.002 -0.109 0.170 0.190 -0.059
## 52 1 -0.165 -0.141 -0.028 -0.230 0.224 -0.137
## 53 1 -0.002 0.186 -0.054 0.092 -0.545 -0.304
## 54 1 -0.184 0.043 0.112 -0.213 0.070 -2.000
## 55 1 -0.213 -0.207 -0.253 -0.262 0.173 -0.141
## 56 1 0.100 0.036 -0.234 0.167 -0.323 0.065
## 57 1 -0.299 0.099 0.171 -0.296 0.073 -0.092
## 58 1 -0.067 -0.023 -0.027 -0.255 0.054 0.021
## 59 1 -0.179 0.031 -0.147 -0.153 0.204 -0.072
## 60 1 -0.016 0.043 -0.146 0.050 0.419 -0.197
## 61 1 0.046 0.143 0.064 0.106 0.096 -0.289
## 62 1 -0.093 0.092 -0.037 -0.239 -0.175 -0.251
## 63 1 -0.107 -0.103 -0.040 -0.220 0.288 -0.300
## 64 1 -0.157 0.099 0.049 -0.035 -0.294 -0.057
## 65 1 -0.342 0.222 -0.032 -0.091 0.005 0.083
## 66 1 -0.281 -0.071 0.030 -0.132 -0.104 -0.191
## 67 1 -0.050 0.186 -0.099 -0.136 -0.150 -0.157
## 68 1 -0.081 -0.034 -0.278 -0.194 -0.184 0.039
## 69 1 0.147 0.031 0.198 -0.032 -0.292 0.097
## 70 1 0.252 0.002 -0.052 -0.184 0.177 -0.195
## 71 1 0.040 -0.107 0.155 -0.089 -0.107 -0.093
## 72 1 0.057 0.043 0.099 -0.015 -0.650 -0.324
## 73 1 0.540 -0.118 -0.445 -0.151 -0.584 0.772
## 74 1 0.019 0.011 -0.114 0.039 -0.326 -0.104
## 75 1 -0.048 0.244 -0.042 0.178 -0.139 -0.048
## 76 1 0.072 0.138 -0.170 0.293 -0.136 0.079
## 77 1 -0.139 -0.070 -0.252 -0.029 -0.186 0.548
## 78 1 -0.092 0.075 -0.040 0.060 0.707 -0.143
## NM_006500 NM_006377 NM_002133 Contig43791_RC
## 1 -0.197 0.101 -0.297 0.146
## 2 -0.109 0.015 -0.039 -0.517
## 3 -0.252 -0.063 -0.177 -0.201
## 4 -0.574 -0.037 -0.177 -0.781
## 5 0.042 -0.026 0.164 -0.217
## 6 -0.236 0.051 -0.419 -0.500
## 7 0.005 0.078 -0.251 0.098
## 8 0.068 -0.172 0.170 -0.299
## 9 -0.135 -0.120 -0.098 0.368
## 10 -0.218 0.105 -0.229 0.114
## 11 -0.095 0.154 0.029 -0.425
## 12 0.370 -0.252 0.151 0.033
## 13 -0.052 -0.027 -0.277 -0.824
## 14 -0.211 0.097 -0.255 -0.037
## 15 -0.268 0.017 -0.467 -0.289
## 16 -0.104 -0.042 -0.046 0.017
## 17 -0.080 0.092 -0.113 0.102
## 18 0.010 0.114 -0.312 -0.119
## 19 -0.020 0.048 -0.028 0.141
## 20 -0.126 -0.357 -0.065 -0.802
## 21 -0.205 0.085 -0.175 0.538
## 22 -0.362 0.689 -0.394 -0.461
## 23 -0.058 0.264 -0.441 -0.278
## 24 0.230 -0.102 -0.122 0.444
## 25 -0.002 0.095 0.648 -0.420
## 26 -0.100 -0.020 0.045 0.148
## 27 -0.129 0.017 -0.335 -0.204
## 28 -0.036 -0.104 -0.056 -0.304
## 29 0.173 0.056 -0.040 0.261
## 30 -0.091 -0.092 -0.234 -0.166
## 31 0.110 0.032 0.110 0.323
## 32 -0.072 0.128 0.394 0.662
## 33 -0.151 -0.327 -0.133 -0.107
## 34 0.050 -0.626 -0.190 -0.925
## 35 -0.041 0.231 0.406 -0.385
## 36 0.274 -0.092 0.222 0.142
## 37 -0.229 0.182 -0.334 -0.651
## 38 -0.010 -0.284 -0.135 0.140
## 39 -0.321 -0.080 -0.189 -0.054
## 40 -0.300 -0.056 0.139 -0.527
## 41 -0.179 0.052 -0.301 -0.554
## 42 -0.104 0.004 -0.271 -0.637
## 43 -0.014 -0.051 -0.162 -0.559
## 44 0.238 -0.210 0.145 0.224
## 45 0.067 -0.189 -0.082 -0.608
## 46 0.064 -0.133 0.006 0.558
## 47 0.127 -0.225 0.200 -0.052
## 48 -0.085 -0.252 -0.080 0.188
## 49 -0.212 0.254 -0.331 0.060
## 50 -0.084 -0.117 -0.215 0.322
## 51 0.081 0.115 0.156 -0.461
## 52 -0.286 0.433 -0.099 -0.570
## 53 0.102 -0.124 0.128 0.216
## 54 -0.288 -0.251 0.432 -1.449
## 55 -0.133 0.389 -0.307 -0.891
## 56 -0.183 0.049 -0.245 -0.102
## 57 -0.213 -0.209 0.043 -0.879
## 58 -0.095 0.053 -0.523 -0.754
## 59 0.025 -0.318 -0.119 -0.342
## 60 0.055 0.091 -0.377 -0.391
## 61 -0.181 0.199 -0.158 0.758
## 62 0.091 0.241 -0.104 -0.663
## 63 -0.158 -0.091 -0.171 -0.439
## 64 -0.052 0.041 0.050 0.181
## 65 0.120 0.041 -0.043 -0.126
## 66 -0.291 -0.191 0.076 -0.989
## 67 0.304 0.003 0.224 -0.062
## 68 0.173 0.059 0.076 -0.383
## 69 0.029 0.070 0.094 -0.470
## 70 -0.111 0.073 -0.502 -0.208
## 71 0.425 -0.128 0.249 -0.233
## 72 0.169 -0.073 -0.253 -0.224
## 73 0.650 0.004 -0.002 -0.232
## 74 0.426 -0.282 0.399 -0.081
## 75 0.274 -0.178 0.115 0.085
## 76 0.030 -0.105 -0.158 -0.166
## 77 0.093 -0.235 -0.081 -0.499
## 78 -0.002 0.139 0.058 -0.234
#Task 1
my_registration_number <- 2404410
subsets <- read.csv("C:/AS/subsets.csv")
# Find the row for the given registration number
idx <- which(subsets$RegId == my_registration_number)
# --- Compute Variance, Covariance, and Correlation Matrices ---
# Variance: Apply the var() function to each of the 10 selected genes (columns)
gene_variance <- apply(X, 2, var)
# Covariance: Compute the covariance matrix of the selected genes
gene_covariance <- cov(X)
# Correlation: Compute the correlation matrix of the selected genes
gene_correlation <- cor(X)
# --- Print and Present the Results ---
cat("Variance of Each Gene:\n")
## Variance of Each Gene:
print(gene_variance)
## AL133047 AL049397 NM_006644 Contig43859_RC AL050370
## 0.02741773 0.03136695 0.03640845 0.03465436 0.07617163
## Contig43678_RC NM_006500 NM_006377 NM_002133 Contig43791_RC
## 0.09993076 0.04053007 0.03723622 0.05419490 0.17263728
cat("\nCovariance Matrix:\n")
##
## Covariance Matrix:
print(gene_covariance)
## AL133047 AL049397 NM_006644 Contig43859_RC
## AL133047 0.0274177323 -0.001446737 -0.001049892 0.015741817
## AL049397 -0.0014467373 0.031366949 0.012329310 0.006344749
## NM_006644 -0.0010498921 0.012329310 0.036408450 0.002768581
## Contig43859_RC 0.0157418172 0.006344749 0.002768581 0.034654356
## AL050370 0.0006118561 -0.008570186 -0.002028670 0.008172685
## Contig43678_RC 0.0094905594 -0.004655989 -0.013345189 0.013303304
## NM_006500 0.0063346653 0.007590656 -0.004877268 0.003070664
## NM_006377 0.0093719510 -0.002863694 -0.002999108 0.003405504
## NM_002133 -0.0073691548 0.009584862 0.002151813 0.002386743
## Contig43791_RC 0.0214331808 0.019688288 0.005725799 0.037643021
## AL050370 Contig43678_RC NM_006500 NM_006377
## AL133047 0.0006118561 0.009490559 0.006334665 0.009371951
## AL049397 -0.0085701863 -0.004655989 0.007590656 -0.002863694
## NM_006644 -0.0020286705 -0.013345189 -0.004877268 -0.002999108
## Contig43859_RC 0.0081726855 0.013303304 0.003070664 0.003405504
## AL050370 0.0761716292 -0.008602086 -0.019293037 0.012048539
## Contig43678_RC -0.0086020859 0.099930761 0.008344803 0.002024284
## NM_006500 -0.0192930370 0.008344803 0.040530072 -0.011104655
## NM_006377 0.0120485388 0.002024284 -0.011104655 0.037236219
## NM_002133 -0.0106134863 -0.015593330 0.019536972 -0.011870773
## Contig43791_RC -0.0050162388 0.026811213 0.021525431 0.003404002
## NM_002133 Contig43791_RC
## AL133047 -0.007369155 0.021433181
## AL049397 0.009584862 0.019688288
## NM_006644 0.002151813 0.005725799
## Contig43859_RC 0.002386743 0.037643021
## AL050370 -0.010613486 -0.005016239
## Contig43678_RC -0.015593330 0.026811213
## NM_006500 0.019536972 0.021525431
## NM_006377 -0.011870773 0.003404002
## NM_002133 0.054194902 0.007357278
## Contig43791_RC 0.007357278 0.172637281
cat("\nCorrelation Matrix:\n")
##
## Correlation Matrix:
print(gene_correlation)
## AL133047 AL049397 NM_006644 Contig43859_RC AL050370
## AL133047 1.00000000 -0.04933303 -0.03322981 0.51069332 0.01338865
## AL049397 -0.04933303 1.00000000 0.36483924 0.19244178 -0.17533051
## NM_006644 -0.03322981 0.36483924 1.00000000 0.07794301 -0.03852244
## Contig43859_RC 0.51069332 0.19244178 0.07794301 1.00000000 0.15907035
## AL050370 0.01338865 -0.17533051 -0.03852244 0.15907035 1.00000000
## Contig43678_RC 0.18131196 -0.08316225 -0.22124529 0.22606378 -0.09859560
## NM_006500 0.19002871 0.21288963 -0.12696582 0.08193411 -0.34722844
## NM_006377 0.29331310 -0.08379300 -0.08145320 0.09480248 0.22623249
## NM_002133 -0.19117130 0.23247192 0.04844225 0.05507412 -0.16518942
## Contig43791_RC 0.31153265 0.26754973 0.07222170 0.48667413 -0.04374358
## Contig43678_RC NM_006500 NM_006377 NM_002133
## AL133047 0.18131196 0.19002871 0.29331310 -0.19117130
## AL049397 -0.08316225 0.21288963 -0.08379300 0.23247192
## NM_006644 -0.22124529 -0.12696582 -0.08145320 0.04844225
## Contig43859_RC 0.22606378 0.08193411 0.09480248 0.05507412
## AL050370 -0.09859560 -0.34722844 0.22623249 -0.16518942
## Contig43678_RC 1.00000000 0.13112268 0.03318478 -0.21188980
## NM_006500 0.13112268 1.00000000 -0.28584698 0.41685916
## NM_006377 0.03318478 -0.28584698 1.00000000 -0.26425121
## NM_002133 -0.21188980 0.41685916 -0.26425121 1.00000000
## Contig43791_RC 0.20412658 0.25733323 0.04245606 0.07606251
## Contig43791_RC
## AL133047 0.31153265
## AL049397 0.26754973
## NM_006644 0.07222170
## Contig43859_RC 0.48667413
## AL050370 -0.04374358
## Contig43678_RC 0.20412658
## NM_006500 0.25733323
## NM_006377 0.04245606
## NM_002133 0.07606251
## Contig43791_RC 1.00000000
# --- Create Tables for the Report ---
# Create a table for variance
variance_table <- data.frame(Gene = colnames(X), Variance = gene_variance)
cat("\nVariance Table:\n")
##
## Variance Table:
print(variance_table)
## Gene Variance
## AL133047 AL133047 0.02741773
## AL049397 AL049397 0.03136695
## NM_006644 NM_006644 0.03640845
## Contig43859_RC Contig43859_RC 0.03465436
## AL050370 AL050370 0.07617163
## Contig43678_RC Contig43678_RC 0.09993076
## NM_006500 NM_006500 0.04053007
## NM_006377 NM_006377 0.03723622
## NM_002133 NM_002133 0.05419490
## Contig43791_RC Contig43791_RC 0.17263728
# Create a table for covariance
covariance_table <- as.data.frame(gene_covariance)
cat("\nCovariance Matrix Table:\n")
##
## Covariance Matrix Table:
print(covariance_table)
## AL133047 AL049397 NM_006644 Contig43859_RC
## AL133047 0.0274177323 -0.001446737 -0.001049892 0.015741817
## AL049397 -0.0014467373 0.031366949 0.012329310 0.006344749
## NM_006644 -0.0010498921 0.012329310 0.036408450 0.002768581
## Contig43859_RC 0.0157418172 0.006344749 0.002768581 0.034654356
## AL050370 0.0006118561 -0.008570186 -0.002028670 0.008172685
## Contig43678_RC 0.0094905594 -0.004655989 -0.013345189 0.013303304
## NM_006500 0.0063346653 0.007590656 -0.004877268 0.003070664
## NM_006377 0.0093719510 -0.002863694 -0.002999108 0.003405504
## NM_002133 -0.0073691548 0.009584862 0.002151813 0.002386743
## Contig43791_RC 0.0214331808 0.019688288 0.005725799 0.037643021
## AL050370 Contig43678_RC NM_006500 NM_006377
## AL133047 0.0006118561 0.009490559 0.006334665 0.009371951
## AL049397 -0.0085701863 -0.004655989 0.007590656 -0.002863694
## NM_006644 -0.0020286705 -0.013345189 -0.004877268 -0.002999108
## Contig43859_RC 0.0081726855 0.013303304 0.003070664 0.003405504
## AL050370 0.0761716292 -0.008602086 -0.019293037 0.012048539
## Contig43678_RC -0.0086020859 0.099930761 0.008344803 0.002024284
## NM_006500 -0.0192930370 0.008344803 0.040530072 -0.011104655
## NM_006377 0.0120485388 0.002024284 -0.011104655 0.037236219
## NM_002133 -0.0106134863 -0.015593330 0.019536972 -0.011870773
## Contig43791_RC -0.0050162388 0.026811213 0.021525431 0.003404002
## NM_002133 Contig43791_RC
## AL133047 -0.007369155 0.021433181
## AL049397 0.009584862 0.019688288
## NM_006644 0.002151813 0.005725799
## Contig43859_RC 0.002386743 0.037643021
## AL050370 -0.010613486 -0.005016239
## Contig43678_RC -0.015593330 0.026811213
## NM_006500 0.019536972 0.021525431
## NM_006377 -0.011870773 0.003404002
## NM_002133 0.054194902 0.007357278
## Contig43791_RC 0.007357278 0.172637281
# Create a table for correlation
correlation_table <- as.data.frame(gene_correlation)
cat("\nCorrelation Matrix Table:\n")
##
## Correlation Matrix Table:
print(correlation_table)
## AL133047 AL049397 NM_006644 Contig43859_RC AL050370
## AL133047 1.00000000 -0.04933303 -0.03322981 0.51069332 0.01338865
## AL049397 -0.04933303 1.00000000 0.36483924 0.19244178 -0.17533051
## NM_006644 -0.03322981 0.36483924 1.00000000 0.07794301 -0.03852244
## Contig43859_RC 0.51069332 0.19244178 0.07794301 1.00000000 0.15907035
## AL050370 0.01338865 -0.17533051 -0.03852244 0.15907035 1.00000000
## Contig43678_RC 0.18131196 -0.08316225 -0.22124529 0.22606378 -0.09859560
## NM_006500 0.19002871 0.21288963 -0.12696582 0.08193411 -0.34722844
## NM_006377 0.29331310 -0.08379300 -0.08145320 0.09480248 0.22623249
## NM_002133 -0.19117130 0.23247192 0.04844225 0.05507412 -0.16518942
## Contig43791_RC 0.31153265 0.26754973 0.07222170 0.48667413 -0.04374358
## Contig43678_RC NM_006500 NM_006377 NM_002133
## AL133047 0.18131196 0.19002871 0.29331310 -0.19117130
## AL049397 -0.08316225 0.21288963 -0.08379300 0.23247192
## NM_006644 -0.22124529 -0.12696582 -0.08145320 0.04844225
## Contig43859_RC 0.22606378 0.08193411 0.09480248 0.05507412
## AL050370 -0.09859560 -0.34722844 0.22623249 -0.16518942
## Contig43678_RC 1.00000000 0.13112268 0.03318478 -0.21188980
## NM_006500 0.13112268 1.00000000 -0.28584698 0.41685916
## NM_006377 0.03318478 -0.28584698 1.00000000 -0.26425121
## NM_002133 -0.21188980 0.41685916 -0.26425121 1.00000000
## Contig43791_RC 0.20412658 0.25733323 0.04245606 0.07606251
## Contig43791_RC
## AL133047 0.31153265
## AL049397 0.26754973
## NM_006644 0.07222170
## Contig43859_RC 0.48667413
## AL050370 -0.04374358
## Contig43678_RC 0.20412658
## NM_006500 0.25733323
## NM_006377 0.04245606
## NM_002133 0.07606251
## Contig43791_RC 1.00000000
# --- Task 1: Variance, Covariance, and Correlation Matrix ---
# Variance
variance_matrix <- apply(My_DataSet[, -1], 2, var)
print("Variance Matrix:")
## [1] "Variance Matrix:"
print(variance_matrix)
## AL133047 AL049397 NM_006644 Contig43859_RC AL050370
## 0.02741773 0.03136695 0.03640845 0.03465436 0.07617163
## Contig43678_RC NM_006500 NM_006377 NM_002133 Contig43791_RC
## 0.09993076 0.04053007 0.03723622 0.05419490 0.17263728
# Covariance
covariance_matrix <- cov(My_DataSet[, -1])
print("Covariance Matrix:")
## [1] "Covariance Matrix:"
print(covariance_matrix)
## AL133047 AL049397 NM_006644 Contig43859_RC
## AL133047 0.0274177323 -0.001446737 -0.001049892 0.015741817
## AL049397 -0.0014467373 0.031366949 0.012329310 0.006344749
## NM_006644 -0.0010498921 0.012329310 0.036408450 0.002768581
## Contig43859_RC 0.0157418172 0.006344749 0.002768581 0.034654356
## AL050370 0.0006118561 -0.008570186 -0.002028670 0.008172685
## Contig43678_RC 0.0094905594 -0.004655989 -0.013345189 0.013303304
## NM_006500 0.0063346653 0.007590656 -0.004877268 0.003070664
## NM_006377 0.0093719510 -0.002863694 -0.002999108 0.003405504
## NM_002133 -0.0073691548 0.009584862 0.002151813 0.002386743
## Contig43791_RC 0.0214331808 0.019688288 0.005725799 0.037643021
## AL050370 Contig43678_RC NM_006500 NM_006377
## AL133047 0.0006118561 0.009490559 0.006334665 0.009371951
## AL049397 -0.0085701863 -0.004655989 0.007590656 -0.002863694
## NM_006644 -0.0020286705 -0.013345189 -0.004877268 -0.002999108
## Contig43859_RC 0.0081726855 0.013303304 0.003070664 0.003405504
## AL050370 0.0761716292 -0.008602086 -0.019293037 0.012048539
## Contig43678_RC -0.0086020859 0.099930761 0.008344803 0.002024284
## NM_006500 -0.0192930370 0.008344803 0.040530072 -0.011104655
## NM_006377 0.0120485388 0.002024284 -0.011104655 0.037236219
## NM_002133 -0.0106134863 -0.015593330 0.019536972 -0.011870773
## Contig43791_RC -0.0050162388 0.026811213 0.021525431 0.003404002
## NM_002133 Contig43791_RC
## AL133047 -0.007369155 0.021433181
## AL049397 0.009584862 0.019688288
## NM_006644 0.002151813 0.005725799
## Contig43859_RC 0.002386743 0.037643021
## AL050370 -0.010613486 -0.005016239
## Contig43678_RC -0.015593330 0.026811213
## NM_006500 0.019536972 0.021525431
## NM_006377 -0.011870773 0.003404002
## NM_002133 0.054194902 0.007357278
## Contig43791_RC 0.007357278 0.172637281
# Correlation
correlation_matrix <- cor(My_DataSet[, -1])
print("Correlation Matrix:")
## [1] "Correlation Matrix:"
print(correlation_matrix)
## AL133047 AL049397 NM_006644 Contig43859_RC AL050370
## AL133047 1.00000000 -0.04933303 -0.03322981 0.51069332 0.01338865
## AL049397 -0.04933303 1.00000000 0.36483924 0.19244178 -0.17533051
## NM_006644 -0.03322981 0.36483924 1.00000000 0.07794301 -0.03852244
## Contig43859_RC 0.51069332 0.19244178 0.07794301 1.00000000 0.15907035
## AL050370 0.01338865 -0.17533051 -0.03852244 0.15907035 1.00000000
## Contig43678_RC 0.18131196 -0.08316225 -0.22124529 0.22606378 -0.09859560
## NM_006500 0.19002871 0.21288963 -0.12696582 0.08193411 -0.34722844
## NM_006377 0.29331310 -0.08379300 -0.08145320 0.09480248 0.22623249
## NM_002133 -0.19117130 0.23247192 0.04844225 0.05507412 -0.16518942
## Contig43791_RC 0.31153265 0.26754973 0.07222170 0.48667413 -0.04374358
## Contig43678_RC NM_006500 NM_006377 NM_002133
## AL133047 0.18131196 0.19002871 0.29331310 -0.19117130
## AL049397 -0.08316225 0.21288963 -0.08379300 0.23247192
## NM_006644 -0.22124529 -0.12696582 -0.08145320 0.04844225
## Contig43859_RC 0.22606378 0.08193411 0.09480248 0.05507412
## AL050370 -0.09859560 -0.34722844 0.22623249 -0.16518942
## Contig43678_RC 1.00000000 0.13112268 0.03318478 -0.21188980
## NM_006500 0.13112268 1.00000000 -0.28584698 0.41685916
## NM_006377 0.03318478 -0.28584698 1.00000000 -0.26425121
## NM_002133 -0.21188980 0.41685916 -0.26425121 1.00000000
## Contig43791_RC 0.20412658 0.25733323 0.04245606 0.07606251
## Contig43791_RC
## AL133047 0.31153265
## AL049397 0.26754973
## NM_006644 0.07222170
## Contig43859_RC 0.48667413
## AL050370 -0.04374358
## Contig43678_RC 0.20412658
## NM_006500 0.25733323
## NM_006377 0.04245606
## NM_002133 0.07606251
## Contig43791_RC 1.00000000
# Save results to CSV files
write.csv(variance_matrix, "variance_matrix.csv")
write.csv(covariance_matrix, "covariance_matrix.csv")
write.csv(correlation_matrix, "correlation_matrix.csv")
# --- Heatmap for Correlation Matrix ---
library(ggplot2)
library(reshape2)
# Reshape the correlation matrix for ggplot
correlation_data <- melt(correlation_matrix)
ggplot(correlation_data, aes(x = Var1, y = Var2, fill = value)) +
geom_tile() +
scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0) +
theme_minimal() +
labs(title = "Heatmap of Correlation Matrix", x = "Variables", y = "Variables", fill = "Correlation")
#Task 2
# --- Task 2: Distance Matrix ---
# Compute distance matrix (Euclidean distance)
distance_matrix <- dist(My_DataSet[, -1], method = "euclidean")
print("Distance Matrix:")
## [1] "Distance Matrix:"
print(as.matrix(distance_matrix))
## 1 2 3 4 5 6 7
## 1 0.0000000 0.8148816 0.5400269 1.1162616 1.0197505 0.9682319 0.8807196
## 2 0.8148816 0.0000000 0.6331201 0.8016620 0.7415221 1.0105508 1.0480739
## 3 0.5400269 0.6331201 0.0000000 0.7120906 0.8424476 0.6463621 0.9868526
## 4 1.1162616 0.8016620 0.7120906 0.0000000 1.2335814 0.8263516 1.3746538
## 5 1.0197505 0.7415221 0.8424476 1.2335814 0.0000000 1.1827045 0.9689830
## 6 0.9682319 1.0105508 0.6463621 0.8263516 1.1827045 0.0000000 1.2491717
## 7 0.8807196 1.0480739 0.9868526 1.3746538 0.9689830 1.2491717 0.0000000
## 8 1.2618344 0.9314193 1.0418680 1.2048394 1.2153448 1.4571057 1.3234262
## 9 0.9287809 1.3547199 0.9113830 1.4112817 1.2483850 1.1430770 0.8517928
## 10 0.5025585 0.8025378 0.5140623 1.1020749 0.7744056 0.8807179 0.7963831
## 11 0.8221539 0.3883980 0.6305712 0.8384742 0.7537679 0.9625477 0.8644744
## 12 1.1353770 0.9533357 1.0366272 1.5181347 0.8176527 1.4515247 1.1279601
## 13 1.2595729 0.9273166 0.9553434 0.8584335 1.4373270 0.9056926 1.4657200
## 14 0.7334937 0.9256257 0.5780381 1.0213995 0.9744629 0.7585723 0.7490300
## 15 1.0272979 0.8448012 0.9462981 1.0274605 1.0616054 1.3387546 0.9514494
## 16 0.6615361 0.7277101 0.5849333 1.0557045 0.9311493 1.0462872 0.8401375
## 17 0.5702938 0.9078530 0.5294129 1.1203629 0.8195755 0.8012578 0.6980573
## 18 0.7028471 0.6888367 0.6744235 1.0975928 0.6225247 0.9979614 0.7029616
## 19 0.6557164 0.8689062 0.6237171 1.2393547 0.5393357 0.9962364 0.8072094
## 20 1.5455834 1.0597717 1.2994133 1.1264724 1.4690054 1.5362887 1.3493728
## 21 0.5875049 1.1505755 0.8521649 1.4584444 1.0273476 1.2528859 0.7274538
## 22 1.1633680 1.0302199 1.1196160 1.1221457 1.1959599 1.1621988 0.9900788
## 23 0.6337815 0.6671589 0.6844370 1.0426270 1.0008516 0.8335178 1.1014972
## 24 0.9644371 1.1559356 1.1107313 1.6818927 1.1684930 1.5591767 1.2985615
## 25 1.1461627 0.8103339 0.9474091 1.1352537 0.9147787 1.3117462 1.4086831
## 26 0.7480401 0.8378126 0.7741880 1.2850019 0.6141702 1.1611180 0.6658371
## 27 0.5533326 0.6174634 0.4592864 0.9005171 0.7985562 0.6925301 0.7651836
## 28 0.7894853 0.4712250 0.7719352 1.0463369 0.8981370 1.1235782 0.9346850
## 29 0.7674125 1.0454339 0.8914320 1.4262097 1.0953315 1.2181301 0.7259566
## 30 0.6154917 0.6277308 0.5116688 0.9440805 0.8348395 0.8150160 0.6446790
## 31 0.7497360 0.9891875 0.8022375 1.4429900 0.7782371 1.2191706 0.9074365
## 32 1.0001145 1.3041139 1.1612002 1.6948678 1.1829497 1.6649511 1.1325255
## 33 0.6527419 0.7983433 0.4807338 0.9295257 0.9278766 0.8544805 0.7863682
## 34 1.4826065 1.0202186 1.2942291 1.2071023 1.6001397 1.5452809 1.7532202
## 35 1.1283005 0.7164496 0.9762116 1.1521675 0.9402282 1.3120507 1.1292533
## 36 1.0126776 1.0072865 1.0179445 1.5192176 0.8134980 1.3570693 0.7503366
## 37 1.0877978 1.0004759 1.0015663 0.9657629 1.6165998 1.0154413 1.5131864
## 38 0.6933066 0.8869510 0.6569559 1.1753221 0.8183013 1.1846582 0.8470307
## 39 0.8892418 0.9805289 0.8269063 1.1237647 0.8471186 1.1162957 0.5124373
## 40 0.9773679 0.5392903 0.6197798 0.6118791 0.9782275 0.9750318 1.1978652
## 41 0.8389613 0.6790744 0.6214716 0.6423737 1.0900307 0.7669974 0.9260783
## 42 1.0679223 0.7448987 0.8726162 0.9466668 0.9956531 0.8369474 0.8749817
## 43 0.9345796 0.5824217 0.7038920 0.7531886 0.9974417 0.9391123 0.8668529
## 44 1.1367115 1.0487168 1.1578385 1.6121703 1.0532246 1.6486716 1.1304088
## 45 0.9875839 0.6828660 0.7028022 0.8086050 1.1564234 0.8476656 1.2295076
## 46 0.8906082 1.2015919 1.0737821 1.6464771 0.9874401 1.5201895 0.6806776
## 47 0.9767369 1.0616482 0.7547861 1.1946510 0.8734472 1.0567838 0.9909601
## 48 1.1211088 1.0751079 1.0936297 1.4164148 1.1790216 1.6295282 1.0946369
## 49 0.6051834 0.7828237 0.8230492 1.1684772 1.1388714 1.2818830 1.0038605
## 50 0.7096443 0.9568171 0.8039179 1.3167327 0.9549262 1.3279962 0.7817736
## 51 0.9505914 0.5966808 0.6444106 0.9216138 0.5564504 0.8720568 0.9738855
## 52 0.9163842 0.7211283 0.6745969 0.6195305 1.0914060 0.8542968 1.2637978
## 53 1.0216526 0.9542442 1.0514728 1.5279666 0.9490601 1.5327169 1.1055564
## 54 2.5992282 2.0880290 2.3507743 2.2336376 2.2882946 2.4984055 3.0771305
## 55 1.1699641 0.8801670 0.8826840 0.6824309 1.3410850 0.7977738 1.4902876
## 56 0.7487009 0.7383014 0.6805101 1.0534937 0.9180349 0.9613137 0.7112890
## 57 1.3077152 0.7531062 0.9132951 0.6084973 1.1516319 1.2048311 1.4724992
## 58 1.0600995 0.7582724 0.7756442 0.6238598 1.2161398 0.8177335 1.2136433
## 59 0.8855546 0.7265625 0.4715188 0.8128142 0.8776480 0.8446656 1.0986528
## 60 0.8547269 0.7951943 0.5527920 0.9027159 0.8185115 0.6124843 1.0665754
## 61 0.8660237 1.3603165 1.1004781 1.6991495 1.1339480 1.5335097 1.0890904
## 62 1.0693704 0.5447320 0.8274285 0.8675373 1.0079692 1.0631613 1.2744426
## 63 0.7809174 0.6064256 0.3905650 0.6331651 0.9010067 0.7477560 1.2123791
## 64 0.7409035 0.8107663 0.7769858 1.2476073 0.8817715 1.3236710 0.8525661
## 65 0.9017483 0.8112299 0.6898703 1.0582041 0.8702063 1.1325595 0.9318696
## 66 1.3145117 0.6659407 0.9354026 0.5973634 1.1786967 1.1692023 1.5257385
## 67 0.9921028 0.8147650 0.8577558 1.2892572 0.8006454 1.2850140 1.0724276
## 68 0.9483839 0.6725935 0.7161892 0.9752077 0.9770379 0.9940297 1.0577036
## 69 1.0242876 0.5230975 0.8841403 0.9950724 0.8333343 1.2216538 0.8775489
## 70 0.6901543 0.7959906 0.5834261 0.9336172 0.9784569 0.7499987 0.9786879
## 71 1.0210382 0.7338494 0.9371457 1.2990793 0.8045993 1.3394051 1.0361390
## 72 1.0085564 0.7024443 1.0262578 1.3308892 1.0538496 1.4033086 1.1181927
## 73 1.7000321 1.6140716 1.6779213 1.8969088 1.7458167 1.7219954 1.3123734
## 74 1.1837931 0.9440964 1.0819718 1.4946264 0.9136788 1.4789966 1.1586635
## 75 0.9947472 0.9063244 0.8931299 1.3951960 0.6813156 1.3274626 0.8722242
## 76 0.8634060 0.7276400 0.6841937 1.0998327 0.6817001 0.9653305 0.6588665
## 77 1.1983785 0.9760989 0.9455453 1.0295392 1.2292372 1.0997418 0.9820876
## 78 1.0027776 0.9987697 0.7166924 1.0669700 0.7553675 0.9264858 1.1703863
## 8 9 10 11 12 13 14
## 1 1.2618344 0.9287809 0.5025585 0.8221539 1.1353770 1.2595729 0.7334937
## 2 0.9314193 1.3547199 0.8025378 0.3883980 0.9533357 0.9273166 0.9256257
## 3 1.0418680 0.9113830 0.5140623 0.6305712 1.0366272 0.9553434 0.5780381
## 4 1.2048394 1.4112817 1.1020749 0.8384742 1.5181347 0.8584335 1.0213995
## 5 1.2153448 1.2483850 0.7744056 0.7537679 0.8176527 1.4373270 0.9744629
## 6 1.4571057 1.1430770 0.8807179 0.9625477 1.4515247 0.9056926 0.7585723
## 7 1.3234262 0.8517928 0.7963831 0.8644744 1.1279601 1.4657200 0.7490300
## 8 0.0000000 1.3802304 1.1478079 0.8165972 0.7891419 0.9814601 1.0809297
## 9 1.3802304 0.0000000 0.8808093 1.1388086 1.2565114 1.4931979 0.6561821
## 10 1.1478079 0.8808093 0.0000000 0.7248379 0.9335545 1.2188105 0.4992054
## 11 0.8165972 1.1388086 0.7248379 0.0000000 0.8945681 0.8601494 0.6818724
## 12 0.7891419 1.2565114 0.9335545 0.8945681 0.0000000 1.3377956 1.0380154
## 13 0.9814601 1.4931979 1.2188105 0.8601494 1.3377956 0.0000000 1.0262928
## 14 1.0809297 0.6561821 0.4992054 0.6818724 1.0380154 1.0262928 0.0000000
## 15 1.1385170 1.3957109 0.9703793 0.8791450 1.2476522 1.3489511 1.0512783
## 16 0.6882979 0.8596057 0.5421282 0.5567270 0.7252841 0.9765050 0.5339110
## 17 1.1970635 0.6156257 0.3897384 0.7500360 0.9990586 1.2162117 0.4326407
## 18 1.1915049 1.1262904 0.5206506 0.7052666 0.9618092 1.2773363 0.7760741
## 19 1.2488411 0.8735273 0.4066116 0.8129533 0.8691553 1.4091636 0.6991030
## 20 0.8392223 1.6223132 1.4747634 0.9712502 1.3214360 0.9837794 1.2925862
## 21 1.3592866 0.7108488 0.5108982 1.0317979 1.0829991 1.5901038 0.7209612
## 22 1.4936750 1.4795489 1.0041106 0.8855112 1.5659151 1.3289737 0.9896464
## 23 1.2976182 1.3603775 0.6522898 0.7806420 1.1899605 1.0453980 0.9012336
## 24 1.1153963 1.3832473 0.8776571 1.1901336 0.7462439 1.5465403 1.1946037
## 25 1.1323802 1.4446290 1.1540017 0.8370245 1.1442771 1.3117709 1.2610226
## 26 1.1432148 0.9501558 0.4613296 0.7513142 0.8009401 1.3979328 0.7328458
## 27 1.1550476 1.0127650 0.4300651 0.6214789 1.0331099 1.0061218 0.5976504
## 28 0.9429883 1.2972983 0.7840395 0.5736044 0.9073720 0.9978332 0.9414553
## 29 1.0049806 0.7319973 0.7244867 0.8272914 0.8330384 1.2406216 0.6600447
## 30 0.9624895 0.8675425 0.5008842 0.5107181 0.8845592 0.9252081 0.4730444
## 31 1.0857495 0.8406616 0.5671111 0.8571318 0.6434338 1.4136513 0.7347510
## 32 1.1969774 1.0485967 0.9343971 1.1655908 0.9947834 1.7502945 1.1103513
## 33 1.0964789 0.7212808 0.7001621 0.7487703 1.0369595 1.0923974 0.6497653
## 34 1.2062637 1.9049352 1.6280433 1.2256382 1.4681121 1.0581881 1.6171750
## 35 0.7426197 1.3210095 1.0026470 0.4674366 0.8878406 1.0451143 0.9518745
## 36 1.0288323 0.9413692 0.8366582 0.8179835 0.5939419 1.3931533 0.8498782
## 37 1.2779233 1.5214802 1.2683008 0.9784932 1.5836549 0.6402421 1.1398267
## 38 1.1102693 0.9172949 0.7020264 0.9198984 0.9165757 1.4148152 0.8950849
## 39 1.3834143 0.8554478 0.7848694 0.8643240 1.2436873 1.4773195 0.7515637
## 40 0.6968529 1.2537368 0.8886782 0.4852783 1.0343892 0.7317500 0.8496146
## 41 1.1291333 1.0867842 0.9248151 0.5848667 1.2952255 0.8195145 0.7400574
## 42 1.2157245 1.2385726 0.9347176 0.6114254 1.2084879 0.8651728 0.7701396
## 43 0.8701661 1.1376287 0.9326800 0.4619805 1.0788735 0.7537340 0.7838954
## 44 0.7445918 1.3088350 1.0022285 0.9779427 0.4180144 1.4502176 1.1253311
## 45 0.8910668 1.2584149 1.0276853 0.6851285 1.1008547 0.5139728 0.9322537
## 46 1.2559256 0.8503499 0.7884022 1.0794267 0.8586222 1.6942925 0.9341617
## 47 1.2328986 0.7551708 0.9420127 0.9606612 1.0664464 1.3762954 0.8928964
## 48 0.7214603 1.2779081 1.0077867 1.0188042 0.8291309 1.4476992 1.0973459
## 49 1.0628702 1.2973369 0.7041008 0.8132663 1.1204615 1.2566085 0.9508365
## 50 0.9720787 0.9467148 0.6012803 0.9006054 0.8120505 1.4152890 0.8052490
## 51 1.0230611 1.1234536 0.7947333 0.4752463 0.9197907 1.0260458 0.7843692
## 52 1.2134603 1.3626570 0.9463419 0.7087150 1.4150905 0.9857282 0.9626697
## 53 0.8068891 1.2869864 0.8394194 0.9031107 0.4459787 1.4035476 1.0381228
## 54 2.4777867 3.1945693 2.5648224 2.3789968 2.4898851 2.3927752 2.7970892
## 55 1.3127170 1.5730079 1.2023955 0.8866324 1.5632495 0.7450248 1.1192672
## 56 0.9091122 0.9550670 0.5001320 0.5370214 0.8739474 0.9677391 0.4321204
## 57 0.9855562 1.5986954 1.2899349 0.8707457 1.3358301 0.9882191 1.2699047
## 58 1.1404898 1.4292288 1.0558693 0.8024849 1.3792599 0.7252358 0.9851112
## 59 0.8775665 1.0319724 0.8225363 0.7453093 0.9162107 0.9212725 0.8027951
## 60 1.2677602 1.1534097 0.7275294 0.8095301 1.1470846 1.0604395 0.7817794
## 61 1.5141278 1.0952329 0.7265122 1.3009489 1.1802889 1.8713281 1.0677931
## 62 0.8357374 1.5211302 0.9965169 0.5880357 1.0598651 0.7684810 1.0400750
## 63 1.0945629 1.2318312 0.7977500 0.7517905 1.1524031 0.9590850 0.9125015
## 64 0.7391089 0.9919940 0.6376747 0.6857747 0.6724440 1.2800156 0.7747212
## 65 0.6936166 0.9712126 0.7887427 0.6508249 0.7753857 1.0924386 0.7286680
## 66 1.0190098 1.6628581 1.3053636 0.8055408 1.3494643 0.8602250 1.2700472
## 67 0.6661456 1.1711806 0.8339682 0.7219453 0.4986412 1.1739506 0.9391427
## 68 0.6229591 1.1287046 0.8695165 0.4952323 0.8227800 0.7091417 0.7768816
## 69 0.8114955 1.3216138 0.9318423 0.4340323 0.9327261 1.0240933 0.9579656
## 70 1.2469904 1.1784859 0.5878673 0.8507362 1.1914286 1.0794235 0.7900215
## 71 0.8809387 1.2790164 1.0133035 0.7454019 0.6967510 1.2297492 1.1171482
## 72 0.8330978 1.5141347 0.9407853 0.7826359 0.7548821 1.1131765 1.1022282
## 73 1.4100819 1.5423317 1.6089183 1.3963574 1.4503110 1.4275745 1.4230264
## 74 0.7787233 1.2728024 1.0759233 0.8759229 0.4404759 1.2929308 1.1353074
## 75 0.8180990 1.0150527 0.7737345 0.7910746 0.3337110 1.3361295 0.8553906
## 76 0.9017550 0.9151350 0.5806384 0.5477709 0.6857179 1.0440057 0.5071164
## 77 0.8615968 1.0460033 1.1457225 0.7600553 1.1167300 0.8213483 0.8373948
## 78 1.3885946 1.1073920 0.8851859 0.9656366 1.2356100 1.4084555 0.9639616
## 15 16 17 18 19 20 21
## 1 1.0272979 0.6615361 0.5702938 0.7028471 0.6557164 1.5455834 0.5875049
## 2 0.8448012 0.7277101 0.9078530 0.6888367 0.8689062 1.0597717 1.1505755
## 3 0.9462981 0.5849333 0.5294129 0.6744235 0.6237171 1.2994133 0.8521649
## 4 1.0274605 1.0557045 1.1203629 1.0975928 1.2393547 1.1264724 1.4584444
## 5 1.0616054 0.9311493 0.8195755 0.6225247 0.5393357 1.4690054 1.0273476
## 6 1.3387546 1.0462872 0.8012578 0.9979614 0.9962364 1.5362887 1.2528859
## 7 0.9514494 0.8401375 0.6980573 0.7029616 0.8072094 1.3493728 0.7274538
## 8 1.1385170 0.6882979 1.1970635 1.1915049 1.2488411 0.8392223 1.3592866
## 9 1.3957109 0.8596057 0.6156257 1.1262904 0.8735273 1.6223132 0.7108488
## 10 0.9703793 0.5421282 0.3897384 0.5206506 0.4066116 1.4747634 0.5108982
## 11 0.8791450 0.5567270 0.7500360 0.7052666 0.8129533 0.9712502 1.0317979
## 12 1.2476522 0.7252841 0.9990586 0.9618092 0.8691553 1.3214360 1.0829991
## 13 1.3489511 0.9765050 1.2162117 1.2773363 1.4091636 0.9837794 1.5901038
## 14 1.0512783 0.5339110 0.4326407 0.7760741 0.6991030 1.2925862 0.7209612
## 15 0.0000000 0.9702551 1.1169163 0.7052950 1.0901977 1.1167144 1.1648592
## 16 0.9702551 0.0000000 0.5951008 0.7728726 0.7275479 1.1023484 0.7259132
## 17 1.1169163 0.5951008 0.0000000 0.6309604 0.3992005 1.4877940 0.5442288
## 18 0.7052950 0.7728726 0.6309604 0.0000000 0.5211718 1.3818705 0.8095048
## 19 1.0901977 0.7275479 0.3992005 0.5211718 0.0000000 1.6049523 0.5841849
## 20 1.1167144 1.1023484 1.4877940 1.3818705 1.6049523 0.0000000 1.7016827
## 21 1.1648592 0.7259132 0.5442288 0.8095048 0.5841849 1.7016827 0.0000000
## 22 0.9499589 1.1644995 1.0780074 0.8693003 1.1731782 1.4365316 1.2720004
## 23 1.0457074 0.8657962 0.8142408 0.6345022 0.8349233 1.5107326 1.0389644
## 24 1.3420499 0.8367706 1.0637105 1.0207110 0.9476692 1.7069848 0.9432057
## 25 1.4282360 1.0379186 1.0806563 1.1468117 1.0213173 1.4854626 1.3703222
## 26 1.0370473 0.6263082 0.5343023 0.5689148 0.4291014 1.4254578 0.5788437
## 27 0.8773437 0.6390767 0.5008233 0.4268196 0.5975006 1.2899353 0.8073134
## 28 0.9714762 0.6409922 0.8711521 0.7314363 0.8989410 1.0584824 1.0468080
## 29 1.2549729 0.4896836 0.6024724 0.9217277 0.7983959 1.3718221 0.6622281
## 30 0.8879420 0.4316063 0.4999650 0.5821477 0.6671926 1.0817745 0.7698013
## 31 1.2723580 0.5926449 0.5625931 0.8241942 0.4689733 1.5908903 0.5733533
## 32 1.4452681 0.8276575 0.9393381 1.1754442 0.9090616 1.7579007 0.7123166
## 33 1.0219046 0.6231485 0.5573625 0.7828614 0.7219017 1.2032689 0.8242257
## 34 1.4257759 1.3476379 1.6737799 1.5383010 1.7096122 1.0705783 1.8925221
## 35 1.2182935 0.7105026 1.0123147 1.0660403 1.0503761 1.0597358 1.2271292
## 36 1.2997650 0.6768043 0.7450953 0.9101989 0.7410628 1.3577607 0.8390375
## 37 1.4572958 1.0755017 1.2659159 1.3883105 1.4874730 1.3060636 1.5417983
## 38 0.8624088 0.7300479 0.6867831 0.6247848 0.6029279 1.4063314 0.7428540
## 39 0.8574415 0.9203190 0.7154174 0.7118560 0.7569313 1.3561641 0.8121779
## 40 1.0122327 0.6359591 0.9262046 0.9602593 1.0130745 0.9041139 1.2286098
## 41 0.8964725 0.8294372 0.8437150 0.8602256 1.0291773 1.0309491 1.1759303
## 42 1.0775282 0.9066047 0.9082472 0.8699839 1.0505960 1.0145354 1.2494671
## 43 0.8308634 0.7065373 0.8657586 0.8028169 1.0165171 0.7602914 1.1929916
## 44 1.2136177 0.7000321 1.1131631 1.0703574 1.0310417 1.2984733 1.0406724
## 45 1.2165562 0.7743643 0.9574774 1.0376483 1.1168285 0.9873773 1.3417600
## 46 1.2030869 0.7774748 0.7781028 0.9005781 0.7283742 1.5937399 0.4965350
## 47 1.2999623 0.9086732 0.6607178 0.9472587 0.7125819 1.4999643 1.0049363
## 48 0.8647323 0.7205963 1.1471007 1.0221727 1.1178278 1.1371820 1.0433758
## 49 0.7846783 0.6856960 0.9184574 0.7358947 0.9421831 1.3703682 0.8579901
## 50 0.8100914 0.5482381 0.7380786 0.6772422 0.7057131 1.3532624 0.5752139
## 51 1.0810564 0.7869320 0.6945524 0.7011876 0.6786177 1.2436784 1.1153188
## 52 1.0275549 0.9819409 0.9459160 0.9031213 1.0327246 1.3833170 1.2855365
## 53 1.1856117 0.6261182 1.0066911 0.9662639 0.9016252 1.3560649 0.9327315
## 54 2.5935158 2.6009373 2.7341375 2.4996138 2.5457630 2.6937225 2.9573490
## 55 1.2448361 1.1813255 1.1884650 1.1428657 1.3173215 1.3739287 1.5904282
## 56 0.9018137 0.4008004 0.6275811 0.6880342 0.7701266 1.0861054 0.7760921
## 57 0.9892634 1.1204932 1.3055512 1.1359547 1.3153513 0.9666121 1.6211271
## 58 0.8503740 1.0087294 1.0760455 0.8806117 1.1992610 1.0574105 1.4257058
## 59 0.9797132 0.6997378 0.7649575 0.7922291 0.8095227 1.1358719 1.1146681
## 60 0.9963619 0.9317027 0.7040760 0.5872461 0.7072934 1.4667911 1.1087056
## 61 1.2880505 1.0023557 0.8738261 0.9473136 0.7356963 1.9862923 0.4983001
## 62 0.9619771 0.8625561 1.0697710 0.8533071 1.0895747 1.0812470 1.3874967
## 63 0.9589166 0.8414690 0.8203176 0.7451644 0.8275434 1.3183239 1.1615421
## 64 0.8998617 0.3807309 0.7404613 0.7574655 0.7221080 1.2400476 0.6891125
## 65 0.8491496 0.5702806 0.7515324 0.7464811 0.7848350 1.1344020 0.9709398
## 66 1.1248422 1.1240601 1.3481498 1.2197717 1.3682131 0.9414377 1.6648847
## 67 1.1391554 0.5987437 0.8268887 0.8262058 0.7722681 1.2625712 1.0310810
## 68 1.1162280 0.5418376 0.7993416 0.8897202 0.9326221 0.9948598 1.1527532
## 69 0.8336186 0.7271444 0.9432486 0.7396181 0.9720118 0.8530328 1.1825671
## 70 0.8712187 0.8230182 0.6866047 0.4903274 0.7544515 1.4216881 0.9614713
## 71 1.1568665 0.8006016 0.9413533 0.8511645 0.8821661 1.2179700 1.1696730
## 72 0.9510589 0.7474637 1.1333495 0.8584544 1.0899890 1.0989577 1.1895091
## 73 1.8197923 1.3303101 1.4489334 1.5852151 1.6671362 1.3968375 1.6763893
## 74 1.3781281 0.7708787 1.0324287 1.0812003 0.9786317 1.2472450 1.1960092
## 75 1.0785291 0.6111203 0.7742913 0.7665233 0.6632435 1.2784412 0.8774326
## 76 0.9062886 0.5158430 0.6008120 0.5984396 0.6442903 1.0800880 0.8442511
## 77 1.1508501 0.8044831 0.9960311 1.1220548 1.2111148 0.7221669 1.3221812
## 78 1.2070799 1.0765319 0.7477928 0.8039210 0.6617273 1.6838774 1.1231389
## 22 23 24 25 26 27 28
## 1 1.1633680 0.6337815 0.9644371 1.1461627 0.7480401 0.5533326 0.7894853
## 2 1.0302199 0.6671589 1.1559356 0.8103339 0.8378126 0.6174634 0.4712250
## 3 1.1196160 0.6844370 1.1107313 0.9474091 0.7741880 0.4592864 0.7719352
## 4 1.1221457 1.0426270 1.6818927 1.1352537 1.2850019 0.9005171 1.0463369
## 5 1.1959599 1.0008516 1.1684930 0.9147787 0.6141702 0.7985562 0.8981370
## 6 1.1621988 0.8335178 1.5591767 1.3117462 1.1611180 0.6925301 1.1235782
## 7 0.9900788 1.1014972 1.2985615 1.4086831 0.6658371 0.7651836 0.9346850
## 8 1.4936750 1.2976182 1.1153963 1.1323802 1.1432148 1.1550476 0.9429883
## 9 1.4795489 1.3603775 1.3832473 1.4446290 0.9501558 1.0127650 1.2972983
## 10 1.0041106 0.6522898 0.8776571 1.1540017 0.4613296 0.4300651 0.7840395
## 11 0.8855112 0.7806420 1.1901336 0.8370245 0.7513142 0.6214789 0.5736044
## 12 1.5659151 1.1899605 0.7462439 1.1442771 0.8009401 1.0331099 0.9073720
## 13 1.3289737 1.0453980 1.5465403 1.3117709 1.3979328 1.0061218 0.9978332
## 14 0.9896464 0.9012336 1.1946037 1.2610226 0.7328458 0.5976504 0.9414553
## 15 0.9499589 1.0457074 1.3420499 1.4282360 1.0370473 0.8773437 0.9714762
## 16 1.1644995 0.8657962 0.8367706 1.0379186 0.6263082 0.6390767 0.6409922
## 17 1.0780074 0.8142408 1.0637105 1.0806563 0.5343023 0.5008233 0.8711521
## 18 0.8693003 0.6345022 1.0207110 1.1468117 0.5689148 0.4268196 0.7314363
## 19 1.1731782 0.8349233 0.9476692 1.0213173 0.4291014 0.5975006 0.8989410
## 20 1.4365316 1.5107326 1.7069848 1.4854626 1.4254578 1.2899353 1.0584824
## 21 1.2720004 1.0389644 0.9432057 1.3703222 0.5788437 0.8073134 1.0468080
## 22 0.0000000 0.9689644 1.6553247 1.4868383 1.1102788 0.9002988 1.1251995
## 23 0.9689644 0.0000000 1.0609449 1.1786696 0.9009279 0.4681175 0.7030903
## 24 1.6553247 1.0609449 0.0000000 1.3843526 0.8968852 1.0616723 0.9930982
## 25 1.4868383 1.1786696 1.3843526 0.0000000 1.0774567 1.1091772 0.9727034
## 26 1.1102788 0.9009279 0.8968852 1.0774567 0.0000000 0.6048843 0.7010827
## 27 0.9002988 0.4681175 1.0616723 1.1091772 0.6048843 0.0000000 0.5770009
## 28 1.1251995 0.7030903 0.9930982 0.9727034 0.7010827 0.5770009 0.0000000
## 29 1.3085782 1.0459909 0.9134446 1.2286476 0.6998128 0.8257754 0.8583839
## 30 0.9915780 0.6998050 1.0377374 1.1046914 0.5682640 0.3294678 0.5148602
## 31 1.3888574 1.0153054 0.7499433 1.0723194 0.5441617 0.8383549 0.9475479
## 32 1.6035342 1.3796710 0.8809200 1.2170103 0.8146355 1.2194195 1.1825134
## 33 1.2771409 0.9467761 1.1984169 1.0688092 0.7385892 0.5671446 0.7484604
## 34 1.8722102 1.4017921 1.6777869 1.4195432 1.6746635 1.3810869 1.1051973
## 35 1.1713561 1.1258495 1.2606233 0.7999056 0.9250892 1.0154492 0.8021403
## 36 1.3866366 1.1856952 0.9830987 1.1225413 0.5648487 0.9208762 0.8522564
## 37 1.3782899 0.9971936 1.6152254 1.3527361 1.4964378 1.0772061 1.0553762
## 38 1.3605958 0.9997135 0.9508780 1.1076574 0.6857390 0.7155494 0.8693866
## 39 1.0124623 1.1410548 1.4578930 1.3207203 0.7222195 0.7508062 1.0162224
## 40 1.1504464 0.9470222 1.2708363 0.7937537 0.9600396 0.7884079 0.6947079
## 41 0.9605410 0.8748343 1.5092611 1.1283745 1.0732605 0.6735317 0.8484191
## 42 0.8937276 0.9084608 1.5190843 1.2773382 0.9537505 0.6621095 0.7636262
## 43 0.9951794 0.9124352 1.3698336 1.0396971 0.9633644 0.6709307 0.6555196
## 44 1.5948423 1.2819735 0.6636098 1.2777793 0.8549789 1.1403149 0.9169427
## 45 1.3369506 0.8951810 1.3173394 0.9631018 1.1192417 0.7739231 0.7007403
## 46 1.4594074 1.2640965 0.8950642 1.3886029 0.5683599 0.9886455 1.0319322
## 47 1.4878649 1.2357896 1.3501022 0.9336809 0.8964748 0.9172099 1.1110248
## 48 1.4690664 1.3193112 0.8976971 1.4105403 0.9532340 1.1187323 0.9958132
## 49 1.0358880 0.6970395 0.8706618 1.2500376 0.8657962 0.7419016 0.7306490
## 50 1.2654161 1.0075971 0.7194567 1.2985261 0.6109100 0.7742842 0.8546496
## 51 1.0519225 0.8795379 1.2869169 0.6900210 0.7856195 0.6872634 0.8094362
## 52 0.9099390 0.7917076 1.4938671 0.9147278 1.1607834 0.8153938 1.0042465
## 53 1.4831760 1.1306233 0.5502445 1.2039963 0.7102704 1.0144747 0.8185188
## 54 2.7818864 2.2847437 2.5595281 2.0861452 2.6355783 2.4754547 2.3455694
## 55 1.0941632 0.8927536 1.6919365 1.1727468 1.4468766 0.9813047 1.1544501
## 56 0.9161124 0.7907869 1.0159016 1.2393506 0.6052644 0.5308559 0.6499800
## 57 1.3669104 1.2174753 1.6189787 0.9870370 1.3494469 1.0925182 1.0421382
## 58 0.9903070 0.8186868 1.5136340 1.2898116 1.2509568 0.7506411 0.9310983
## 59 1.3437931 0.9410909 1.1586294 0.9654729 0.9312438 0.6896463 0.8462127
## 60 1.0541523 0.6851255 1.2831395 1.1337923 0.9567905 0.5635610 0.9914308
## 61 1.4619747 1.1993273 0.8676347 1.5172495 0.7999094 1.0812400 1.3016006
## 62 1.0399731 0.7662467 1.2373561 0.9407465 1.1102175 0.8286640 0.7730006
## 63 1.2084366 0.7143298 1.2292368 0.8858685 0.9903646 0.6189192 0.8290700
## 64 1.2185454 0.9936805 0.7350150 1.0491925 0.6124263 0.8184528 0.7643736
## 65 1.1864776 1.0316409 1.0519292 1.0152246 0.8665518 0.8292653 0.9352844
## 66 1.3749269 1.1798102 1.6544739 0.9791180 1.3738315 1.1012448 0.9852411
## 67 1.3591516 1.0222196 0.7920865 0.8439639 0.7526088 0.8883192 0.7922380
## 68 1.1851662 0.8998383 1.1039977 0.8443749 0.9129425 0.7646352 0.6904730
## 69 0.9545418 0.9403095 1.2272840 0.9005509 0.7989612 0.7570575 0.5114000
## 70 0.9515713 0.4860514 1.0978361 1.2509580 0.8302957 0.3582066 0.7883794
## 71 1.4215006 1.0478311 1.0159163 0.7592286 0.8408264 0.9042334 0.6782964
## 72 1.2784487 0.8613066 0.8123097 1.2859211 0.9262958 0.8683542 0.5714867
## 73 1.6897994 1.6703401 1.6985129 1.7762365 1.4676597 1.4709324 1.3338501
## 74 1.6268599 1.2586648 0.9361245 0.9355282 0.8632728 1.0815799 0.8226585
## 75 1.3881898 1.1269414 0.8134513 1.0780617 0.6058614 0.8809784 0.8632560
## 76 1.0420312 0.8955250 1.0451368 1.1612506 0.5516194 0.5619867 0.7085612
## 77 1.3054823 1.2727671 1.5163792 1.2578625 1.1399004 0.9696721 0.9572032
## 78 1.2605999 1.0546393 1.4219072 0.9304676 0.9852122 0.8777437 1.2125939
## 29 30 31 32 33 34 35
## 1 0.7674125 0.6154917 0.7497360 1.0001145 0.6527419 1.4826065 1.1283005
## 2 1.0454339 0.6277308 0.9891875 1.3041139 0.7983433 1.0202186 0.7164496
## 3 0.8914320 0.5116688 0.8022375 1.1612002 0.4807338 1.2942291 0.9762116
## 4 1.4262097 0.9440805 1.4429900 1.6948678 0.9295257 1.2071023 1.1521675
## 5 1.0953315 0.8348395 0.7782371 1.1829497 0.9278766 1.6001397 0.9402282
## 6 1.2181301 0.8150160 1.2191706 1.6649511 0.8544805 1.5452809 1.3120507
## 7 0.7259566 0.6446790 0.9074365 1.1325255 0.7863682 1.7532202 1.1292533
## 8 1.0049806 0.9624895 1.0857495 1.1969774 1.0964789 1.2062637 0.7426197
## 9 0.7319973 0.8675425 0.8406616 1.0485967 0.7212808 1.9049352 1.3210095
## 10 0.7244867 0.5008842 0.5671111 0.9343971 0.7001621 1.6280433 1.0026470
## 11 0.8272914 0.5107181 0.8571318 1.1655908 0.7487703 1.2256382 0.4674366
## 12 0.8330384 0.8845592 0.6434338 0.9947834 1.0369595 1.4681121 0.8878406
## 13 1.2406216 0.9252081 1.4136513 1.7502945 1.0923974 1.0581881 1.0451143
## 14 0.6600447 0.4730444 0.7347510 1.1103513 0.6497653 1.6171750 0.9518745
## 15 1.2549729 0.8879420 1.2723580 1.4452681 1.0219046 1.4257759 1.2182935
## 16 0.4896836 0.4316063 0.5926449 0.8276575 0.6231485 1.3476379 0.7105026
## 17 0.6024724 0.4999650 0.5625931 0.9393381 0.5573625 1.6737799 1.0123147
## 18 0.9217277 0.5821477 0.8241942 1.1754442 0.7828614 1.5383010 1.0660403
## 19 0.7983959 0.6671926 0.4689733 0.9090616 0.7219017 1.7096122 1.0503761
## 20 1.3718221 1.0817745 1.5908903 1.7579007 1.2032689 1.0705783 1.0597358
## 21 0.6622281 0.7698013 0.5733533 0.7123166 0.8242257 1.8925221 1.2271292
## 22 1.3085782 0.9915780 1.3888574 1.6035342 1.2771409 1.8722102 1.1713561
## 23 1.0459909 0.6998050 1.0153054 1.3796710 0.9467761 1.4017921 1.1258495
## 24 0.9134446 1.0377374 0.7499433 0.8809200 1.1984169 1.6777869 1.2606233
## 25 1.2286476 1.1046914 1.0723194 1.2170103 1.0688092 1.4195432 0.7999056
## 26 0.6998128 0.5682640 0.5441617 0.8146355 0.7385892 1.6746635 0.9250892
## 27 0.8257754 0.3294678 0.8383549 1.2194195 0.5671446 1.3810869 1.0154492
## 28 0.8583839 0.5148602 0.9475479 1.1825134 0.7484604 1.1051973 0.8021403
## 29 0.0000000 0.6181764 0.5563991 0.7737525 0.7709734 1.6316329 0.9161747
## 30 0.6181764 0.0000000 0.7489352 1.1136279 0.4380936 1.2946320 0.8581142
## 31 0.5563991 0.7489352 0.0000000 0.6407925 0.8434501 1.7182014 0.9309393
## 32 0.7737525 1.1136279 0.6407925 0.0000000 1.1532584 1.9834099 1.0997422
## 33 0.7709734 0.4380936 0.8434501 1.1532584 0.0000000 1.2803179 1.0624274
## 34 1.6316329 1.2946320 1.7182014 1.9834099 1.2803179 0.0000000 1.4010475
## 35 0.9161747 0.8581142 0.9309393 1.0997422 1.0624274 1.4010475 0.0000000
## 36 0.5170068 0.7205914 0.5299207 0.8405349 0.8641099 1.6571988 0.8238701
## 37 1.2711514 1.0335686 1.4796331 1.7347245 1.1412046 1.1254537 1.1809208
## 38 0.8807190 0.7081412 0.7705219 0.9833804 0.5733184 1.4566242 1.1960903
## 39 1.0109169 0.6997621 1.0039288 1.2561744 0.6688864 1.6968403 1.1881536
## 40 1.0440757 0.7023432 1.0555918 1.2672652 0.7937544 1.0960703 0.6351913
## 41 1.0306716 0.6182168 1.1750438 1.4969860 0.6503645 1.1640679 0.9884847
## 42 1.0475724 0.5743118 1.1846088 1.5871752 0.8332599 1.3335786 0.9442680
## 43 0.9238079 0.5325702 1.1090090 1.3982747 0.6518305 1.0584900 0.8117444
## 44 0.8031532 0.9578272 0.7470442 0.8389851 1.1266282 1.5199510 0.9214830
## 45 1.0036573 0.6861210 1.1476445 1.4758174 0.7315203 0.8935916 0.9145709
## 46 0.6284322 0.8504981 0.5841310 0.6558658 0.9037317 1.8572897 1.1880366
## 47 0.9306584 0.8587869 0.8434388 1.1450179 0.6123765 1.6031853 1.1503439
## 48 0.9753343 0.9613870 1.0001755 0.9720093 1.0734398 1.5033978 1.0931455
## 49 0.9168146 0.7739709 0.9685933 1.0360946 0.9879114 1.4507822 1.0498005
## 50 0.7092722 0.6880807 0.6761649 0.7760580 0.7879461 1.5831207 1.1023271
## 51 0.9615768 0.6859534 0.8452432 1.2479235 0.7764767 1.3991440 0.7077726
## 52 1.2546840 0.9333467 1.2315218 1.4671186 1.0088161 1.4250130 0.9982996
## 53 0.7835330 0.8745216 0.6435153 0.7751239 1.0810874 1.5430256 0.8675828
## 54 2.9607220 2.6036334 2.6724631 2.9267084 2.6449856 2.1193770 2.4246433
## 55 1.4357590 1.0782829 1.4794485 1.8116630 1.1836410 1.3125456 1.1784447
## 56 0.6335116 0.3396454 0.7549497 1.0738762 0.7220173 1.4495182 0.7910708
## 57 1.4944755 1.0862555 1.4696738 1.6977797 1.0570000 0.9766335 1.0905214
## 58 1.2869448 0.8229587 1.3929806 1.7223043 0.9469176 1.1321515 1.1946962
## 59 0.9851025 0.6530368 0.9350503 1.2989334 0.5519610 1.1361967 1.0358653
## 60 1.1177996 0.7423732 1.0043675 1.4690436 0.8156188 1.4752430 1.1911541
## 61 1.0070715 1.1238011 0.7400061 0.7372883 1.1970401 2.1386994 1.4495665
## 62 1.1625347 0.8625399 1.1705678 1.4582963 1.0809019 1.1493803 0.7989262
## 63 1.1602638 0.7502493 1.0592365 1.3890439 0.7055381 1.1663987 1.0945620
## 64 0.6091913 0.6802191 0.5625975 0.6282571 0.8265289 1.4953140 0.7650163
## 65 0.7898038 0.7228720 0.7704466 1.0282398 0.7933915 1.4093381 0.8342050
## 66 1.5074963 1.0740163 1.4835286 1.7525325 1.0938542 0.8420742 0.9949548
## 67 0.7439731 0.7961533 0.6466622 0.8779197 0.9313141 1.4402486 0.7234445
## 68 0.7452302 0.6313113 0.8753468 1.1608501 0.7981792 1.2012677 0.6017475
## 69 0.9404834 0.6595370 1.0424591 1.2297512 0.8763829 1.2313915 0.6129054
## 70 1.0277290 0.6205377 1.0284342 1.3564712 0.7847656 1.4759881 1.2348559
## 71 0.8672503 0.8181436 0.8615109 1.0962655 0.8706383 1.2461416 0.8226974
## 72 0.9704123 0.7849038 1.0189230 1.2667158 1.0869811 1.1642869 0.9292642
## 73 1.1091046 1.2778556 1.5434335 1.6924379 1.4703357 1.9037660 1.3863524
## 74 0.8128518 0.9068318 0.7732968 1.0026649 0.9903828 1.3738537 0.7876179
## 75 0.6863177 0.7326923 0.5207571 0.8634553 0.8486837 1.5343872 0.8621647
## 76 0.6781784 0.3736951 0.6816935 1.1198513 0.6502615 1.4268350 0.8123817
## 77 0.9150055 0.7249076 1.1928089 1.4690888 0.7624389 1.2216951 0.9373948
## 78 1.2190312 0.9994423 0.9848274 1.3353015 0.9187366 1.7396899 1.2214979
## 36 37 38 39 40 41 42
## 1 1.0126776 1.0877978 0.6933066 0.8892418 0.9773679 0.8389613 1.0679223
## 2 1.0072865 1.0004759 0.8869510 0.9805289 0.5392903 0.6790744 0.7448987
## 3 1.0179445 1.0015663 0.6569559 0.8269063 0.6197798 0.6214716 0.8726162
## 4 1.5192176 0.9657629 1.1753221 1.1237647 0.6118791 0.6423737 0.9466668
## 5 0.8134980 1.6165998 0.8183013 0.8471186 0.9782275 1.0900307 0.9956531
## 6 1.3570693 1.0154413 1.1846582 1.1162957 0.9750318 0.7669974 0.8369474
## 7 0.7503366 1.5131864 0.8470307 0.5124373 1.1978652 0.9260783 0.8749817
## 8 1.0288323 1.2779233 1.1102693 1.3834143 0.6968529 1.1291333 1.2157245
## 9 0.9413692 1.5214802 0.9172949 0.8554478 1.2537368 1.0867842 1.2385726
## 10 0.8366582 1.2683008 0.7020264 0.7848694 0.8886782 0.9248151 0.9347176
## 11 0.8179835 0.9784932 0.9198984 0.8643240 0.4852783 0.5848667 0.6114254
## 12 0.5939419 1.5836549 0.9165757 1.2436873 1.0343892 1.2952255 1.2084879
## 13 1.3931533 0.6402421 1.4148152 1.4773195 0.7317500 0.8195145 0.8651728
## 14 0.8498782 1.1398267 0.8950849 0.7515637 0.8496146 0.7400574 0.7701396
## 15 1.2997650 1.4572958 0.8624088 0.8574415 1.0122327 0.8964725 1.0775282
## 16 0.6768043 1.0755017 0.7300479 0.9203190 0.6359591 0.8294372 0.9066047
## 17 0.7450953 1.2659159 0.6867831 0.7154174 0.9262046 0.8437150 0.9082472
## 18 0.9101989 1.3883105 0.6247848 0.7118560 0.9602593 0.8602256 0.8699839
## 19 0.7410628 1.4874730 0.6029279 0.7569313 1.0130745 1.0291773 1.0505960
## 20 1.3577607 1.3060636 1.4063314 1.3561641 0.9041139 1.0309491 1.0145354
## 21 0.8390375 1.5417983 0.7428540 0.8121779 1.2286098 1.1759303 1.2494671
## 22 1.3866366 1.3782899 1.3605958 1.0124623 1.1504464 0.9605410 0.8937276
## 23 1.1856952 0.9971936 0.9997135 1.1410548 0.9470222 0.8748343 0.9084608
## 24 0.9830987 1.6152254 0.9508780 1.4578930 1.2708363 1.5092611 1.5190843
## 25 1.1225413 1.3527361 1.1076574 1.3207203 0.7937537 1.1283745 1.2773382
## 26 0.5648487 1.4964378 0.6857390 0.7222195 0.9600396 1.0732605 0.9537505
## 27 0.9208762 1.0772061 0.7155494 0.7508062 0.7884079 0.6735317 0.6621095
## 28 0.8522564 1.0553762 0.8693866 1.0162224 0.6947079 0.8484191 0.7636262
## 29 0.5170068 1.2711514 0.8807190 1.0109169 1.0440757 1.0306716 1.0475724
## 30 0.7205914 1.0335686 0.7081412 0.6997621 0.7023432 0.6182168 0.5743118
## 31 0.5299207 1.4796331 0.7705219 1.0039288 1.0555918 1.1750438 1.1846088
## 32 0.8405349 1.7347245 0.9833804 1.2561744 1.2672652 1.4969860 1.5871752
## 33 0.8641099 1.1412046 0.5733184 0.6688864 0.7937544 0.6503645 0.8332599
## 34 1.6571988 1.1254537 1.4566242 1.6968403 1.0960703 1.1640679 1.3335786
## 35 0.8238701 1.1809208 1.1960903 1.1881536 0.6351913 0.9884847 0.9442680
## 36 0.0000000 1.5397506 0.9086275 0.9725672 1.0778154 1.1703640 1.0220176
## 37 1.5397506 0.0000000 1.4894798 1.5357731 0.9327400 0.8219270 1.0620989
## 38 0.9086275 1.4894798 0.0000000 0.7644783 0.9928565 0.9750549 1.1829641
## 39 0.9725672 1.5357731 0.7644783 0.0000000 1.0908451 0.8302451 0.8811135
## 40 1.0778154 0.9327400 0.9928565 1.0908451 0.0000000 0.7237389 0.8552766
## 41 1.1703640 0.8219270 0.9750549 0.8302451 0.7237389 0.0000000 0.6288354
## 42 1.0220176 1.0620989 1.1829641 0.8811135 0.8552766 0.6288354 0.0000000
## 43 0.9890101 0.9307078 0.9072712 0.8696057 0.5953495 0.3783398 0.5739207
## 44 0.6888476 1.6104307 0.9705282 1.3022872 1.1016565 1.3827715 1.3442124
## 45 1.1093304 0.7269347 1.0492092 1.2300061 0.5771152 0.6547015 0.7966015
## 46 0.5850256 1.7358367 0.7390649 0.8802500 1.3041683 1.3136769 1.3049448
## 47 0.8903724 1.4995463 0.6846233 0.8778758 1.0217774 0.9635232 1.1596254
## 48 1.0104420 1.6091945 0.8422286 1.1661115 1.0406224 1.2776850 1.3745643
## 49 1.1364088 1.1589405 0.8642124 1.0997209 0.9429353 0.9921608 1.1694311
## 50 0.8227873 1.4901111 0.5042985 0.8649035 1.0224720 1.0948676 1.2038310
## 51 0.8448621 1.2254713 0.8889859 0.8998794 0.6738472 0.7383752 0.7618898
## 52 1.3865966 0.9588472 1.1058020 1.1395056 0.7128394 0.6770953 1.0255145
## 53 0.6771219 1.5438705 0.9399032 1.2471876 1.0228969 1.3442068 1.2717437
## 54 2.8290071 2.4971302 2.5969238 2.8779413 2.1987512 2.5745211 2.6076428
## 55 1.5847725 0.7961080 1.3790881 1.4082603 0.8637025 0.7240912 1.0184999
## 56 0.7474938 1.1056125 0.8987163 0.8144507 0.7509814 0.7917354 0.6589757
## 57 1.4771632 1.2257565 1.1219764 1.2744136 0.6401336 0.8533270 1.1297146
## 58 1.4200968 0.9291841 1.0961218 1.1459442 0.7979881 0.5600616 0.8186422
## 59 1.0215992 1.1658546 0.6323741 0.9753194 0.6538693 0.7296157 0.9565997
## 60 1.1700068 1.2355914 0.8415403 0.9601536 0.9312078 0.7557063 0.8987436
## 61 1.1098419 1.8547547 0.8943327 1.1415673 1.4584721 1.5190961 1.6039866
## 62 1.2062815 1.0005933 1.1058169 1.2915347 0.6192859 0.8250424 0.9374001
## 63 1.2337544 1.0570667 0.7515704 1.0397514 0.6492303 0.7063101 0.9975410
## 64 0.6894969 1.3483523 0.6702447 0.9509274 0.8255592 1.0291433 1.1407848
## 65 0.8607613 1.2924875 0.6825262 0.9505425 0.7574483 0.8286507 1.0609109
## 66 1.4772579 1.0624467 1.2717299 1.3376240 0.5780977 0.8382595 1.0241333
## 67 0.6670667 1.3923556 0.7975851 1.1833237 0.8053459 1.1113262 1.1507580
## 68 0.8294950 0.9562698 0.9524621 1.1483096 0.5348476 0.7596262 0.8461206
## 69 0.8578211 1.2035119 0.9339374 0.9502273 0.6364032 0.7878052 0.7462580
## 70 1.1749557 1.1777457 0.7745715 0.9580042 0.9227844 0.8294992 0.9182837
## 71 0.7188400 1.3780758 0.7907825 1.1474101 0.8874790 1.0349101 1.0874047
## 72 0.9683894 1.2526572 1.0300262 1.2787623 0.9424362 1.1156110 1.0307201
## 73 1.1673701 1.6523259 1.6826666 1.6748033 1.5501048 1.5232272 1.3017899
## 74 0.5534817 1.5069512 0.9728515 1.2933093 0.9683646 1.2613683 1.1940570
## 75 0.4568676 1.5622433 0.6899087 0.9793207 0.9676508 1.1395332 1.1028264
## 76 0.5885066 1.2878152 0.7720337 0.7186355 0.7962864 0.8041890 0.6371185
## 77 0.9829237 1.1079842 1.0945250 1.0366591 0.8105560 0.6853780 0.7584042
## 78 1.1889142 1.5357067 0.8426963 0.9751020 1.0432071 0.9997185 1.2075583
## 43 44 45 46 47 48 49
## 1 0.9345796 1.1367115 0.9875839 0.8906082 0.9767369 1.1211088 0.6051834
## 2 0.5824217 1.0487168 0.6828660 1.2015919 1.0616482 1.0751079 0.7828237
## 3 0.7038920 1.1578385 0.7028022 1.0737821 0.7547861 1.0936297 0.8230492
## 4 0.7531886 1.6121703 0.8086050 1.6464771 1.1946510 1.4164148 1.1684772
## 5 0.9974417 1.0532246 1.1564234 0.9874401 0.8734472 1.1790216 1.1388714
## 6 0.9391123 1.6486716 0.8476656 1.5201895 1.0567838 1.6295282 1.2818830
## 7 0.8668529 1.1304088 1.2295076 0.6806776 0.9909601 1.0946369 1.0038605
## 8 0.8701661 0.7445918 0.8910668 1.2559256 1.2328986 0.7214603 1.0628702
## 9 1.1376287 1.3088350 1.2584149 0.8503499 0.7551708 1.2779081 1.2973369
## 10 0.9326800 1.0022285 1.0276853 0.7884022 0.9420127 1.0077867 0.7041008
## 11 0.4619805 0.9779427 0.6851285 1.0794267 0.9606612 1.0188042 0.8132663
## 12 1.0788735 0.4180144 1.1008547 0.8586222 1.0664464 0.8291309 1.1204615
## 13 0.7537340 1.4502176 0.5139728 1.6942925 1.3762954 1.4476992 1.2566085
## 14 0.7838954 1.1253311 0.9322537 0.9341617 0.8928964 1.0973459 0.9508365
## 15 0.8308634 1.2136177 1.2165562 1.2030869 1.2999623 0.8647323 0.7846783
## 16 0.7065373 0.7000321 0.7743643 0.7774748 0.9086732 0.7205963 0.6856960
## 17 0.8657586 1.1131631 0.9574774 0.7781028 0.6607178 1.1471007 0.9184574
## 18 0.8028169 1.0703574 1.0376483 0.9005781 0.9472587 1.0221727 0.7358947
## 19 1.0165171 1.0310417 1.1168285 0.7283742 0.7125819 1.1178278 0.9421831
## 20 0.7602914 1.2984733 0.9873773 1.5937399 1.4999643 1.1371820 1.3703682
## 21 1.1929916 1.0406724 1.3417600 0.4965350 1.0049363 1.0433758 0.8579901
## 22 0.9951794 1.5948423 1.3369506 1.4594074 1.4878649 1.4690664 1.0358880
## 23 0.9124352 1.2819735 0.8951810 1.2640965 1.2357896 1.3193112 0.6970395
## 24 1.3698336 0.6636098 1.3173394 0.8950642 1.3501022 0.8976971 0.8706618
## 25 1.0396971 1.2777793 0.9631018 1.3886029 0.9336809 1.4105403 1.2500376
## 26 0.9633644 0.8549789 1.1192417 0.5683599 0.8964748 0.9532340 0.8657962
## 27 0.6709307 1.1403149 0.7739231 0.9886455 0.9172099 1.1187323 0.7419016
## 28 0.6555196 0.9169427 0.7007403 1.0319322 1.1110248 0.9958132 0.7306490
## 29 0.9238079 0.8031532 1.0036573 0.6284322 0.9306584 0.9753343 0.9168146
## 30 0.5325702 0.9578272 0.6861210 0.8504981 0.8587869 0.9613870 0.7739709
## 31 1.1090090 0.7470442 1.1476445 0.5841310 0.8434388 1.0001755 0.9685933
## 32 1.3982747 0.8389851 1.4758174 0.6558658 1.1450179 0.9720093 1.0360946
## 33 0.6518305 1.1266282 0.7315203 0.9037317 0.6123765 1.0734398 0.9879114
## 34 1.0584900 1.5199510 0.8935916 1.8572897 1.6031853 1.5033978 1.4507822
## 35 0.8117444 0.9214830 0.9145709 1.1880366 1.1503439 1.0931455 1.0498005
## 36 0.9890101 0.6888476 1.1093304 0.5850256 0.8903724 1.0104420 1.1364088
## 37 0.9307078 1.6104307 0.7269347 1.7358367 1.4995463 1.6091945 1.1589405
## 38 0.9072712 0.9705282 1.0492092 0.7390649 0.6846233 0.8422286 0.8642124
## 39 0.8696057 1.3022872 1.2300061 0.8802500 0.8778758 1.1661115 1.0997209
## 40 0.5953495 1.1016565 0.5771152 1.3041683 1.0217774 1.0406224 0.9429353
## 41 0.3783398 1.3827715 0.6547015 1.3136769 0.9635232 1.2776850 0.9921608
## 42 0.5739207 1.3442124 0.7966015 1.3049448 1.1596254 1.3745643 1.1694311
## 43 0.0000000 1.1567152 0.5307702 1.2088391 0.9352069 1.0745808 0.9489879
## 44 1.1567152 0.0000000 1.2327761 0.7736588 1.2588431 0.5899814 0.9886941
## 45 0.5307702 1.2327761 0.0000000 1.3965175 0.9891779 1.2703972 1.0933805
## 46 1.2088391 0.7736588 1.3965175 0.0000000 1.0110104 0.8798932 1.0180629
## 47 0.9352069 1.2588431 0.9891779 1.0110104 0.0000000 1.2869468 1.3119863
## 48 1.0745808 0.5899814 1.2703972 0.8798932 1.2869468 0.0000000 0.8495022
## 49 0.9489879 0.9886941 1.0933805 1.0180629 1.3119863 0.8495022 0.0000000
## 50 0.9860811 0.7009251 1.1714090 0.5485654 1.0170438 0.5189316 0.6398156
## 51 0.6569391 1.1516002 0.7618425 1.1578087 0.7001721 1.2423184 1.0966618
## 52 0.7966938 1.5096877 0.8747057 1.5140987 1.1089567 1.4063630 0.9460661
## 53 1.1466608 0.2562011 1.1966938 0.7529588 1.2446289 0.6574914 0.8814562
## 54 2.5409270 2.6589539 2.3236904 3.0323535 2.7009258 2.7423453 2.5405035
## 55 0.8538015 1.7046809 0.8025846 1.7982989 1.3246347 1.6396661 1.2083315
## 56 0.6980014 0.8859187 0.8801733 0.8668852 1.0832110 0.8875641 0.7452409
## 57 0.7537931 1.4488368 0.8213592 1.6562132 1.1727532 1.2723286 1.2449394
## 58 0.5731946 1.4886927 0.7015761 1.5614500 1.2171015 1.3202825 1.0200333
## 59 0.6453557 1.1034600 0.6030216 1.1625515 0.6592283 1.0314882 1.0428730
## 60 0.8194504 1.3725097 0.8777289 1.2874327 0.8630962 1.3392016 1.0545487
## 61 1.5115131 1.1225925 1.6383696 0.7223849 1.2580994 1.1069417 0.9585604
## 62 0.6749000 1.1725016 0.6976869 1.4518175 1.2136276 1.1625446 0.8916064
## 63 0.7425840 1.3055746 0.6774009 1.3275749 0.8623590 1.2155892 0.9307776
## 64 0.8895330 0.5417887 1.0486553 0.6415427 0.9834577 0.5328630 0.6209871
## 65 0.6983244 0.8644877 0.8875911 0.9650788 0.7780688 0.7714370 0.8811305
## 66 0.7722513 1.4665333 0.7583726 1.7150907 1.2924937 1.3796681 1.2785414
## 67 0.8886512 0.6347322 0.8994354 0.9233131 0.8756969 0.8350563 0.9386826
## 68 0.5447945 0.9389542 0.4869250 1.1589767 0.8942332 1.0278701 0.9436572
## 69 0.4943703 0.9632539 0.7905776 1.1091943 1.0560284 0.9548120 0.8703666
## 70 0.8325623 1.2912049 0.8983635 1.1761514 1.0535967 1.1810741 0.7591113
## 71 0.7911018 0.8291936 0.8258408 1.0032876 0.8333067 1.0248171 1.0388831
## 72 0.8996438 0.6944242 0.9727949 1.1027697 1.3994674 0.8185261 0.7257059
## 73 1.2745156 1.4617531 1.3304349 1.5120807 1.5780767 1.6247221 1.6810723
## 74 1.0027587 0.5951832 0.9650969 0.9498721 0.9717896 0.9802923 1.2062508
## 75 0.9380357 0.5249752 1.0620311 0.6533582 0.8294185 0.7456252 1.0247912
## 76 0.6569696 0.8395945 0.8661397 0.8091421 0.8706429 0.9019928 0.9467191
## 77 0.4758088 1.2021664 0.6762344 1.2657978 0.9604738 1.1552376 1.2689539
## 78 1.0530802 1.4619172 1.1310575 1.2782504 0.6306679 1.4399514 1.2613675
## 50 51 52 53 54 55 56
## 1 0.7096443 0.9505914 0.9163842 1.0216526 2.599228 1.1699641 0.7487009
## 2 0.9568171 0.5966808 0.7211283 0.9542442 2.088029 0.8801670 0.7383014
## 3 0.8039179 0.6444106 0.6745969 1.0514728 2.350774 0.8826840 0.6805101
## 4 1.3167327 0.9216138 0.6195305 1.5279666 2.233638 0.6824309 1.0534937
## 5 0.9549262 0.5564504 1.0914060 0.9490601 2.288295 1.3410850 0.9180349
## 6 1.3279962 0.8720568 0.8542968 1.5327169 2.498405 0.7977738 0.9613137
## 7 0.7817736 0.9738855 1.2637978 1.1055564 3.077130 1.4902876 0.7112890
## 8 0.9720787 1.0230611 1.2134603 0.8068891 2.477787 1.3127170 0.9091122
## 9 0.9467148 1.1234536 1.3626570 1.2869864 3.194569 1.5730079 0.9550670
## 10 0.6012803 0.7947333 0.9463419 0.8394194 2.564822 1.2023955 0.5001320
## 11 0.9006054 0.4752463 0.7087150 0.9031107 2.378997 0.8866324 0.5370214
## 12 0.8120505 0.9197907 1.4150905 0.4459787 2.489885 1.5632495 0.8739474
## 13 1.4152890 1.0260458 0.9857282 1.4035476 2.392775 0.7450248 0.9677391
## 14 0.8052490 0.7843692 0.9626697 1.0381228 2.797089 1.1192672 0.4321204
## 15 0.8100914 1.0810564 1.0275549 1.1856117 2.593516 1.2448361 0.9018137
## 16 0.5482381 0.7869320 0.9819409 0.6261182 2.600937 1.1813255 0.4008004
## 17 0.7380786 0.6945524 0.9459160 1.0066911 2.734138 1.1884650 0.6275811
## 18 0.6772422 0.7011876 0.9031213 0.9662639 2.499614 1.1428657 0.6880342
## 19 0.7057131 0.6786177 1.0327246 0.9016252 2.545763 1.3173215 0.7701266
## 20 1.3532624 1.2436784 1.3833170 1.3560649 2.693723 1.3739287 1.0861054
## 21 0.5752139 1.1153188 1.2855365 0.9327315 2.957349 1.5904282 0.7760921
## 22 1.2654161 1.0519225 0.9099390 1.4831760 2.781886 1.0941632 0.9161124
## 23 1.0075971 0.8795379 0.7917076 1.1306233 2.284744 0.8927536 0.7907869
## 24 0.7194567 1.2869169 1.4938671 0.5502445 2.559528 1.6919365 1.0159016
## 25 1.2985261 0.6900210 0.9147278 1.2039963 2.086145 1.1727468 1.2393506
## 26 0.6109100 0.7856195 1.1607834 0.7102704 2.635578 1.4468766 0.6052644
## 27 0.7742842 0.6872634 0.8153938 1.0144747 2.475455 0.9813047 0.5308559
## 28 0.8546496 0.8094362 1.0042465 0.8185188 2.345569 1.1544501 0.6499800
## 29 0.7092722 0.9615768 1.2546840 0.7835330 2.960722 1.4357590 0.6335116
## 30 0.6880807 0.6859534 0.9333467 0.8745216 2.603633 1.0782829 0.3396454
## 31 0.6761649 0.8452432 1.2315218 0.6435153 2.672463 1.4794485 0.7549497
## 32 0.7760580 1.2479235 1.4671186 0.7751239 2.926708 1.8116630 1.0738762
## 33 0.7879461 0.7764767 1.0088161 1.0810874 2.644986 1.1836410 0.7220173
## 34 1.5831207 1.3991440 1.4250130 1.5430256 2.119377 1.3125456 1.4495182
## 35 1.1023271 0.7077726 0.9982996 0.8675828 2.424643 1.1784447 0.7910708
## 36 0.8227873 0.8448621 1.3865966 0.6771219 2.829007 1.5847725 0.7474938
## 37 1.4901111 1.2254713 0.9588472 1.5438705 2.497130 0.7961080 1.1056125
## 38 0.5042985 0.8889859 1.1058020 0.9399032 2.596924 1.3790881 0.8987163
## 39 0.8649035 0.8998794 1.1395056 1.2471876 2.877941 1.4082603 0.8144507
## 40 1.0224720 0.6738472 0.7128394 1.0228969 2.198751 0.8637025 0.7509814
## 41 1.0948676 0.7383752 0.6770953 1.3442068 2.574521 0.7240912 0.7917354
## 42 1.2038310 0.7618898 1.0255145 1.2717437 2.607643 1.0184999 0.6589757
## 43 0.9860811 0.6569391 0.7966938 1.1466608 2.540927 0.8538015 0.6980014
## 44 0.7009251 1.1516002 1.5096877 0.2562011 2.658954 1.7046809 0.8859187
## 45 1.1714090 0.7618425 0.8747057 1.1966938 2.323690 0.8025846 0.8801733
## 46 0.5485654 1.1578087 1.5140987 0.7529588 3.032354 1.7982989 0.8668852
## 47 1.0170438 0.7001721 1.1089567 1.2446289 2.700926 1.3246347 1.0832110
## 48 0.5189316 1.2423184 1.4063630 0.6574914 2.742345 1.6396661 0.8875641
## 49 0.6398156 1.0966618 0.9460661 0.8814562 2.540503 1.2083315 0.7452409
## 50 0.0000000 1.0482428 1.2174067 0.6550946 2.753699 1.4914386 0.6846474
## 51 1.0482428 0.0000000 0.7305683 1.0776799 2.310080 0.9070634 0.8179004
## 52 1.2174067 0.7305683 0.0000000 1.4096900 2.251900 0.4822613 1.0198122
## 53 0.6550946 1.0776799 1.4096900 0.0000000 2.541981 1.6245147 0.7796031
## 54 2.7536986 2.3100799 2.2518999 2.5419805 0.000000 2.2263349 2.6715647
## 55 1.4914386 0.9070634 0.4822613 1.6245147 2.226335 0.0000000 1.1723212
## 56 0.6846474 0.8179004 1.0198122 0.7796031 2.671565 1.1723212 0.0000000
## 57 1.3142907 0.8888425 0.8230899 1.4270652 2.037355 0.8837494 1.2153872
## 58 1.1999833 0.8939558 0.6874089 1.4381617 2.376666 0.5713729 0.9521113
## 59 0.8780752 0.6483818 0.8761284 1.0746120 2.331844 0.9737541 0.8577657
## 60 1.0384551 0.6163149 0.7297780 1.2820008 2.354788 0.8079616 0.9019418
## 61 0.6907185 1.3337837 1.4556342 0.9946643 2.920284 1.7980915 1.0850991
## 62 1.1225720 0.6962722 0.6476874 1.1074687 2.107933 0.6704200 0.9012946
## 63 1.0004974 0.6734968 0.5907808 1.2137158 2.100983 0.7493437 0.9462510
## 64 0.3897858 0.8850401 1.0821109 0.4905018 2.625080 1.3670947 0.6252799
## 65 0.6813083 0.6751104 0.8930666 0.8814148 2.581360 1.0941654 0.7605846
## 66 1.4146512 0.9035701 0.8587264 1.4219842 1.918435 0.8467556 1.1782521
## 67 0.7650797 0.6950439 1.0815267 0.6143126 2.432266 1.2784217 0.8337224
## 68 0.9563028 0.5852640 0.8342014 0.9135743 2.441874 0.9053949 0.7062245
## 69 0.9273780 0.6499854 0.9035834 0.9298564 2.440191 1.0869503 0.7253785
## 70 0.8481120 0.8633348 0.8101117 1.1698594 2.457179 0.9561260 0.7623844
## 71 0.9314966 0.6903832 1.1238163 0.8491213 2.406974 1.2930039 0.9872771
## 72 0.8353484 1.0606140 1.2453241 0.6450302 2.373860 1.3355089 0.7469250
## 73 1.5815322 1.4906244 1.8277360 1.5138359 3.404439 1.8219092 1.3049115
## 74 0.9737130 0.8752188 1.3948477 0.6457755 2.508329 1.5423677 0.9808970
## 75 0.6232279 0.7738385 1.2767169 0.5414998 2.619980 1.4807221 0.7574464
## 76 0.7022713 0.6366255 1.0770125 0.7803025 2.625153 1.2155147 0.3835036
## 77 1.1352101 0.8801346 1.1527571 1.2490969 2.837265 1.1520977 0.8369540
## 78 1.1384902 0.6120204 0.8210913 1.3792937 2.410671 1.0830111 1.1583298
## 57 58 59 60 61 62 63
## 1 1.3077152 1.0600995 0.8855546 0.8547269 0.8660237 1.0693704 0.7809174
## 2 0.7531062 0.7582724 0.7265625 0.7951943 1.3603165 0.5447320 0.6064256
## 3 0.9132951 0.7756442 0.4715188 0.5527920 1.1004781 0.8274285 0.3905650
## 4 0.6084973 0.6238598 0.8128142 0.9027159 1.6991495 0.8675373 0.6331651
## 5 1.1516319 1.2161398 0.8776480 0.8185115 1.1339480 1.0079692 0.9010067
## 6 1.2048311 0.8177335 0.8446656 0.6124843 1.5335097 1.0631613 0.7477560
## 7 1.4724992 1.2136433 1.0986528 1.0665754 1.0890904 1.2744426 1.2123791
## 8 0.9855562 1.1404898 0.8775665 1.2677602 1.5141278 0.8357374 1.0945629
## 9 1.5986954 1.4292288 1.0319724 1.1534097 1.0952329 1.5211302 1.2318312
## 10 1.2899349 1.0558693 0.8225363 0.7275294 0.7265122 0.9965169 0.7977500
## 11 0.8707457 0.8024849 0.7453093 0.8095301 1.3009489 0.5880357 0.7517905
## 12 1.3358301 1.3792599 0.9162107 1.1470846 1.1802889 1.0598651 1.1524031
## 13 0.9882191 0.7252358 0.9212725 1.0604395 1.8713281 0.7684810 0.9590850
## 14 1.2699047 0.9851112 0.8027951 0.7817794 1.0677931 1.0400750 0.9125015
## 15 0.9892634 0.8503740 0.9797132 0.9963619 1.2880505 0.9619771 0.9589166
## 16 1.1204932 1.0087294 0.6997378 0.9317027 1.0023557 0.8625561 0.8414690
## 17 1.3055512 1.0760455 0.7649575 0.7040760 0.8738261 1.0697710 0.8203176
## 18 1.1359547 0.8806117 0.7922291 0.5872461 0.9473136 0.8533071 0.7451644
## 19 1.3153513 1.1992610 0.8095227 0.7072934 0.7356963 1.0895747 0.8275434
## 20 0.9666121 1.0574105 1.1358719 1.4667911 1.9862923 1.0812470 1.3183239
## 21 1.6211271 1.4257058 1.1146681 1.1087056 0.4983001 1.3874967 1.1615421
## 22 1.3669104 0.9903070 1.3437931 1.0541523 1.4619747 1.0399731 1.2084366
## 23 1.2174753 0.8186868 0.9410909 0.6851255 1.1993273 0.7662467 0.7143298
## 24 1.6189787 1.5136340 1.1586294 1.2831395 0.8676347 1.2373561 1.2292368
## 25 0.9870370 1.2898116 0.9654729 1.1337923 1.5172495 0.9407465 0.8858685
## 26 1.3494469 1.2509568 0.9312438 0.9567905 0.7999094 1.1102175 0.9903646
## 27 1.0925182 0.7506411 0.6896463 0.5635610 1.0812400 0.8286640 0.6189192
## 28 1.0421382 0.9310983 0.8462127 0.9914308 1.3016006 0.7730006 0.8290700
## 29 1.4944755 1.2869448 0.9851025 1.1177996 1.0070715 1.1625347 1.1602638
## 30 1.0862555 0.8229587 0.6530368 0.7423732 1.1238011 0.8625399 0.7502493
## 31 1.4696738 1.3929806 0.9350503 1.0043675 0.7400061 1.1705678 1.0592365
## 32 1.6977797 1.7223043 1.2989334 1.4690436 0.7372883 1.4582963 1.3890439
## 33 1.0570000 0.9469176 0.5519610 0.8156188 1.1970401 1.0809019 0.7055381
## 34 0.9766335 1.1321515 1.1361967 1.4752430 2.1386994 1.1493803 1.1663987
## 35 1.0905214 1.1946962 1.0358653 1.1911541 1.4495665 0.7989262 1.0945620
## 36 1.4771632 1.4200968 1.0215992 1.1700068 1.1098419 1.2062815 1.2337544
## 37 1.2257565 0.9291841 1.1658546 1.2355914 1.8547547 1.0005933 1.0570667
## 38 1.1219764 1.0961218 0.6323741 0.8415403 0.8943327 1.1058169 0.7515704
## 39 1.2744136 1.1459442 0.9753194 0.9601536 1.1415673 1.2915347 1.0397514
## 40 0.6401336 0.7979881 0.6538693 0.9312078 1.4584721 0.6192859 0.6492303
## 41 0.8533270 0.5600616 0.7296157 0.7557063 1.5190961 0.8250424 0.7063101
## 42 1.1297146 0.8186422 0.9565997 0.8987436 1.6039866 0.9374001 0.9975410
## 43 0.7537931 0.5731946 0.6453557 0.8194504 1.5115131 0.6749000 0.7425840
## 44 1.4488368 1.4886927 1.1034600 1.3725097 1.1225925 1.1725016 1.3055746
## 45 0.8213592 0.7015761 0.6030216 0.8777289 1.6383696 0.6976869 0.6774009
## 46 1.6562132 1.5614500 1.1625515 1.2874327 0.7223849 1.4518175 1.3275749
## 47 1.1727532 1.2171015 0.6592283 0.8630962 1.2580994 1.2136276 0.8623590
## 48 1.2723286 1.3202825 1.0314882 1.3392016 1.1069417 1.1625446 1.2155892
## 49 1.2449394 1.0200333 1.0428730 1.0545487 0.9585604 0.8916064 0.9307776
## 50 1.3142907 1.1999833 0.8780752 1.0384551 0.6907185 1.1225720 1.0004974
## 51 0.8888425 0.8939558 0.6483818 0.6163149 1.3337837 0.6962722 0.6734968
## 52 0.8230899 0.6874089 0.8761284 0.7297780 1.4556342 0.6476874 0.5907808
## 53 1.4270652 1.4381617 1.0746120 1.2820008 0.9946643 1.1074687 1.2137158
## 54 2.0373547 2.3766662 2.3318443 2.3547877 2.9202842 2.1079331 2.1009833
## 55 0.8837494 0.5713729 0.9737541 0.8079616 1.7980915 0.6704200 0.7493437
## 56 1.2153872 0.9521113 0.8577657 0.9019418 1.0850991 0.9012946 0.9462510
## 57 0.0000000 0.7357119 0.7357282 1.0052557 1.7947172 0.7341417 0.6883306
## 58 0.7357119 0.0000000 0.7459316 0.6869651 1.6507186 0.6280637 0.6442243
## 59 0.7357282 0.7459316 0.0000000 0.6057384 1.3246773 0.7914531 0.4418699
## 60 1.0052557 0.6869651 0.6057384 0.0000000 1.2686193 0.7948541 0.5145250
## 61 1.7947172 1.6507186 1.3246773 1.2686193 0.0000000 1.5244468 1.3249940
## 62 0.7341417 0.6280637 0.7914531 0.7948541 1.5244468 0.0000000 0.6944429
## 63 0.6883306 0.6442243 0.4418699 0.5145250 1.3249940 0.6944429 0.0000000
## 64 1.2046381 1.1869688 0.8617291 1.0581578 0.8288383 0.9494498 0.9721749
## 65 0.9398165 0.9164982 0.5779991 0.7807022 1.1232635 0.7600770 0.7831947
## 66 0.3697675 0.8052105 0.8568676 1.0876300 1.8791205 0.7468039 0.7750400
## 67 1.1110837 1.1555038 0.7434588 0.9607070 1.1252124 0.7780726 0.9110620
## 68 0.9101390 0.8320511 0.6318821 0.8524318 1.3935419 0.5576334 0.7724429
## 69 0.8655622 0.8669302 0.8525444 0.9863716 1.4112101 0.6353944 0.8947318
## 70 1.1108114 0.6848723 0.7405863 0.5221676 1.1169324 0.8317884 0.5972596
## 71 1.0517699 1.1352039 0.7764483 1.0122999 1.3454969 0.8387300 0.9142095
## 72 1.2131080 1.0710840 1.0202260 1.1452624 1.3242209 0.8025765 1.0724645
## 73 1.8815972 1.6233946 1.5752295 1.7138638 1.9895804 1.5484257 1.7973556
## 74 1.2801769 1.3961594 0.9262953 1.2418188 1.3713552 1.0602901 1.1607937
## 75 1.2544166 1.2656465 0.7874179 0.9955662 1.0126080 1.0286219 1.0386029
## 76 1.1375065 0.9617780 0.7001336 0.7734481 1.1271145 0.9021291 0.8965746
## 77 1.0174222 0.9072486 0.7825011 1.0832474 1.6814214 1.0055904 1.0596013
## 78 1.0959535 1.0894650 0.7595683 0.5687029 1.2237639 1.0529131 0.6944213
## 64 65 66 67 68 69 70
## 1 0.7409035 0.9017483 1.3145117 0.9921028 0.9483839 1.0242876 0.6901543
## 2 0.8107663 0.8112299 0.6659407 0.8147650 0.6725935 0.5230975 0.7959906
## 3 0.7769858 0.6898703 0.9354026 0.8577558 0.7161892 0.8841403 0.5834261
## 4 1.2476073 1.0582041 0.5973634 1.2892572 0.9752077 0.9950724 0.9336172
## 5 0.8817715 0.8702063 1.1786967 0.8006454 0.9770379 0.8333343 0.9784569
## 6 1.3236710 1.1325595 1.1692023 1.2850140 0.9940297 1.2216538 0.7499987
## 7 0.8525661 0.9318696 1.5257385 1.0724276 1.0577036 0.8775489 0.9786879
## 8 0.7391089 0.6936166 1.0190098 0.6661456 0.6229591 0.8114955 1.2469904
## 9 0.9919940 0.9712126 1.6628581 1.1711806 1.1287046 1.3216138 1.1784859
## 10 0.6376747 0.7887427 1.3053636 0.8339682 0.8695165 0.9318423 0.5878673
## 11 0.6857747 0.6508249 0.8055408 0.7219453 0.4952323 0.4340323 0.8507362
## 12 0.6724440 0.7753857 1.3494643 0.4986412 0.8227800 0.9327261 1.1914286
## 13 1.2800156 1.0924386 0.8602250 1.1739506 0.7091417 1.0240933 1.0794235
## 14 0.7747212 0.7286680 1.2700472 0.9391427 0.7768816 0.9579656 0.7900215
## 15 0.8998617 0.8491496 1.1248422 1.1391554 1.1162280 0.8336186 0.8712187
## 16 0.3807309 0.5702806 1.1240601 0.5987437 0.5418376 0.7271444 0.8230182
## 17 0.7404613 0.7515324 1.3481498 0.8268887 0.7993416 0.9432486 0.6866047
## 18 0.7574655 0.7464811 1.2197717 0.8262058 0.8897202 0.7396181 0.4903274
## 19 0.7221080 0.7848350 1.3682131 0.7722681 0.9326221 0.9720118 0.7544515
## 20 1.2400476 1.1344020 0.9414377 1.2625712 0.9948598 0.8530328 1.4216881
## 21 0.6891125 0.9709398 1.6648847 1.0310810 1.1527532 1.1825671 0.9614713
## 22 1.2185454 1.1864776 1.3749269 1.3591516 1.1851662 0.9545418 0.9515713
## 23 0.9936805 1.0316409 1.1798102 1.0222196 0.8998383 0.9403095 0.4860514
## 24 0.7350150 1.0519292 1.6544739 0.7920865 1.1039977 1.2272840 1.0978361
## 25 1.0491925 1.0152246 0.9791180 0.8439639 0.8443749 0.9005509 1.2509580
## 26 0.6124263 0.8665518 1.3738315 0.7526088 0.9129425 0.7989612 0.8302957
## 27 0.8184528 0.8292653 1.1012448 0.8883192 0.7646352 0.7570575 0.3582066
## 28 0.7643736 0.9352844 0.9852411 0.7922380 0.6904730 0.5114000 0.7883794
## 29 0.6091913 0.7898038 1.5074963 0.7439731 0.7452302 0.9404834 1.0277290
## 30 0.6802191 0.7228720 1.0740163 0.7961533 0.6313113 0.6595370 0.6205377
## 31 0.5625975 0.7704466 1.4835286 0.6466622 0.8753468 1.0424591 1.0284342
## 32 0.6282571 1.0282398 1.7525325 0.8779197 1.1608501 1.2297512 1.3564712
## 33 0.8265289 0.7933915 1.0938542 0.9313141 0.7981792 0.8763829 0.7847656
## 34 1.4953140 1.4093381 0.8420742 1.4402486 1.2012677 1.2313915 1.4759881
## 35 0.7650163 0.8342050 0.9949548 0.7234445 0.6017475 0.6129054 1.2348559
## 36 0.6894969 0.8607613 1.4772579 0.6670667 0.8294950 0.8578211 1.1749557
## 37 1.3483523 1.2924875 1.0624467 1.3923556 0.9562698 1.2035119 1.1777457
## 38 0.6702447 0.6825262 1.2717299 0.7975851 0.9524621 0.9339374 0.7745715
## 39 0.9509274 0.9505425 1.3376240 1.1833237 1.1483096 0.9502273 0.9580042
## 40 0.8255592 0.7574483 0.5780977 0.8053459 0.5348476 0.6364032 0.9227844
## 41 1.0291433 0.8286507 0.8382595 1.1113262 0.7596262 0.7878052 0.8294992
## 42 1.1407848 1.0609109 1.0241333 1.1507580 0.8461206 0.7462580 0.9182837
## 43 0.8895330 0.6983244 0.7722513 0.8886512 0.5447945 0.4943703 0.8325623
## 44 0.5417887 0.8644877 1.4665333 0.6347322 0.9389542 0.9632539 1.2912049
## 45 1.0486553 0.8875911 0.7583726 0.8994354 0.4869250 0.7905776 0.8983635
## 46 0.6415427 0.9650788 1.7150907 0.9233131 1.1589767 1.1091943 1.1761514
## 47 0.9834577 0.7780688 1.2924937 0.8756969 0.8942332 1.0560284 1.0535967
## 48 0.5328630 0.7714370 1.3796681 0.8350563 1.0278701 0.9548120 1.1810741
## 49 0.6209871 0.8811305 1.2785414 0.9386826 0.9436572 0.8703666 0.7591113
## 50 0.3897858 0.6813083 1.4146512 0.7650797 0.9563028 0.9273780 0.8481120
## 51 0.8850401 0.6751104 0.9035701 0.6950439 0.5852640 0.6499854 0.8633348
## 52 1.0821109 0.8930666 0.8587264 1.0815267 0.8342014 0.9035834 0.8101117
## 53 0.4905018 0.8814148 1.4219842 0.6143126 0.9135743 0.9298564 1.1698594
## 54 2.6250804 2.5813603 1.9184348 2.4322658 2.4418741 2.4401906 2.4571793
## 55 1.3670947 1.0941654 0.8467556 1.2784217 0.9053949 1.0869503 0.9561260
## 56 0.6252799 0.7605846 1.1782521 0.8337224 0.7062245 0.7253785 0.7623844
## 57 1.2046381 0.9398165 0.3697675 1.1110837 0.9101390 0.8655622 1.1108114
## 58 1.1869688 0.9164982 0.8052105 1.1555038 0.8320511 0.8669302 0.6848723
## 59 0.8617291 0.5779991 0.8568676 0.7434588 0.6318821 0.8525444 0.7405863
## 60 1.0581578 0.7807022 1.0876300 0.9607070 0.8524318 0.9863716 0.5221676
## 61 0.8288383 1.1232635 1.8791205 1.1252124 1.3935419 1.4112101 1.1169324
## 62 0.9494498 0.7600770 0.7468039 0.7780726 0.5576334 0.6353944 0.8317884
## 63 0.9721749 0.7831947 0.7750400 0.9110620 0.7724429 0.8947318 0.5972596
## 64 0.0000000 0.5482098 1.2604059 0.5471417 0.7393998 0.7590184 0.9542049
## 65 0.5482098 0.0000000 1.0787618 0.5342134 0.5707732 0.7527383 0.8882246
## 66 1.2604059 1.0787618 0.0000000 1.1883741 0.9189173 0.8889916 1.1932996
## 67 0.5471417 0.5342134 1.1883741 0.0000000 0.5192109 0.7141547 0.9815615
## 68 0.7393998 0.5707732 0.9189173 0.5192109 0.0000000 0.5939756 0.8910662
## 69 0.7590184 0.7527383 0.8889916 0.7141547 0.5939756 0.0000000 0.9198717
## 70 0.9542049 0.8882246 1.1932996 0.9815615 0.8910662 0.9198717 0.0000000
## 71 0.7737887 0.7422648 1.1178166 0.4777939 0.6266889 0.6181666 1.0450273
## 72 0.7533445 0.9369920 1.1749404 0.8008783 0.8360801 0.7380467 0.9765301
## 73 1.4930429 1.4780125 1.8874968 1.3459372 1.1743777 1.2653087 1.6129321
## 74 0.7728234 0.8592729 1.2863580 0.4765669 0.7138950 0.8286042 1.2694711
## 75 0.5275794 0.5817560 1.3232018 0.4293786 0.7542957 0.8121102 1.0387189
## 76 0.6668433 0.6396014 1.1425240 0.7110851 0.6744776 0.6850759 0.7981598
## 77 1.0363267 0.8055439 1.0379229 0.9958891 0.6500669 0.7985800 1.1420639
## 78 1.1025139 0.8349892 1.2335299 0.9797444 1.0098104 1.1146659 0.8930073
## 71 72 73 74 75 76 77
## 1 1.0210382 1.0085564 1.700032 1.1837931 0.9947472 0.8634060 1.1983785
## 2 0.7338494 0.7024443 1.614072 0.9440964 0.9063244 0.7276400 0.9760989
## 3 0.9371457 1.0262578 1.677921 1.0819718 0.8931299 0.6841937 0.9455453
## 4 1.2990793 1.3308892 1.896909 1.4946264 1.3951960 1.0998327 1.0295392
## 5 0.8045993 1.0538496 1.745817 0.9136788 0.6813156 0.6817001 1.2292372
## 6 1.3394051 1.4033086 1.721995 1.4789966 1.3274626 0.9653305 1.0997418
## 7 1.0361390 1.1181927 1.312373 1.1586635 0.8722242 0.6588665 0.9820876
## 8 0.8809387 0.8330978 1.410082 0.7787233 0.8180990 0.9017550 0.8615968
## 9 1.2790164 1.5141347 1.542332 1.2728024 1.0150527 0.9151350 1.0460033
## 10 1.0133035 0.9407853 1.608918 1.0759233 0.7737345 0.5806384 1.1457225
## 11 0.7454019 0.7826359 1.396357 0.8759229 0.7910746 0.5477709 0.7600553
## 12 0.6967510 0.7548821 1.450311 0.4404759 0.3337110 0.6857179 1.1167300
## 13 1.2297492 1.1131765 1.427575 1.2929308 1.3361295 1.0440057 0.8213483
## 14 1.1171482 1.1022282 1.423026 1.1353074 0.8553906 0.5071164 0.8373948
## 15 1.1568665 0.9510589 1.819792 1.3781281 1.0785291 0.9062886 1.1508501
## 16 0.8006016 0.7474637 1.330310 0.7708787 0.6111203 0.5158430 0.8044831
## 17 0.9413533 1.1333495 1.448933 1.0324287 0.7742913 0.6008120 0.9960311
## 18 0.8511645 0.8584544 1.585215 1.0812003 0.7665233 0.5984396 1.1220548
## 19 0.8821661 1.0899890 1.667136 0.9786317 0.6632435 0.6442903 1.2111148
## 20 1.2179700 1.0989577 1.396837 1.2472450 1.2784412 1.0800880 0.7221669
## 21 1.1696730 1.1895091 1.676389 1.1960092 0.8774326 0.8442511 1.3221812
## 22 1.4215006 1.2784487 1.689799 1.6268599 1.3881898 1.0420312 1.3054823
## 23 1.0478311 0.8613066 1.670340 1.2586648 1.1269414 0.8955250 1.2727671
## 24 1.0159163 0.8123097 1.698513 0.9361245 0.8134513 1.0451368 1.5163792
## 25 0.7592286 1.2859211 1.776236 0.9355282 1.0780617 1.1612506 1.2578625
## 26 0.8408264 0.9262958 1.467660 0.8632728 0.6058614 0.5516194 1.1399004
## 27 0.9042334 0.8683542 1.470932 1.0815799 0.8809784 0.5619867 0.9696721
## 28 0.6782964 0.5714867 1.333850 0.8226585 0.8632560 0.7085612 0.9572032
## 29 0.8672503 0.9704123 1.109105 0.8128518 0.6863177 0.6781784 0.9150055
## 30 0.8181436 0.7849038 1.277856 0.9068318 0.7326923 0.3736951 0.7249076
## 31 0.8615109 1.0189230 1.543434 0.7732968 0.5207571 0.6816935 1.1928089
## 32 1.0962655 1.2667158 1.692438 1.0026649 0.8634553 1.1198513 1.4690888
## 33 0.8706383 1.0869811 1.470336 0.9903828 0.8486837 0.6502615 0.7624389
## 34 1.2461416 1.1642869 1.903766 1.3738537 1.5343872 1.4268350 1.2216951
## 35 0.8226974 0.9292642 1.386352 0.7876179 0.8621647 0.8123817 0.9373948
## 36 0.7188400 0.9683894 1.167370 0.5534817 0.4568676 0.5885066 0.9829237
## 37 1.3780758 1.2526572 1.652326 1.5069512 1.5622433 1.2878152 1.1079842
## 38 0.7907825 1.0300262 1.682667 0.9728515 0.6899087 0.7720337 1.0945250
## 39 1.1474101 1.2787623 1.674803 1.2933093 0.9793207 0.7186355 1.0366591
## 40 0.8874790 0.9424362 1.550105 0.9683646 0.9676508 0.7962864 0.8105560
## 41 1.0349101 1.1156110 1.523227 1.2613683 1.1395332 0.8041890 0.6853780
## 42 1.0874047 1.0307201 1.301790 1.1940570 1.1028264 0.6371185 0.7584042
## 43 0.7911018 0.8996438 1.274516 1.0027587 0.9380357 0.6569696 0.4758088
## 44 0.8291936 0.6944242 1.461753 0.5951832 0.5249752 0.8395945 1.2021664
## 45 0.8258408 0.9727949 1.330435 0.9650969 1.0620311 0.8661397 0.6762344
## 46 1.0032876 1.1027697 1.512081 0.9498721 0.6533582 0.8091421 1.2657978
## 47 0.8333067 1.3994674 1.578077 0.9717896 0.8294185 0.8706429 0.9604738
## 48 1.0248171 0.8185261 1.624722 0.9802923 0.7456252 0.9019928 1.1552376
## 49 1.0388831 0.7257059 1.681072 1.2062508 1.0247912 0.9467191 1.2689539
## 50 0.9314966 0.8353484 1.581532 0.9737130 0.6232279 0.7022713 1.1352101
## 51 0.6903832 1.0606140 1.490624 0.8752188 0.7738385 0.6366255 0.8801346
## 52 1.1238163 1.2453241 1.827736 1.3948477 1.2767169 1.0770125 1.1527571
## 53 0.8491213 0.6450302 1.513836 0.6457755 0.5414998 0.7803025 1.2490969
## 54 2.4069736 2.3738604 3.404439 2.5083291 2.6199803 2.6251528 2.8372649
## 55 1.2930039 1.3355089 1.821909 1.5423677 1.4807221 1.2155147 1.1520977
## 56 0.9872771 0.7469250 1.304911 0.9808970 0.7574464 0.3835036 0.8369540
## 57 1.0517699 1.2131080 1.881597 1.2801769 1.2544166 1.1375065 1.0174222
## 58 1.1352039 1.0710840 1.623395 1.3961594 1.2656465 0.9617780 0.9072486
## 59 0.7764483 1.0202260 1.575230 0.9262953 0.7874179 0.7001336 0.7825011
## 60 1.0122999 1.1452624 1.713864 1.2418188 0.9955662 0.7734481 1.0832474
## 61 1.3454969 1.3242209 1.989580 1.3713552 1.0126080 1.1271145 1.6814214
## 62 0.8387300 0.8025765 1.548426 1.0602901 1.0286219 0.9021291 1.0055904
## 63 0.9142095 1.0724645 1.797356 1.1607937 1.0386029 0.8965746 1.0596013
## 64 0.7737887 0.7533445 1.493043 0.7728234 0.5275794 0.6668433 1.0363267
## 65 0.7422648 0.9369920 1.478013 0.8592729 0.5817560 0.6396014 0.8055439
## 66 1.1178166 1.1749404 1.887497 1.2863580 1.3232018 1.1425240 1.0379229
## 67 0.4777939 0.8008783 1.345937 0.4765669 0.4293786 0.7110851 0.9958891
## 68 0.6266889 0.8360801 1.174378 0.7138950 0.7542957 0.6744776 0.6500669
## 69 0.6181666 0.7380467 1.265309 0.8286042 0.8121102 0.6850759 0.7985800
## 70 1.0450273 0.9765301 1.612932 1.2694711 1.0387189 0.7981598 1.1420639
## 71 0.0000000 0.8368136 1.311781 0.4695881 0.6232760 0.8183612 0.9597448
## 72 0.8368136 0.0000000 1.442071 0.8714425 0.8359474 0.7973795 1.1346766
## 73 1.3117812 1.4420711 0.000000 1.2582754 1.3807755 1.2896693 1.0811836
## 74 0.4695881 0.8714425 1.258275 0.0000000 0.5133420 0.8135097 1.0090188
## 75 0.6232760 0.8359474 1.380776 0.5133420 0.0000000 0.5232380 0.9832258
## 76 0.8183612 0.7973795 1.289669 0.8135097 0.5232380 0.0000000 0.7472222
## 77 0.9597448 1.1346766 1.081184 1.0090188 0.9832258 0.7472222 0.0000000
## 78 1.0324582 1.4468542 1.896328 1.2613719 1.0251054 0.9868267 1.2607442
## 78
## 1 1.0027776
## 2 0.9987697
## 3 0.7166924
## 4 1.0669700
## 5 0.7553675
## 6 0.9264858
## 7 1.1703863
## 8 1.3885946
## 9 1.1073920
## 10 0.8851859
## 11 0.9656366
## 12 1.2356100
## 13 1.4084555
## 14 0.9639616
## 15 1.2070799
## 16 1.0765319
## 17 0.7477928
## 18 0.8039210
## 19 0.6617273
## 20 1.6838774
## 21 1.1231389
## 22 1.2605999
## 23 1.0546393
## 24 1.4219072
## 25 0.9304676
## 26 0.9852122
## 27 0.8777437
## 28 1.2125939
## 29 1.2190312
## 30 0.9994423
## 31 0.9848274
## 32 1.3353015
## 33 0.9187366
## 34 1.7396899
## 35 1.2214979
## 36 1.1889142
## 37 1.5357067
## 38 0.8426963
## 39 0.9751020
## 40 1.0432071
## 41 0.9997185
## 42 1.2075583
## 43 1.0530802
## 44 1.4619172
## 45 1.1310575
## 46 1.2782504
## 47 0.6306679
## 48 1.4399514
## 49 1.2613675
## 50 1.1384902
## 51 0.6120204
## 52 0.8210913
## 53 1.3792937
## 54 2.4106713
## 55 1.0830111
## 56 1.1583298
## 57 1.0959535
## 58 1.0894650
## 59 0.7595683
## 60 0.5687029
## 61 1.2237639
## 62 1.0529131
## 63 0.6944213
## 64 1.1025139
## 65 0.8349892
## 66 1.2335299
## 67 0.9797444
## 68 1.0098104
## 69 1.1146659
## 70 0.8930073
## 71 1.0324582
## 72 1.4468542
## 73 1.8963275
## 74 1.2613719
## 75 1.0251054
## 76 0.9868267
## 77 1.2607442
## 78 0.0000000
# Save the distance matrix
write.csv(as.matrix(distance_matrix), "distance_matrix.csv")
# --- Heatmap for Distance Matrix ---
distance_data <- melt(as.matrix(distance_matrix))
ggplot(distance_data, aes(x = Var1, y = Var2, fill = value)) +
geom_tile() +
scale_fill_gradient(low = "white", high = "red") +
theme_minimal() +
labs(title = "Heatmap of Distance Matrix", x = "Observations", y = "Observations", fill = "Distance")
#Task 3
# --- Task 3: Q-Q Plots ---
# Generate univariate Q-Q plots for each variable
par(mfrow = c(2, 5)) # Adjust layout for 10 variables
for (i in 2:ncol(My_DataSet)) {
qqnorm(My_DataSet[, i], main = paste("Q-Q Plot for Var", i - 1))
qqline(My_DataSet[, i])
}
# Generalized distance Q-Q plot
library(MASS)
mahalanobis_dist <- mahalanobis(My_DataSet[, -1], colMeans(My_DataSet[, -1]), cov(My_DataSet[, -1]))
qqplot(qchisq(ppoints(nrow(My_DataSet)), df = ncol(My_DataSet) - 1), mahalanobis_dist,
main = "Generalized Distance Q-Q Plot")
abline(0, 1, col="red")
#4
# --- Task 4: PCA ---
# Perform PCA on the subset
pca_result <- prcomp(My_DataSet[, -1], scale. = TRUE)
summary(pca_result)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.4819 1.4299 1.2067 0.99027 0.91930 0.84481 0.73992
## Proportion of Variance 0.2196 0.2045 0.1456 0.09806 0.08451 0.07137 0.05475
## Cumulative Proportion 0.2196 0.4241 0.5697 0.66772 0.75223 0.82360 0.87835
## PC8 PC9 PC10
## Standard deviation 0.71778 0.68130 0.48695
## Proportion of Variance 0.05152 0.04642 0.02371
## Cumulative Proportion 0.92987 0.97629 1.00000
# Biplot of the PCA
biplot(pca_result, main = "PCA Biplot", cex = 0.3)
#Task 5
# --- Task 5: MANOVA ---
# Perform MANOVA
manova_result <- manova(as.matrix(My_DataSet[, -1]) ~ My_DataSet$Class)
summary(manova_result)
## Df Pillai approx F num Df den Df Pr(>F)
## My_DataSet$Class 1 0.36249 3.8096 10 67 0.0004209 ***
## Residuals 76
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Save the results
capture.output(summary(manova_result), file = "manova_results.txt")
# --- Boxplot for Variables by Class ---
par(mfrow = c(2, 5)) # Adjust layout for 10 variables
for (i in 2:ncol(My_DataSet)) {
boxplot(My_DataSet[, i] ~ My_DataSet$Class,
main = paste("Boxplot for Var", i - 1),
xlab = "Class", ylab = "Expression Level")
}
#Task 6
# --- Task 6: PCA Visualization ---
library(ggplot2)
# Create a dataframe for PCA results
pca_df <- as.data.frame(pca_result$x)
pca_df$Class <- as.factor(My_DataSet$Class)
# Scatter plot using the first two principal components
ggplot(pca_df, aes(x = PC1, y = PC2, color = Class)) +
geom_point(size = 2) +
labs(title = "PCA: Invasive vs Noninvasive", x = "Invasive", y = "Noninvasive")
#Task 7
# --- Task 7: LDA ---
library(MASS)
# Fit LDA model
lda_result <- lda(Class ~ ., data = My_DataSet)
# Predict using LDA
lda_pred <- predict(lda_result)
# Confusion matrix
conf_matrix <- table(Predicted = lda_pred$class, Actual = My_DataSet$Class)
print("Confusion Matrix:")
## [1] "Confusion Matrix:"
print(conf_matrix)
## Actual
## Predicted 1 2
## 1 23 8
## 2 11 36
# Calculate metrics
sensitivity <- conf_matrix[2, 2] / sum(conf_matrix[, 2])
specificity <- conf_matrix[1, 1] / sum(conf_matrix[, 1])
misclassification_error <- 1 - sum(diag(conf_matrix)) / sum(conf_matrix)
cat("Sensitivity:", sensitivity, "\n")
## Sensitivity: 0.8181818
cat("Specificity:", specificity, "\n")
## Specificity: 0.6764706
cat("Misclassification Error:", misclassification_error, "\n")
## Misclassification Error: 0.2435897
# --- LDA Scatter Plot (LD1 Only) ---
lda_df <- data.frame(LD1 = lda_pred$x[, 1], Class = My_DataSet$Class)
ggplot(lda_df, aes(x = LD1, fill = as.factor(Class))) +
geom_density(alpha = 0.5) +
labs(title = "LDA: Density Plot of LD1",
x = "Linear Discriminant 1", fill = "Class") +
theme_minimal()
