Rank Predicting Model
Anubhav Agarwal
3 January 2018
Read
toptrend.df=read.csv(paste("USvideos.csv",sep=""))
attach(toptrend.df)View(toptrend.df)
str(toptrend.df)## 'data.frame': 7800 obs. of 16 variables:
## $ video_id : Factor w/ 1909 levels "-1yT-K3c6YI",..: 141 121 226 1335 569 767 166 1176 954 1577 ...
## $ trending_date : Factor w/ 39 levels "17.01.12","17.02.12",..: 14 14 14 14 14 14 14 14 14 14 ...
## $ title : Factor w/ 1927 levels "'I have taken poison' claims war criminal",..: 1809 1677 1342 1231 788 42 1391 78 1615 1882 ...
## $ channel_title : Factor w/ 992 levels "12 News","1theK (ì›ë”ì¼€ì´)",..: 143 491 738 339 643 399 748 207 3 956 ...
## $ category_id : int 22 24 23 24 24 28 24 28 1 25 ...
## $ publish_time : Factor w/ 1875 levels "2008-06-17T00:07:56.000Z",..: 260 229 213 233 211 265 198 216 239 237 ...
## $ tags : Factor w/ 1823 levels "[none]","08282016NtflxUSCAN|Black Mirror|Netflix|Netflix Original Series|San Junipero|Charlie Brooker|Arkangel|USS Calli"| __truncated__,..: 1388 905 1271 1320 1341 708 1430 20 1673 1743 ...
## $ views : int 748374 2418783 3191434 343168 2095731 119180 2103417 817732 826059 256426 ...
## $ likes : int 57527 97185 146033 10172 132235 9763 15993 23663 3543 12654 ...
## $ dislikes : int 2966 6146 5339 666 1989 511 2445 778 119 1363 ...
## $ comment_count : int 15954 12703 8181 2146 17518 1434 1970 3432 340 2368 ...
## $ thumbnail_link : Factor w/ 1909 levels "https://i.ytimg.com/vi/-1yT-K3c6YI/default.jpg",..: 141 121 226 1335 569 767 166 1176 954 1577 ...
## $ comments_disabled : Factor w/ 2 levels "False","True": 1 1 1 1 1 1 1 1 1 1 ...
## $ ratings_disabled : Factor w/ 2 levels "False","True": 1 1 1 1 1 1 1 1 1 1 ...
## $ video_error_or_removed: Factor w/ 2 levels "False","True": 1 1 1 1 1 1 1 1 1 1 ...
## $ description : Factor w/ 1970 levels "","'A curious cat helps his owner with home improvements.'\\nWe're releasing a NEW BLACK & WHITE episode every wee"| __truncated__,..: 1380 1209 1827 1754 717 1794 432 747 817 499 ...summary(toptrend.df[,c(2,5,8,9,10,11,13,14,15)])## trending_date category_id views likes
## 17.01.12: 200 Min. : 1.00 Min. : 687 Min. : 0
## 17.02.12: 200 1st Qu.:17.00 1st Qu.: 84184 1st Qu.: 2018
## 17.03.12: 200 Median :24.00 Median : 299548 Median : 8901
## 17.04.12: 200 Mean :20.06 Mean : 1322532 Mean : 48448
## 17.05.12: 200 3rd Qu.:25.00 3rd Qu.: 951049 3rd Qu.: 28695
## 17.06.12: 200 Max. :29.00 Max. :149376127 Max. :3093544
## (Other) :6600
## dislikes comment_count comments_disabled ratings_disabled
## Min. : 0.0 Min. : 0 False:7638 False:7762
## 1st Qu.: 78.0 1st Qu.: 270 True : 162 True : 38
## Median : 305.5 Median : 1010
## Mean : 3168.3 Mean : 6114
## 3rd Qu.: 1038.0 3rd Qu.: 3281
## Max. :1643059.0 Max. :827755
##
## video_error_or_removed
## False:7799
## True : 1
##
##
##
##
## Assigning rank to the top trending videos of a day
toptrend.df$rank=c(1:200)
View(toptrend.df)library(psych)## Warning: package 'psych' was built under R version 3.4.3describe(toptrend.df[,c(8,9,10,11)])## vars n mean sd median trimmed mad
## views 1 7800 1322531.64 5583792.65 299548.5 518626.71 387107.60
## likes 2 7800 48447.69 182830.40 8901.0 16775.61 12386.38
## dislikes 3 7800 3168.35 43058.34 305.5 577.79 408.46
## comment_count 4 7800 6113.48 33087.42 1010.0 1834.47 1341.75
## min max range skew kurtosis se
## views 687 149376127 149375440 14.13 259.15 63224.00
## likes 0 3093544 3093544 10.05 123.61 2070.15
## dislikes 0 1643059 1643059 32.23 1102.97 487.54
## comment_count 0 827755 827755 16.50 333.03 374.64Count number of words in description
library(stringr)
toptrend.df$numworddes<-str_count(toptrend.df$description,'\\w+')
View(toptrend.df)Convert the factor trending_date to date
library(lubridate)## Warning: package 'lubridate' was built under R version 3.4.3##
## Attaching package: 'lubridate'## The following object is masked from 'package:base':
##
## datestr(toptrend.df$trending_date)## Factor w/ 39 levels "17.01.12","17.02.12",..: 14 14 14 14 14 14 14 14 14 14 ...toptrend.df$trending_date=as.Date(trending_date, format = "%Y.%d.%m")
View(toptrend.df)
str(toptrend.df$trending_date)## Date[1:7800], format: "0017-11-14" "0017-11-14" "0017-11-14" "0017-11-14" "0017-11-14" ...Publish date
library(lubridate)
toptrend.df$publish_time=as.Date(publish_time, format = "%Y-%m-%d")
View(toptrend.df)
str(toptrend.df$publish_time)## Date[1:7800], format: "2017-11-13" "2017-11-13" "2017-11-12" "2017-11-13" "2017-11-12" ...Date Difference
str(toptrend.df$trending_date)## Date[1:7800], format: "0017-11-14" "0017-11-14" "0017-11-14" "0017-11-14" "0017-11-14" ...str(toptrend.df$publish_time)## Date[1:7800], format: "2017-11-13" "2017-11-13" "2017-11-12" "2017-11-13" "2017-11-12" ...toptrend.df$datediff=toptrend.df$trending_date-toptrend.df$publish_time+730486
toptrend.df$datediff=as.numeric(toptrend.df$datediff,units="days")
str(toptrend.df$datediff)## num [1:7800] 2 2 3 2 3 2 3 3 2 2 ...View(toptrend.df)Corrgram
library(corrgram)## Warning: package 'corrgram' was built under R version 3.4.3corrgram(toptrend.df)
Correlations
cor.test(toptrend.df$numworddes,toptrend.df$numtags)##
## Pearson's product-moment correlation
##
## data: toptrend.df$numworddes and toptrend.df$numtags
## t = 29.86, df = 7798, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3002615 0.3400950
## sample estimates:
## cor
## 0.3203198The number of tags and the length of description of a video are positively correlated.
cor.test(toptrend.df$views,toptrend.df$comment_count)##
## Pearson's product-moment correlation
##
## data: toptrend.df$views and toptrend.df$comment_count
## t = 114.73, df = 7798, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.7840472 0.8005647
## sample estimates:
## cor
## 0.7924512cor.test(toptrend.df$views,toptrend.df$likes)##
## Pearson's product-moment correlation
##
## data: toptrend.df$views and toptrend.df$likes
## t = 167.78, df = 7798, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8800092 0.8896409
## sample estimates:
## cor
## 0.8849196cor.test(toptrend.df$views,toptrend.df$dislikes)##
## Pearson's product-moment correlation
##
## data: toptrend.df$views and toptrend.df$dislikes
## t = 80.357, df = 7798, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.6607087 0.6849943
## sample estimates:
## cor
## 0.6730329cor.test(toptrend.df$views,toptrend.df$datediff)##
## Pearson's product-moment correlation
##
## data: toptrend.df$views and toptrend.df$datediff
## t = -1.7455, df = 7798, p-value = 0.08094
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.041936613 0.002431754
## sample estimates:
## cor
## -0.01976216There is a very strong correlation between the number of views of a video and the number of comments and likes on it. The number of dislikes also has a healthy positive correlation with the number of views. However, the number of days from publishing and the number of views do not have a statistically significant correlation.
cor.test(toptrend.df$likes,toptrend.df$datediff)##
## Pearson's product-moment correlation
##
## data: toptrend.df$likes and toptrend.df$datediff
## t = -2.0817, df = 7798, p-value = 0.0374
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.045736065 -0.001375012
## sample estimates:
## cor
## -0.02356714cor.test(toptrend.df$likes,toptrend.df$dislikes)##
## Pearson's product-moment correlation
##
## data: toptrend.df$likes and toptrend.df$dislikes
## t = 54.485, df = 7798, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.508829 0.540981
## sample estimates:
## cor
## 0.5250923Unexpectedly, there is a minor negative correlation between the number of likes and the number of days from publishing. This means that when we talk about top trending videos, we cannot expect that older videos would have more likes.
Another observation to be made is that videos with higher number of likes are likely to have higher number of dislikes as well.
Let us give a score to each video based on its rank. The highest ranked video gets the maximum marks while the lowest ranked video gets the minimum marks
toptrend.df$score=seq(200000,1000,-1000)
View(toptrend.df) Score Predictor
str(title)## Factor w/ 1927 levels "'I have taken poison' claims war criminal",..: 1809 1677 1342 1231 788 42 1391 78 1615 1882 ...scorepre=lm(score~datediff+views+numtags+dislikes+comment_count+title+category_id,data=toptrend.df)
summary(scorepre)[c(1,2,6,7,8,9,10)]## $call
## lm(formula = score ~ datediff + views + numtags + dislikes +
## comment_count + title + category_id, data = toptrend.df)
##
## $terms
## score ~ datediff + views + numtags + dislikes + comment_count +
## title + category_id
## attr(,"variables")
## list(score, datediff, views, numtags, dislikes, comment_count,
## title, category_id)
## attr(,"factors")
## datediff views numtags dislikes comment_count title
## score 0 0 0 0 0 0
## datediff 1 0 0 0 0 0
## views 0 1 0 0 0 0
## numtags 0 0 1 0 0 0
## dislikes 0 0 0 1 0 0
## comment_count 0 0 0 0 1 0
## title 0 0 0 0 0 1
## category_id 0 0 0 0 0 0
## category_id
## score 0
## datediff 0
## views 0
## numtags 0
## dislikes 0
## comment_count 0
## title 0
## category_id 1
## attr(,"term.labels")
## [1] "datediff" "views" "numtags" "dislikes"
## [5] "comment_count" "title" "category_id"
## attr(,"order")
## [1] 1 1 1 1 1 1 1
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 1
## attr(,".Environment")
## <environment: R_GlobalEnv>
## attr(,"predvars")
## list(score, datediff, views, numtags, dislikes, comment_count,
## title, category_id)
## attr(,"dataClasses")
## score datediff views numtags dislikes
## "numeric" "numeric" "numeric" "numeric" "numeric"
## comment_count title category_id
## "numeric" "factor" "numeric"
##
## $sigma
## [1] 14903.61
##
## $df
## [1] 1933 5867 1933
##
## $r.squared
## [1] 0.949877
##
## $adj.r.squared
## [1] 0.9333716
##
## $fstatistic
## value numdf dendf
## 57.54926 1932.00000 5867.00000fitted(scorepre)[1:400]## 1 2 3 4 5 6
## 193556.361 191593.277 174968.982 177467.655 168537.286 192332.734
## 7 8 9 10 11 12
## 159406.492 164560.391 197056.759 188200.281 190000.000 165078.050
## 13 14 15 16 17 18
## 179482.218 153237.731 155416.453 209667.434 147611.146 182755.291
## 19 20 21 22 23 24
## 158435.305 164901.527 174673.806 141997.862 157266.719 156128.361
## 25 26 27 28 29 30
## 171264.223 138384.126 146376.139 145933.635 154680.468 131965.620
## 31 32 33 34 35 36
## 161414.405 133617.734 129469.353 138000.390 140730.416 130210.238
## 37 38 39 40 41 42
## 164000.000 157180.559 132621.966 171578.709 166280.431 159000.000
## 43 44 45 46 47 48
## 141621.164 124210.990 156000.000 124814.064 154000.000 134398.477
## 49 50 51 52 53 54
## 143621.028 116885.965 124680.297 116222.683 130400.036 115346.356
## 55 56 57 58 59 60
## 112219.837 145000.000 114469.590 139134.444 130798.005 112432.566
## 61 62 63 64 65 66
## 112817.891 154340.571 110787.967 108769.935 122634.586 105949.383
## 67 68 69 70 71 72
## 109734.717 104027.415 137146.021 102457.427 98683.397 95480.162
## 73 74 75 76 77 78
## 95813.994 88158.009 98709.059 96972.844 124000.000 98448.769
## 79 80 81 82 83 84
## 122000.000 93142.448 97811.704 95780.773 93406.914 99721.874
## 85 86 87 88 89 90
## 88812.649 92798.011 83410.020 97812.872 87436.810 88333.976
## 91 92 93 94 95 96
## 87816.072 85132.141 87149.296 79750.655 87874.852 84795.885
## 97 98 99 100 101 102
## 82707.992 82474.383 75378.867 81817.129 80886.328 75072.286
## 103 104 105 106 107 108
## 98000.000 76406.982 96000.000 78897.798 94000.000 78403.233
## 109 110 111 112 113 114
## 75390.363 78402.364 70808.188 74897.705 73792.190 71887.933
## 115 116 117 118 119 120
## 71872.614 67405.443 63401.658 83000.000 59406.639 66900.589
## 121 122 123 124 125 126
## 62905.413 63390.272 78000.000 65408.122 63859.086 61904.743
## 127 128 129 130 131 132
## 62402.390 73000.000 56901.247 57406.421 54349.984 52433.154
## 133 134 135 136 137 138
## 54407.086 50900.527 52901.614 54907.681 64000.000 54901.382
## 139 140 141 142 143 144
## 45907.771 61000.000 60000.000 45377.825 45403.979 57000.000
## 145 146 147 148 149 150
## 56000.000 55000.000 54000.000 53000.000 52000.000 51000.000
## 151 152 153 154 155 156
## 50000.000 43388.347 48000.000 37905.295 46000.000 45000.000
## 157 158 159 160 161 162
## 37400.912 43000.000 42000.000 41000.000 40000.000 39000.000
## 163 164 165 166 167 168
## 38000.000 37000.000 36000.000 35000.000 34000.000 33000.000
## 169 170 171 172 173 174
## 32000.000 31000.000 30000.000 29000.000 28000.000 27000.000
## 175 176 177 178 179 180
## 26000.000 25000.000 24000.000 23000.000 22000.000 21000.000
## 181 182 183 184 185 186
## 20000.000 19000.000 18000.000 17000.000 16000.000 15000.000
## 187 188 189 190 191 192
## 14000.000 13000.000 12000.000 11000.000 10000.000 9000.000
## 193 194 195 196 197 198
## 8000.000 7000.000 6000.000 5000.000 4000.000 3000.000
## 199 200 201 202 203 204
## 2000.000 1000.000 208334.702 212389.080 205696.075 202777.335
## 205 206 207 208 209 210
## 200748.459 207482.482 199730.080 195121.548 192000.000 184980.853
## 211 212 213 214 215 216
## 187623.009 186634.997 177672.155 177145.980 179256.840 206885.631
## 217 218 219 220 221 222
## 192902.310 167644.007 172761.600 169416.359 180372.695 165404.464
## 223 224 225 226 227 228
## 183034.784 164912.620 177389.578 169943.241 167313.132 161827.217
## 229 230 231 232 233 234
## 180352.102 160702.191 170000.000 151153.025 155062.786 140954.789
## 235 236 237 238 239 240
## 155336.417 151012.399 149120.458 147425.964 147655.689 161000.000
## 241 242 243 244 245 246
## 143031.064 176525.210 160799.719 143492.793 152808.525 143866.554
## 247 248 249 250 251 252
## 142207.118 141117.527 129417.026 126561.778 134907.133 137396.067
## 253 254 255 256 257 258
## 139232.437 147000.000 148405.817 136899.060 148981.614 131247.064
## 259 260 261 262 263 264
## 141401.911 126895.129 124435.342 137389.639 129558.717 130918.194
## 265 266 267 268 269 270
## 131830.724 133762.624 128376.209 113818.667 115961.062 129386.399
## 271 272 273 274 275 276
## 127670.328 125577.695 119964.616 121961.007 101973.632 115817.339
## 277 278 279 280 281 282
## 119835.974 118618.623 118216.473 137098.473 114219.308 128365.893
## 283 284 285 286 287 288
## 114462.133 118243.024 118630.264 124210.538 105211.009 111340.132
## 289 290 291 292 293 294
## 110222.242 113010.991 105817.179 123824.599 110626.204 100720.322
## 295 296 297 298 299 300
## 109333.785 96149.553 98479.097 103000.000 102149.000 94914.010
## 301 302 303 304 305 306
## 96147.892 104953.488 103001.706 102412.237 104156.173 96436.461
## 307 308 309 310 311 312
## 97190.417 86149.689 87144.070 82147.308 88603.802 97016.874
## 313 314 315 316 317 318
## 106601.523 79816.123 89169.826 102599.964 88408.428 84831.130
## 319 320 321 322 323 324
## 77406.986 84409.446 86655.387 84596.901 83010.822 81311.353
## 325 326 327 328 329 330
## 84998.679 82012.171 78160.140 76131.261 71907.615 74233.621
## 331 332 333 334 335 336
## 70000.966 70905.804 70831.702 65335.381 69163.657 70002.267
## 337 338 339 340 341 342
## 73597.557 62386.601 59676.129 68004.632 45408.315 65002.919
## 343 344 345 346 347 348
## 68000.823 56815.704 61641.922 67666.258 59999.734 57003.484
## 349 350 351 352 353 354
## 47402.191 55002.025 57390.124 53996.284 59333.356 54666.474
## 355 356 357 358 359 360
## 55684.577 60340.203 61001.233 52020.789 60125.148 65593.086
## 361 362 363 364 365 366
## 47692.832 47347.618 50597.636 42999.837 50596.767 51102.202
## 367 368 369 370 371 372
## 53113.672 47102.295 46207.810 47609.637 44127.386 44112.067
## 373 374 375 376 377 378
## 48593.018 27000.000 37591.878 39099.411 36140.914 34597.610
## 379 380 381 382 383 384
## 39594.557 34095.257 35609.728 27098.618 35094.587 27092.319
## 385 386 387 388 389 390
## 29593.579 35598.342 29098.753 26592.914 25098.386 26650.016
## 391 392 393 394 395 396
## 15611.653 31593.361 24566.846 23099.473 6000.000 17596.021
## 397 398 399 400
## 17622.175 9599.088 18092.229 10094.705Rank Predictor
rankpre=lm(rank~datediff+views+dislikes+comment_count+numtags+category_id+title+channel_title,data=toptrend.df)
summary(rankpre)[c(1,2,6,7,8,9,10)]## $call
## lm(formula = rank ~ datediff + views + dislikes + comment_count +
## numtags + category_id + title + channel_title, data = toptrend.df)
##
## $terms
## rank ~ datediff + views + dislikes + comment_count + numtags +
## category_id + title + channel_title
## attr(,"variables")
## list(rank, datediff, views, dislikes, comment_count, numtags,
## category_id, title, channel_title)
## attr(,"factors")
## datediff views dislikes comment_count numtags category_id
## rank 0 0 0 0 0 0
## datediff 1 0 0 0 0 0
## views 0 1 0 0 0 0
## dislikes 0 0 1 0 0 0
## comment_count 0 0 0 1 0 0
## numtags 0 0 0 0 1 0
## category_id 0 0 0 0 0 1
## title 0 0 0 0 0 0
## channel_title 0 0 0 0 0 0
## title channel_title
## rank 0 0
## datediff 0 0
## views 0 0
## dislikes 0 0
## comment_count 0 0
## numtags 0 0
## category_id 0 0
## title 1 0
## channel_title 0 1
## attr(,"term.labels")
## [1] "datediff" "views" "dislikes" "comment_count"
## [5] "numtags" "category_id" "title" "channel_title"
## attr(,"order")
## [1] 1 1 1 1 1 1 1 1
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 1
## attr(,".Environment")
## <environment: R_GlobalEnv>
## attr(,"predvars")
## list(rank, datediff, views, dislikes, comment_count, numtags,
## category_id, title, channel_title)
## attr(,"dataClasses")
## rank datediff views dislikes comment_count
## "numeric" "numeric" "numeric" "numeric" "numeric"
## numtags category_id title channel_title
## "numeric" "numeric" "factor" "factor"
##
## $sigma
## [1] 14.89518
##
## $df
## [1] 1937 5863 2924
##
## $r.squared
## [1] 0.9499679
##
## $adj.r.squared
## [1] 0.933447
##
## $fstatistic
## value numdf dendf
## 57.5009 1936.0000 5863.0000fitted(rankpre)[1:400]## 1 2 3 4 5 6
## 7.4444654 9.4080341 26.0334404 23.3572085 32.4640445 8.6693290
## 7 8 9 10 11 12
## 41.5949398 36.4418443 3.9438861 12.7998390 11.0000000 35.9236517
## 13 14 15 16 17 18
## 21.0874520 47.7639379 45.5850841 -8.6686335 53.3903669 18.2465816
## 19 20 21 22 23 24
## 42.5662677 36.0988666 26.3274608 59.0036583 43.7350951 44.8723991
## 25 26 27 28 29 30
## 29.7380345 62.6173395 54.6253255 55.0677664 46.3214001 69.0354925
## 31 32 33 34 35 36
## 39.5876233 67.3837977 71.5349888 63.0010986 60.2711011 70.7908756
## 37 38 39 40 41 42
## 37.0000000 43.8213298 68.3791326 29.4234652 34.7202278 42.0000000
## 43 44 45 46 47 48
## 59.3803278 76.7900326 45.0000000 76.1870108 47.0000000 66.6019088
## 49 50 51 52 53 54
## 57.3804805 84.1151945 76.3203063 84.7784416 70.6003816 85.6564899
## 55 56 57 58 59 60
## 88.7812936 56.0000000 86.5315450 61.8662937 70.2027585 88.5684676
## 61 62 63 64 65 66
## 88.1828684 46.6612582 90.2127445 92.2316677 78.3664689 95.0517504
## 67 68 69 70 71 72
## 91.2660318 96.9741437 63.8547308 98.5445961 102.3177802 105.5205857
## 73 74 75 76 77 78
## 105.1867555 112.8427591 102.2920964 104.0282941 77.0000000 102.5526914
## 79 80 81 82 83 84
## 79.0000000 107.8583034 103.1890606 105.2199463 107.5934620 101.2792485
## 85 86 87 88 89 90
## 112.1881049 108.2027391 117.5907988 103.1878781 113.5639576 112.5630979
## 91 92 93 94 95 96
## 113.1846795 115.8690970 113.8514541 121.2500661 113.1255074 116.2048579
## 97 98 99 100 101 102
## 118.2928242 118.5263813 125.6218541 119.1836498 120.1140474 125.9285203
## 103 104 105 106 107 108
## 103.0000000 124.5933949 105.0000000 122.1026427 107.0000000 122.5971444
## 109 110 111 112 113 114
## 125.6100129 122.5980104 130.1925990 126.1026700 127.2081656 129.1124375
## 115 116 117 118 119 120
## 129.1277780 133.5949332 137.5987203 118.0000000 141.5937411 134.0997850
## 121 122 123 124 125 126
## 138.0949640 137.6100997 123.0000000 135.5922563 137.1413258 139.0956324
## 127 128 129 130 131 132
## 138.5979845 128.0000000 144.0991360 143.5939550 146.6503736 148.5672766
## 133 134 135 136 137 138
## 146.5932889 150.0998380 148.0987683 146.0926935 137.0000000 146.0989926
## 139 140 141 142 143 144
## 155.0926052 140.0000000 141.0000000 155.6225564 155.5963990 144.0000000
## 145 146 147 148 149 150
## 145.0000000 146.0000000 147.0000000 148.0000000 149.0000000 150.0000000
## 151 152 153 154 155 156
## 151.0000000 157.6120517 153.0000000 163.0950787 155.0000000 156.0000000
## 157 158 159 160 161 162
## 163.5994619 158.0000000 159.0000000 160.0000000 161.0000000 162.0000000
## 163 164 165 166 167 168
## 163.0000000 164.0000000 165.0000000 166.0000000 167.0000000 168.0000000
## 169 170 171 172 173 174
## 169.0000000 170.0000000 171.0000000 172.0000000 173.0000000 174.0000000
## 175 176 177 178 179 180
## 175.0000000 176.0000000 177.0000000 178.0000000 179.0000000 180.0000000
## 181 182 183 184 185 186
## 181.0000000 182.0000000 183.0000000 184.0000000 185.0000000 186.0000000
## 187 188 189 190 191 192
## 187.0000000 188.0000000 189.0000000 190.0000000 191.0000000 192.0000000
## 193 194 195 196 197 198
## 193.0000000 194.0000000 195.0000000 196.0000000 197.0000000 198.0000000
## 199 200 201 202 203 204
## 199.0000000 200.0000000 -7.3320293 -11.3876315 -4.6935173 -1.7747304
## 205 206 207 208 209 210
## 0.2534911 -6.9162355 1.2702509 5.6699691 9.0000000 16.0198668
## 211 212 213 214 215 216
## 13.3792556 14.3673344 23.3296648 23.8555550 21.7449241 -5.8837434
## 217 218 219 220 221 222
## 8.1001663 33.3586968 28.2405881 31.5860455 20.6276466 35.5972766
## 223 224 225 226 227 228
## 17.9668457 36.0889213 23.6107864 31.0561139 33.6886648 39.1746015
## 229 230 231 232 233 234
## 20.6497594 40.2992259 31.0000000 49.8781780 45.9383559 60.0466057
## 235 236 237 238 239 240
## 45.6984156 49.9890943 51.8810426 53.5754565 53.3458677 40.0000000
## 241 242 243 244 245 246
## 57.9704458 24.4766603 40.2001610 57.5087115 48.1922275 57.1349450
## 247 248 249 250 251 252
## 58.7943523 59.8834397 71.5844537 74.4393528 66.0932433 63.6050608
## 253 254 255 256 257 258
## 61.7689132 54.0000000 52.5945594 64.1024541 52.0202382 69.7541714
## 259 260 261 262 263 264
## 59.5984654 74.1059968 76.5657150 63.6107339 71.4423985 70.0830001
## 265 266 267 268 269 270
## 69.1700783 67.2388162 72.6241485 87.1820848 85.0400474 71.6147295
## 271 272 273 274 275 276
## 73.3305301 75.4234004 81.0365134 79.0401200 99.0274937 85.1834126
## 277 278 279 280 281 282
## 81.1648110 82.3821307 82.7846527 63.9011334 86.7814422 72.6341537
## 283 284 285 286 287 288
## 86.5389855 82.7577746 82.3712356 76.7909289 95.7901133 89.6598752
## 289 290 291 292 293 294
## 90.7785289 87.9897951 95.1835667 77.1758555 90.3745814 100.2807993
## 295 296 297 298 299 300
## 91.6662148 104.8511967 102.5216516 98.0000000 98.8521765 106.0863500
## 301 302 303 304 305 306
## 104.8528555 96.0469712 97.9982968 98.5881414 96.8441967 104.5638986
## 307 308 309 310 311 312
## 103.8099766 114.8510617 113.8566843 118.8534411 112.3969190 103.9831485
## 313 314 315 316 317 318
## 94.3980912 121.1846273 111.8305682 98.3996184 112.5919471 116.1697424
## 319 320 321 322 323 324
## 123.5933904 116.5909300 114.3449846 116.4033319 117.9891980 119.6891334
## 325 326 327 328 329 330
## 116.0013171 118.9878296 122.8402385 124.8690934 129.0927591 126.7664721
## 331 332 333 334 335 336
## 130.9990344 130.0945710 130.1687735 135.6646173 131.8367314 130.9977309
## 337 338 339 340 341 342
## 127.4025693 138.6137765 141.3238675 132.9953658 155.5920618 135.9970827
## 343 344 345 346 347 348
## 132.9991770 144.1850466 139.4097941 133.3337411 141.0002649 143.9965176
## 349 350 351 352 353 354
## 153.5981862 145.9979560 143.6102380 147.0037042 141.6666438 146.3335222
## 355 356 357 358 359 360
## 145.3154175 140.6598111 139.9987661 148.9792222 140.8744926 135.4065380
## 361 362 363 364 365 366
## 153.3071764 153.6523706 150.4019896 158.0001484 150.4028556 149.8973573
## 367 368 369 370 371 372
## 147.8859526 153.8973300 154.7918344 153.3899871 156.8722220 156.8875625
## 373 374 375 376 377 378
## 152.4066051 174.0000000 163.4077437 161.9002150 164.8586742 166.4020155
## 379 380 381 382 383 384
## 161.4050668 166.9043676 165.3899003 173.9010074 165.9050360 173.9073065
## 385 386 387 388 389 390
## 171.4060450 165.4012797 171.9008640 174.4067111 175.9012317 174.3496264
## 391 392 393 394 395 396
## 185.3879483 169.4062589 176.4327234 177.9001620 195.0000000 183.4036010
## 397 398 399 400
## 183.3774436 191.4005381 182.9073948 190.9049213