Chapter 8 Support Vector Machines Model

# load data 'nj.SOC'

# Promote to spatialPointsDataFrame
coordinates(nj.SOC) <- ~ X + Y
class(nj.SOC)
## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"
nj.SOC@proj4string <- CRS(projargs = "+proj=longlat +datum=WGS84")

# Get the covariates names
library(raster)
covs <- stack(files)
names(covs) 
##  [1] "annualPET"                "aridityIndexThornthwaite"
##  [3] "climaticMoistureIndex"    "continentality"          
##  [5] "embergerQ"                "growingDegDays0"         
##  [7] "growingDegDays5"          "maxTempColdest"          
##  [9] "meanTempColdest"          "meanTempWarmest"         
## [11] "minTempWarmest"           "monthCountByTemp10"      
## [13] "PETColdestQuarter"        "PETDriestQuarter"        
## [15] "PETseasonality"           "PETWarmestQuarter"       
## [17] "PETWettestQuarter"        "thermicityIndex"
# plot the names of the covariates
names(nj.SOC@data)
##  [1] "X.1"                      "id"                      
##  [3] "SOC"                      "CRFVOL"                  
##  [5] "OCSKGM"                   "annualPET"               
##  [7] "aridityIndexThornthwaite" "climaticMoistureIndex"   
##  [9] "continentality"           "embergerQ"               
## [11] "growingDegDays0"          "growingDegDays5"         
## [13] "maxTempColdest"           "meanTempColdest"         
## [15] "meanTempWarmest"          "minTempWarmest"          
## [17] "monthCountByTemp10"       "PETColdestQuarter"       
## [19] "PETDriestQuarter"         "PETseasonality"          
## [21] "PETWarmestQuarter"        "PETWettestQuarter"       
## [23] "thermicityIndex"          "optional"
# plot the names of the covariates
names(nj.SOC@data)
##  [1] "X.1"                      "id"                      
##  [3] "SOC"                      "CRFVOL"                  
##  [5] "OCSKGM"                   "annualPET"               
##  [7] "aridityIndexThornthwaite" "climaticMoistureIndex"   
##  [9] "continentality"           "embergerQ"               
## [11] "growingDegDays0"          "growingDegDays5"         
## [13] "maxTempColdest"           "meanTempColdest"         
## [15] "meanTempWarmest"          "minTempWarmest"          
## [17] "monthCountByTemp10"       "PETColdestQuarter"       
## [19] "PETDriestQuarter"         "PETseasonality"          
## [21] "PETWarmestQuarter"        "PETWettestQuarter"       
## [23] "thermicityIndex"          "optional"
# variable selection using correlation analysis
selectedCovs <- cor(x = as.matrix(nj.SOC@data[,5]), y = as.matrix(nj.SOC@data[,-c(1:7,13,24)]))
# print correlation results
selectedCovs
##      climaticMoistureIndex continentality embergerQ growingDegDays0
## [1,]              0.272089     -0.2334364 0.2270038       0.1119405
##      growingDegDays5 meanTempColdest meanTempWarmest minTempWarmest
## [1,]      0.08452238       0.1764367      0.01067156      0.1549844
##      monthCountByTemp10 PETColdestQuarter PETDriestQuarter PETseasonality
## [1,]          0.1867504        -0.0128005      0.006004338     -0.2210748
##      PETWarmestQuarter PETWettestQuarter thermicityIndex
## [1,]        -0.2223287        -0.2165423      0.09363423
library(reshape)
x <- subset(melt(selectedCovs), value != 1 | value != NA)
x <- x[with(x, order(-abs(x$value))),]

idx <- as.character(x$X2[1:5])

nj.SOC2 <- nj.SOC[c('OCSKGM', idx)]
names(nj.SOC2)
## [1] "OCSKGM"                "climaticMoistureIndex" "continentality"       
## [4] "embergerQ"             "PETWarmestQuarter"     "PETseasonality"
COV <- covs[[idx]]

# Selected covariates
names(COV)
## [1] "climaticMoistureIndex" "continentality"        "embergerQ"            
## [4] "PETWarmestQuarter"     "PETseasonality"
# Categorical variables in svm models
dummyRaster <- function(rast){
  rast <- as.factor(rast)
  result <- list()
  for(i in 1:length(levels(rast)[[1]][[1]])){
    result[[i]] <- rast == levels(rast)[[1]][[1]][i]
    names(result[[i]]) <- paste0(names(rast),
                                 levels(rast)[[1]][[1]][i])
  }
  return(stack(result))
}
# convert soilmap from factor to dummy
# nj.shp <- dummyRaster(covs$soilmap)

# convert annualPET from factor to dummy
annualPET_dummy <- dummyRaster(covs$annualPET)

# Stack the 5 COV layers with the 2 dummies
COV <- stack(COV, annualPET_dummy)

# print the final layer names
names(COV)
##    [1] "climaticMoistureIndex"     "continentality"           
##    [3] "embergerQ"                 "PETWarmestQuarter"        
##    [5] "PETseasonality"            "annualPET737.104614257812"
##    [7] "annualPET737.245056152344" "annualPET737.316345214844"
##    [9] "annualPET737.651733398438" "annualPET737.779296875"   
##   [11] "annualPET737.934265136719" "annualPET738.463928222656"
##   [13] "annualPET738.50439453125"  "annualPET739.441650390625"
##   [15] "annualPET739.486022949219" "annualPET739.822021484375"
##   [17] "annualPET739.828002929688" "annualPET740.079406738281"
##   [19] "annualPET740.092224121094" "annualPET741.117126464844"
##   [21] "annualPET741.482421875"    "annualPET742.479064941406"
##   [23] "annualPET743.068176269531" "annualPET743.626647949219"
##   [25] "annualPET743.682800292969" "annualPET743.716186523438"
##   [27] "annualPET744.026245117188" "annualPET744.648071289062"
##   [29] "annualPET744.791625976562" "annualPET744.890319824219"
##   [31] "annualPET745.207885742188" "annualPET745.278076171875"
##   [33] "annualPET745.429016113281" "annualPET745.752258300781"
##   [35] "annualPET747.237243652344" "annualPET748.211242675781"
##   [37] "annualPET748.497924804688" "annualPET748.599609375"   
##   [39] "annualPET748.785522460938" "annualPET748.903869628906"
##   [41] "annualPET748.987670898438" "annualPET748.991455078125"
##   [43] "annualPET749.105590820312" "annualPET749.516052246094"
##   [45] "annualPET749.779907226562" "annualPET750.097900390625"
##   [47] "annualPET750.316711425781" "annualPET751.417602539062"
##   [49] "annualPET751.445434570312" "annualPET751.868957519531"
##   [51] "annualPET752.179748535156" "annualPET752.254516601562"
##   [53] "annualPET752.311950683594" "annualPET752.614868164062"
##   [55] "annualPET752.686340332031" "annualPET753.418518066406"
##   [57] "annualPET753.556884765625" "annualPET753.632446289062"
##   [59] "annualPET753.683715820312" "annualPET753.709228515625"
##   [61] "annualPET753.836303710938" "annualPET754.51611328125" 
##   [63] "annualPET755.673034667969" "annualPET755.852600097656"
##   [65] "annualPET755.930969238281" "annualPET756.051513671875"
##   [67] "annualPET756.178955078125" "annualPET756.380798339844"
##   [69] "annualPET756.459228515625" "annualPET756.522277832031"
##   [71] "annualPET756.657531738281" "annualPET756.744567871094"
##   [73] "annualPET757.202941894531" "annualPET757.497436523438"
##   [75] "annualPET757.615600585938" "annualPET758.310119628906"
##   [77] "annualPET758.566589355469" "annualPET759.317321777344"
##   [79] "annualPET759.391052246094" "annualPET759.425842285156"
##   [81] "annualPET759.493835449219" "annualPET759.530029296875"
##   [83] "annualPET759.765563964844" "annualPET759.827453613281"
##   [85] "annualPET759.858825683594" "annualPET759.864196777344"
##   [87] "annualPET760.466186523438" "annualPET760.630676269531"
##   [89] "annualPET760.880798339844" "annualPET761.020263671875"
##   [91] "annualPET761.764221191406" "annualPET762.172729492188"
##   [93] "annualPET762.221130371094" "annualPET762.239624023438"
##   [95] "annualPET762.467895507812" "annualPET762.752136230469"
##   [97] "annualPET763.209838867188" "annualPET763.396118164062"
##   [99] "annualPET763.572631835938" "annualPET763.663330078125"
##  [101] "annualPET763.747253417969" "annualPET763.848571777344"
##  [103] "annualPET763.950012207031" "annualPET764.192504882812"
##  [105] "annualPET764.255615234375" "annualPET764.325744628906"
##  [107] "annualPET764.33203125"     "annualPET764.356872558594"
##  [109] "annualPET764.485961914062" "annualPET764.509704589844"
##  [111] "annualPET764.581787109375" "annualPET764.672058105469"
##  [113] "annualPET764.805969238281" "annualPET764.919189453125"
##  [115] "annualPET764.993530273438" "annualPET765.053405761719"
##  [117] "annualPET765.0869140625"   "annualPET765.18310546875" 
##  [119] "annualPET765.369445800781" "annualPET765.395568847656"
##  [121] "annualPET765.64208984375"  "annualPET765.768920898438"
##  [123] "annualPET766.106201171875" "annualPET766.354309082031"
##  [125] "annualPET766.461853027344" "annualPET766.668823242188"
##  [127] "annualPET766.673278808594" "annualPET766.784057617188"
##  [129] "annualPET766.966979980469" "annualPET767.40234375"    
##  [131] "annualPET767.48291015625"  "annualPET767.663391113281"
##  [133] "annualPET767.684143066406" "annualPET767.699157714844"
##  [135] "annualPET767.816833496094" "annualPET768.007873535156"
##  [137] "annualPET768.106689453125" "annualPET768.202575683594"
##  [139] "annualPET768.336303710938" "annualPET768.336791992188"
##  [141] "annualPET768.555419921875" "annualPET768.734313964844"
##  [143] "annualPET768.745971679688" "annualPET768.768676757812"
##  [145] "annualPET768.889404296875" "annualPET769.023864746094"
##  [147] "annualPET769.078002929688" "annualPET769.164978027344"
##  [149] "annualPET769.168762207031" "annualPET769.172546386719"
##  [151] "annualPET769.184387207031" "annualPET769.195251464844"
##  [153] "annualPET769.227355957031" "annualPET769.597717285156"
##  [155] "annualPET769.829772949219" "annualPET769.852661132812"
##  [157] "annualPET770.136962890625" "annualPET770.319580078125"
##  [159] "annualPET770.323120117188" "annualPET770.58349609375" 
##  [161] "annualPET770.632446289062" "annualPET770.670349121094"
##  [163] "annualPET770.76416015625"  "annualPET771.216247558594"
##  [165] "annualPET771.263671875"    "annualPET771.282897949219"
##  [167] "annualPET771.329711914062" "annualPET771.391052246094"
##  [169] "annualPET771.491943359375" "annualPET771.6162109375"  
##  [171] "annualPET771.870483398438" "annualPET771.920043945312"
##  [173] "annualPET771.923706054688" "annualPET771.992492675781"
##  [175] "annualPET772.034240722656" "annualPET772.034545898438"
##  [177] "annualPET772.154541015625" "annualPET772.288452148438"
##  [179] "annualPET772.296508789062" "annualPET772.406188964844"
##  [181] "annualPET772.407104492188" "annualPET772.597595214844"
##  [183] "annualPET772.764709472656" "annualPET772.920043945312"
##  [185] "annualPET773.127014160156" "annualPET773.223815917969"
##  [187] "annualPET773.245910644531" "annualPET773.417846679688"
##  [189] "annualPET773.547424316406" "annualPET773.58203125"    
##  [191] "annualPET773.819519042969" "annualPET773.883056640625"
##  [193] "annualPET773.914367675781" "annualPET774.080810546875"
##  [195] "annualPET774.0947265625"   "annualPET774.125366210938"
##  [197] "annualPET774.238220214844" "annualPET774.276550292969"
##  [199] "annualPET774.623168945312" "annualPET774.786743164062"
##  [201] "annualPET774.859985351562" "annualPET775.094665527344"
##  [203] "annualPET775.312194824219" "annualPET775.465087890625"
##  [205] "annualPET775.523559570312" "annualPET775.804138183594"
##  [207] "annualPET776.030456542969" "annualPET776.055480957031"
##  [209] "annualPET776.073852539062" "annualPET776.20166015625" 
##  [211] "annualPET776.268249511719" "annualPET776.497741699219"
##  [213] "annualPET776.930419921875" "annualPET776.944580078125"
##  [215] "annualPET777.16748046875"  "annualPET777.265502929688"
##  [217] "annualPET777.328796386719" "annualPET777.575805664062"
##  [219] "annualPET777.588500976562" "annualPET777.631958007812"
##  [221] "annualPET777.826049804688" "annualPET778.068420410156"
##  [223] "annualPET778.085693359375" "annualPET778.115356445312"
##  [225] "annualPET778.299133300781" "annualPET778.309265136719"
##  [227] "annualPET778.312133789062" "annualPET778.356323242188"
##  [229] "annualPET778.835388183594" "annualPET778.8935546875"  
##  [231] "annualPET778.928771972656" "annualPET779.060913085938"
##  [233] "annualPET779.180480957031" "annualPET779.183959960938"
##  [235] "annualPET779.196411132812" "annualPET779.245483398438"
##  [237] "annualPET779.619689941406" "annualPET779.633850097656"
##  [239] "annualPET780.377868652344" "annualPET780.428833007812"
##  [241] "annualPET780.481323242188" "annualPET780.629455566406"
##  [243] "annualPET780.634887695312" "annualPET780.722839355469"
##  [245] "annualPET780.763793945312" "annualPET781.011535644531"
##  [247] "annualPET781.052917480469" "annualPET781.176452636719"
##  [249] "annualPET781.197570800781" "annualPET781.436157226562"
##  [251] "annualPET781.62353515625"  "annualPET781.6640625"     
##  [253] "annualPET781.799682617188" "annualPET781.801147460938"
##  [255] "annualPET781.9375"         "annualPET781.992004394531"
##  [257] "annualPET782.011596679688" "annualPET782.042053222656"
##  [259] "annualPET782.134887695312" "annualPET782.201904296875"
##  [261] "annualPET782.315368652344" "annualPET782.384765625"   
##  [263] "annualPET782.592346191406" "annualPET782.734802246094"
##  [265] "annualPET782.991760253906" "annualPET783.05615234375" 
##  [267] "annualPET783.334594726562" "annualPET783.403747558594"
##  [269] "annualPET783.484008789062" "annualPET783.72216796875" 
##  [271] "annualPET783.790222167969" "annualPET783.791809082031"
##  [273] "annualPET783.865234375"    "annualPET783.996276855469"
##  [275] "annualPET784.214782714844" "annualPET784.364318847656"
##  [277] "annualPET784.473693847656" "annualPET784.550048828125"
##  [279] "annualPET784.562377929688" "annualPET784.573181152344"
##  [281] "annualPET784.587097167969" "annualPET784.815124511719"
##  [283] "annualPET785.088439941406" "annualPET785.167724609375"
##  [285] "annualPET785.311462402344" "annualPET785.383666992188"
##  [287] "annualPET785.736206054688" "annualPET785.767150878906"
##  [289] "annualPET785.918762207031" "annualPET785.971496582031"
##  [291] "annualPET786.001953125"    "annualPET786.166015625"   
##  [293] "annualPET786.182067871094" "annualPET786.220703125"   
##  [295] "annualPET786.412048339844" "annualPET786.426147460938"
##  [297] "annualPET786.682189941406" "annualPET786.911987304688"
##  [299] "annualPET787.039489746094" "annualPET787.105834960938"
##  [301] "annualPET787.341552734375" "annualPET787.380737304688"
##  [303] "annualPET787.576416015625" "annualPET787.771850585938"
##  [305] "annualPET787.77587890625"  "annualPET788.094055175781"
##  [307] "annualPET788.13916015625"  "annualPET788.214599609375"
##  [309] "annualPET788.222473144531" "annualPET788.302124023438"
##  [311] "annualPET788.351440429688" "annualPET788.373229980469"
##  [313] "annualPET788.449951171875" "annualPET788.499816894531"
##  [315] "annualPET788.505493164062" "annualPET788.835815429688"
##  [317] "annualPET788.889343261719" "annualPET788.963195800781"
##  [319] "annualPET789.003845214844" "annualPET789.044982910156"
##  [321] "annualPET789.1689453125"   "annualPET789.316589355469"
##  [323] "annualPET789.334716796875" "annualPET789.637634277344"
##  [325] "annualPET790.002868652344" "annualPET790.016784667969"
##  [327] "annualPET790.041870117188" "annualPET790.130187988281"
##  [329] "annualPET790.486267089844" "annualPET790.583740234375"
##  [331] "annualPET790.644104003906" "annualPET790.685302734375"
##  [333] "annualPET790.840515136719" "annualPET790.875061035156"
##  [335] "annualPET791.0498046875"   "annualPET791.143127441406"
##  [337] "annualPET791.259643554688" "annualPET791.448547363281"
##  [339] "annualPET791.463134765625" "annualPET791.600708007812"
##  [341] "annualPET791.608581542969" "annualPET791.612426757812"
##  [343] "annualPET791.626647949219" "annualPET791.850036621094"
##  [345] "annualPET791.85205078125"  "annualPET791.878479003906"
##  [347] "annualPET792.086364746094" "annualPET792.167907714844"
##  [349] "annualPET792.357421875"    "annualPET792.391235351562"
##  [351] "annualPET792.404113769531" "annualPET792.409790039062"
##  [353] "annualPET792.473449707031" "annualPET792.613647460938"
##  [355] "annualPET792.805358886719" "annualPET792.849304199219"
##  [357] "annualPET793.006713867188" "annualPET793.231140136719"
##  [359] "annualPET793.386047363281" "annualPET793.445922851562"
##  [361] "annualPET793.462280273438" "annualPET793.507995605469"
##  [363] "annualPET793.601867675781" "annualPET793.76025390625" 
##  [365] "annualPET793.934753417969" "annualPET793.984802246094"
##  [367] "annualPET794.017028808594" "annualPET794.088012695312"
##  [369] "annualPET794.159606933594" "annualPET794.262878417969"
##  [371] "annualPET794.297668457031" "annualPET794.426330566406"
##  [373] "annualPET794.534973144531" "annualPET794.671936035156"
##  [375] "annualPET794.769592285156" "annualPET794.936706542969"
##  [377] "annualPET794.972595214844" "annualPET794.979309082031"
##  [379] "annualPET795.172180175781" "annualPET795.201354980469"
##  [381] "annualPET795.287963867188" "annualPET795.433532714844"
##  [383] "annualPET795.443542480469" "annualPET795.448547363281"
##  [385] "annualPET795.754943847656" "annualPET795.774536132812"
##  [387] "annualPET795.82373046875"  "annualPET796.037109375"   
##  [389] "annualPET796.371215820312" "annualPET796.447265625"   
##  [391] "annualPET796.456237792969" "annualPET796.496643066406"
##  [393] "annualPET796.564880371094" "annualPET796.638671875"   
##  [395] "annualPET796.63916015625"  "annualPET796.698120117188"
##  [397] "annualPET796.730163574219" "annualPET797.274475097656"
##  [399] "annualPET797.275024414062" "annualPET797.456481933594"
##  [401] "annualPET797.459655761719" "annualPET797.794128417969"
##  [403] "annualPET797.92236328125"  "annualPET797.973693847656"
##  [405] "annualPET798.097717285156" "annualPET798.261840820312"
##  [407] "annualPET798.320007324219" "annualPET798.337585449219"
##  [409] "annualPET798.427307128906" "annualPET798.444152832031"
##  [411] "annualPET798.447631835938" "annualPET798.655883789062"
##  [413] "annualPET798.672973632812" "annualPET798.828125"      
##  [415] "annualPET798.965270996094" "annualPET799.02294921875" 
##  [417] "annualPET799.1103515625"   "annualPET799.138732910156"
##  [419] "annualPET799.182556152344" "annualPET799.358825683594"
##  [421] "annualPET799.5322265625"   "annualPET799.729614257812"
##  [423] "annualPET799.920837402344" "annualPET799.974975585938"
##  [425] "annualPET800.106811523438" "annualPET800.178771972656"
##  [427] "annualPET800.23193359375"  "annualPET800.2431640625"  
##  [429] "annualPET800.30029296875"  "annualPET800.300842285156"
##  [431] "annualPET800.469360351562" "annualPET800.527770996094"
##  [433] "annualPET800.559509277344" "annualPET800.712951660156"
##  [435] "annualPET800.963684082031" "annualPET800.981018066406"
##  [437] "annualPET801.260620117188" "annualPET801.40234375"    
##  [439] "annualPET801.403625488281" "annualPET801.434997558594"
##  [441] "annualPET801.604553222656" "annualPET801.621032714844"
##  [443] "annualPET801.757507324219" "annualPET801.968933105469"
##  [445] "annualPET801.971557617188" "annualPET801.988586425781"
##  [447] "annualPET802.25439453125"  "annualPET802.575378417969"
##  [449] "annualPET802.947814941406" "annualPET802.951416015625"
##  [451] "annualPET803.182983398438" "annualPET803.315612792969"
##  [453] "annualPET803.338989257812" "annualPET803.669982910156"
##  [455] "annualPET803.71923828125"  "annualPET803.749267578125"
##  [457] "annualPET803.786376953125" "annualPET803.8408203125"  
##  [459] "annualPET803.879150390625" "annualPET803.880004882812"
##  [461] "annualPET803.889526367188" "annualPET803.947326660156"
##  [463] "annualPET804.121887207031" "annualPET804.32958984375" 
##  [465] "annualPET804.373901367188" "annualPET804.480285644531"
##  [467] "annualPET804.522033691406" "annualPET804.525695800781"
##  [469] "annualPET804.604187011719" "annualPET804.627197265625"
##  [471] "annualPET804.700927734375" "annualPET804.750854492188"
##  [473] "annualPET804.973205566406" "annualPET804.989196777344"
##  [475] "annualPET805.057067871094" "annualPET805.105285644531"
##  [477] "annualPET805.327392578125" "annualPET805.4306640625"  
##  [479] "annualPET805.492858886719" "annualPET805.585815429688"
##  [481] "annualPET805.643310546875" "annualPET805.697937011719"
##  [483] "annualPET805.804870605469" "annualPET805.935729980469"
##  [485] "annualPET805.98193359375"  "annualPET806.090026855469"
##  [487] "annualPET806.118347167969" "annualPET806.210083007812"
##  [489] "annualPET806.283996582031" "annualPET806.369567871094"
##  [491] "annualPET806.502136230469" "annualPET806.688598632812"
##  [493] "annualPET806.731323242188" "annualPET806.9453125"     
##  [495] "annualPET807.099304199219" "annualPET807.185668945312"
##  [497] "annualPET807.225036621094" "annualPET807.238891601562"
##  [499] "annualPET807.339416503906" "annualPET807.361633300781"
##  [501] "annualPET807.535339355469" "annualPET807.599548339844"
##  [503] "annualPET807.726196289062" "annualPET807.783142089844"
##  [505] "annualPET808.26171875"     "annualPET808.295288085938"
##  [507] "annualPET808.318786621094" "annualPET808.497497558594"
##  [509] "annualPET808.632507324219" "annualPET808.64453125"    
##  [511] "annualPET808.650939941406" "annualPET808.664245605469"
##  [513] "annualPET808.670227050781" "annualPET808.888000488281"
##  [515] "annualPET808.903503417969" "annualPET808.935119628906"
##  [517] "annualPET808.950622558594" "annualPET809.055297851562"
##  [519] "annualPET809.121765136719" "annualPET809.408508300781"
##  [521] "annualPET809.693542480469" "annualPET809.748474121094"
##  [523] "annualPET809.784057617188" "annualPET809.785827636719"
##  [525] "annualPET810.053894042969" "annualPET810.062866210938"
##  [527] "annualPET810.123291015625" "annualPET810.312744140625"
##  [529] "annualPET810.356079101562" "annualPET810.447143554688"
##  [531] "annualPET810.500122070312" "annualPET810.788513183594"
##  [533] "annualPET810.838134765625" "annualPET810.845153808594"
##  [535] "annualPET810.851867675781" "annualPET810.99560546875" 
##  [537] "annualPET811.056335449219" "annualPET811.103271484375"
##  [539] "annualPET811.117431640625" "annualPET811.24755859375" 
##  [541] "annualPET811.2763671875"   "annualPET811.322387695312"
##  [543] "annualPET811.541442871094" "annualPET811.543518066406"
##  [545] "annualPET811.642456054688" "annualPET811.656311035156"
##  [547] "annualPET811.744506835938" "annualPET811.752624511719"
##  [549] "annualPET811.810852050781" "annualPET811.86669921875" 
##  [551] "annualPET811.881530761719" "annualPET811.966979980469"
##  [553] "annualPET812.111511230469" "annualPET812.148986816406"
##  [555] "annualPET812.813110351562" "annualPET812.8466796875"  
##  [557] "annualPET812.887390136719" "annualPET812.889038085938"
##  [559] "annualPET812.983764648438" "annualPET812.997802734375"
##  [561] "annualPET813.158142089844" "annualPET813.302185058594"
##  [563] "annualPET813.303955078125" "annualPET813.499084472656"
##  [565] "annualPET813.757568359375" "annualPET813.873352050781"
##  [567] "annualPET814.045166015625" "annualPET814.171752929688"
##  [569] "annualPET814.235595703125" "annualPET814.369567871094"
##  [571] "annualPET814.370971679688" "annualPET814.443969726562"
##  [573] "annualPET814.487487792969" "annualPET814.561096191406"
##  [575] "annualPET814.635803222656" "annualPET814.649658203125"
##  [577] "annualPET814.710510253906" "annualPET815.068176269531"
##  [579] "annualPET815.089416503906" "annualPET815.124206542969"
##  [581] "annualPET815.170288085938" "annualPET815.194885253906"
##  [583] "annualPET815.223083496094" "annualPET815.274353027344"
##  [585] "annualPET815.310180664062" "annualPET815.335021972656"
##  [587] "annualPET815.379943847656" "annualPET815.442504882812"
##  [589] "annualPET815.550415039062" "annualPET815.613952636719"
##  [591] "annualPET815.615417480469" "annualPET815.628295898438"
##  [593] "annualPET815.68505859375"  "annualPET815.771179199219"
##  [595] "annualPET815.934020996094" "annualPET816.075927734375"
##  [597] "annualPET816.177185058594" "annualPET816.182922363281"
##  [599] "annualPET816.421081542969" "annualPET816.453674316406"
##  [601] "annualPET816.913269042969" "annualPET816.947631835938"
##  [603] "annualPET817.070922851562" "annualPET817.433959960938"
##  [605] "annualPET817.445068359375" "annualPET817.448059082031"
##  [607] "annualPET817.474426269531" "annualPET817.6494140625"  
##  [609] "annualPET817.780334472656" "annualPET817.969421386719"
##  [611] "annualPET818.003112792969" "annualPET818.334228515625"
##  [613] "annualPET818.392272949219" "annualPET818.4453125"     
##  [615] "annualPET818.474487304688" "annualPET818.530883789062"
##  [617] "annualPET818.627258300781" "annualPET818.64697265625" 
##  [619] "annualPET818.835144042969" "annualPET818.856994628906"
##  [621] "annualPET818.889770507812" "annualPET818.911926269531"
##  [623] "annualPET818.920166015625" "annualPET819.176940917969"
##  [625] "annualPET819.218872070312" "annualPET819.255737304688"
##  [627] "annualPET819.363159179688" "annualPET819.451843261719"
##  [629] "annualPET819.522766113281" "annualPET819.601318359375"
##  [631] "annualPET819.602478027344" "annualPET819.670104980469"
##  [633] "annualPET819.80517578125"  "annualPET820.032409667969"
##  [635] "annualPET820.138549804688" "annualPET820.21533203125" 
##  [637] "annualPET820.343017578125" "annualPET820.445922851562"
##  [639] "annualPET820.471801757812" "annualPET820.648864746094"
##  [641] "annualPET820.7041015625"   "annualPET821.045593261719"
##  [643] "annualPET821.073120117188" "annualPET821.188354492188"
##  [645] "annualPET821.516357421875" "annualPET821.606262207031"
##  [647] "annualPET821.632446289062" "annualPET821.727844238281"
##  [649] "annualPET821.822631835938" "annualPET821.828063964844"
##  [651] "annualPET821.970825195312" "annualPET821.971923828125"
##  [653] "annualPET822.3505859375"   "annualPET822.408142089844"
##  [655] "annualPET822.439331054688" "annualPET822.464721679688"
##  [657] "annualPET822.543762207031" "annualPET822.562438964844"
##  [659] "annualPET822.742553710938" "annualPET822.766052246094"
##  [661] "annualPET822.906555175781" "annualPET823.134704589844"
##  [663] "annualPET823.146484375"    "annualPET823.161926269531"
##  [665] "annualPET823.1640625"      "annualPET823.17431640625" 
##  [667] "annualPET823.234985351562" "annualPET823.275573730469"
##  [669] "annualPET823.330627441406" "annualPET823.348571777344"
##  [671] "annualPET823.350708007812" "annualPET823.357604980469"
##  [673] "annualPET823.57666015625"  "annualPET823.618835449219"
##  [675] "annualPET823.768249511719" "annualPET823.796020507812"
##  [677] "annualPET823.90625"        "annualPET823.955261230469"
##  [679] "annualPET823.97265625"     "annualPET824.224548339844"
##  [681] "annualPET824.254455566406" "annualPET824.453186035156"
##  [683] "annualPET824.621520996094" "annualPET824.627563476562"
##  [685] "annualPET824.629577636719" "annualPET824.7158203125"  
##  [687] "annualPET824.716918945312" "annualPET824.849548339844"
##  [689] "annualPET824.874816894531" "annualPET824.890197753906"
##  [691] "annualPET825.007202148438" "annualPET825.076049804688"
##  [693] "annualPET825.0966796875"   "annualPET825.111938476562"
##  [695] "annualPET825.24658203125"  "annualPET825.285766601562"
##  [697] "annualPET825.388427734375" "annualPET825.440307617188"
##  [699] "annualPET825.768493652344" "annualPET825.886901855469"
##  [701] "annualPET825.924255371094" "annualPET825.98291015625" 
##  [703] "annualPET826.016235351562" "annualPET826.046508789062"
##  [705] "annualPET826.240112304688" "annualPET826.267639160156"
##  [707] "annualPET826.397155761719" "annualPET826.415588378906"
##  [709] "annualPET826.47119140625"  "annualPET826.5185546875"  
##  [711] "annualPET826.532592773438" "annualPET826.548522949219"
##  [713] "annualPET826.573913574219" "annualPET826.600463867188"
##  [715] "annualPET826.609313964844" "annualPET826.943664550781"
##  [717] "annualPET827.060974121094" "annualPET827.081115722656"
##  [719] "annualPET827.251037597656" "annualPET827.295471191406"
##  [721] "annualPET827.355529785156" "annualPET827.464294433594"
##  [723] "annualPET827.485595703125" "annualPET827.597412109375"
##  [725] "annualPET827.63623046875"  "annualPET827.691101074219"
##  [727] "annualPET827.85791015625"  "annualPET827.968200683594"
##  [729] "annualPET827.98046875"     "annualPET828.018188476562"
##  [731] "annualPET828.187255859375" "annualPET828.204467773438"
##  [733] "annualPET828.209350585938" "annualPET828.415771484375"
##  [735] "annualPET828.418518066406" "annualPET828.524841308594"
##  [737] "annualPET828.55810546875"  "annualPET828.648498535156"
##  [739] "annualPET828.733276367188" "annualPET828.834899902344"
##  [741] "annualPET828.897155761719" "annualPET828.932373046875"
##  [743] "annualPET829.13525390625"  "annualPET829.186767578125"
##  [745] "annualPET829.259704589844" "annualPET829.285095214844"
##  [747] "annualPET829.357421875"    "annualPET829.375549316406"
##  [749] "annualPET829.482299804688" "annualPET829.7705078125"  
##  [751] "annualPET829.778564453125" "annualPET829.924865722656"
##  [753] "annualPET830.07861328125"  "annualPET830.082397460938"
##  [755] "annualPET830.092407226562" "annualPET830.102966308594"
##  [757] "annualPET830.116882324219" "annualPET830.138000488281"
##  [759] "annualPET830.22119140625"  "annualPET830.235656738281"
##  [761] "annualPET830.340148925781" "annualPET830.409057617188"
##  [763] "annualPET830.517028808594" "annualPET830.570556640625"
##  [765] "annualPET830.801147460938" "annualPET830.816040039062"
##  [767] "annualPET831.021850585938" "annualPET831.154968261719"
##  [769] "annualPET831.162414550781" "annualPET831.502319335938"
##  [771] "annualPET831.507019042969" "annualPET831.565307617188"
##  [773] "annualPET831.763549804688" "annualPET831.795776367188"
##  [775] "annualPET831.81103515625"  "annualPET831.842407226562"
##  [777] "annualPET831.951904296875" "annualPET832.068237304688"
##  [779] "annualPET832.095947265625" "annualPET832.24462890625" 
##  [781] "annualPET832.422058105469" "annualPET832.425170898438"
##  [783] "annualPET832.45458984375"  "annualPET832.513854980469"
##  [785] "annualPET832.562377929688" "annualPET832.586608886719"
##  [787] "annualPET832.607849121094" "annualPET832.6328125"     
##  [789] "annualPET832.728454589844" "annualPET832.760864257812"
##  [791] "annualPET832.860046386719" "annualPET833.060913085938"
##  [793] "annualPET833.1103515625"   "annualPET833.282104492188"
##  [795] "annualPET833.291442871094" "annualPET833.3720703125"  
##  [797] "annualPET833.482299804688" "annualPET833.561706542969"
##  [799] "annualPET833.718017578125" "annualPET833.77734375"    
##  [801] "annualPET833.798156738281" "annualPET833.939270019531"
##  [803] "annualPET834.037841796875" "annualPET834.038513183594"
##  [805] "annualPET834.077758789062" "annualPET834.122192382812"
##  [807] "annualPET834.148254394531" "annualPET834.429809570312"
##  [809] "annualPET834.518127441406" "annualPET834.536437988281"
##  [811] "annualPET834.699340820312" "annualPET834.805114746094"
##  [813] "annualPET834.861389160156" "annualPET834.923400878906"
##  [815] "annualPET835.032470703125" "annualPET835.135192871094"
##  [817] "annualPET835.201477050781" "annualPET835.202575683594"
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##  [821] "annualPET835.276916503906" "annualPET835.316528320312"
##  [823] "annualPET835.360290527344" "annualPET835.537170410156"
##  [825] "annualPET835.601623535156" "annualPET835.640014648438"
##  [827] "annualPET835.697326660156" "annualPET835.779602050781"
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##  [841] "annualPET836.608947753906" "annualPET836.66357421875" 
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##  [849] "annualPET837.050231933594" "annualPET837.076599121094"
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##  [857] "annualPET837.798400878906" "annualPET837.799926757812"
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##  [863] "annualPET837.998291015625" "annualPET838.049011230469"
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##  [869] "annualPET838.615173339844" "annualPET838.622314453125"
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##  [883] "annualPET839.583068847656" "annualPET839.770324707031"
##  [885] "annualPET839.844787597656" "annualPET840.000671386719"
##  [887] "annualPET840.078979492188" "annualPET840.156921386719"
##  [889] "annualPET840.17578125"     "annualPET840.263671875"   
##  [891] "annualPET840.334594726562" "annualPET840.413879394531"
##  [893] "annualPET840.460327148438" "annualPET840.5634765625"  
##  [895] "annualPET840.612976074219" "annualPET840.761474609375"
##  [897] "annualPET840.765197753906" "annualPET840.81396484375" 
##  [899] "annualPET840.849792480469" "annualPET840.903015136719"
##  [901] "annualPET841.069885253906" "annualPET841.110107421875"
##  [903] "annualPET841.13916015625"  "annualPET841.251525878906"
##  [905] "annualPET841.328063964844" "annualPET841.42138671875" 
##  [907] "annualPET841.42333984375"  "annualPET841.521911621094"
##  [909] "annualPET841.7041015625"   "annualPET841.765197753906"
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##  [927] "annualPET843.395385742188" "annualPET843.501770019531"
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##  [975] "annualPET846.361938476562" "annualPET846.391906738281"
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##  [987] "annualPET847.348022460938" "annualPET847.416259765625"
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##  [993] "annualPET847.542541503906" "annualPET847.557983398438"
##  [995] "annualPET847.634338378906" "annualPET847.638977050781"
##  [997] "annualPET847.678100585938" "annualPET847.719787597656"
##  [999] "annualPET847.745483398438" "annualPET847.79150390625" 
## [1001] "annualPET847.815551757812" "annualPET848.015502929688"
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## [1077] "annualPET852.815979003906" "annualPET852.897521972656"
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## [1933] "annualPET898.593688964844" "annualPET898.627014160156"
## [1935] "annualPET898.665710449219" "annualPET898.671081542969"
## [1937] "annualPET898.674621582031" "annualPET898.688049316406"
## [1939] "annualPET898.719665527344" "annualPET898.763000488281"
## [1941] "annualPET898.874755859375" "annualPET898.983093261719"
## [1943] "annualPET899.009521484375" "annualPET899.050720214844"
## [1945] "annualPET899.066589355469" "annualPET899.101623535156"
## [1947] "annualPET899.244567871094" "annualPET899.258728027344"
## [1949] "annualPET899.437927246094" "annualPET899.486633300781"
## [1951] "annualPET899.500915527344" "annualPET899.547485351562"
## [1953] "annualPET899.564147949219" "annualPET899.627258300781"
## [1955] "annualPET899.640869140625" "annualPET899.654052734375"
## [1957] "annualPET899.808532714844" "annualPET899.826416015625"
## [1959] "annualPET899.835510253906" "annualPET899.856201171875"
## [1961] "annualPET899.85888671875"  "annualPET899.890808105469"
## [1963] "annualPET899.956359863281" "annualPET899.969421386719"
## [1965] "annualPET899.9912109375"   "annualPET900.038269042969"
## [1967] "annualPET900.0615234375"   "annualPET900.188903808594"
## [1969] "annualPET900.22412109375"  "annualPET900.361328125"   
## [1971] "annualPET900.422668457031" "annualPET900.428955078125"
## [1973] "annualPET900.463439941406" "annualPET900.464599609375"
## [1975] "annualPET900.5029296875"   "annualPET900.553527832031"
## [1977] "annualPET900.5703125"      "annualPET900.609130859375"
## [1979] "annualPET900.657958984375" "annualPET900.664367675781"
## [1981] "annualPET900.686950683594" "annualPET900.768005371094"
## [1983] "annualPET900.784301757812" "annualPET900.931701660156"
## [1985] "annualPET900.946899414062" "annualPET900.976196289062"
## [1987] "annualPET900.983337402344" "annualPET901.067932128906"
## [1989] "annualPET901.126159667969" "annualPET901.145324707031"
## [1991] "annualPET901.155151367188" "annualPET901.247436523438"
## [1993] "annualPET901.272277832031" "annualPET901.273681640625"
## [1995] "annualPET901.354431152344" "annualPET901.377197265625"
## [1997] "annualPET901.381652832031" "annualPET901.40625"       
## [1999] "annualPET901.612121582031" "annualPET901.620056152344"
## [2001] "annualPET901.639099121094" "annualPET901.649536132812"
## [2003] "annualPET901.651489257812" "annualPET901.71337890625" 
## [2005] "annualPET901.717651367188" "annualPET901.817993164062"
## [2007] "annualPET901.843872070312" "annualPET902.169738769531"
## [2009] "annualPET902.333435058594" "annualPET902.354919433594"
## [2011] "annualPET902.427368164062" "annualPET902.435913085938"
## [2013] "annualPET902.449401855469" "annualPET902.567321777344"
## [2015] "annualPET902.640747070312" "annualPET902.741088867188"
## [2017] "annualPET902.820434570312" "annualPET902.829711914062"
## [2019] "annualPET902.860107421875" "annualPET902.88232421875" 
## [2021] "annualPET902.920837402344" "annualPET902.988830566406"
## [2023] "annualPET903.027465820312" "annualPET903.028625488281"
## [2025] "annualPET903.039489746094" "annualPET903.146423339844"
## [2027] "annualPET903.192199707031" "annualPET903.217163085938"
## [2029] "annualPET903.3076171875"   "annualPET903.353576660156"
## [2031] "annualPET903.505310058594" "annualPET903.50732421875" 
## [2033] "annualPET903.520080566406" "annualPET903.567260742188"
## [2035] "annualPET903.575317382812" "annualPET903.771667480469"
## [2037] "annualPET903.876892089844" "annualPET903.977600097656"
## [2039] "annualPET903.995300292969" "annualPET904.038696289062"
## [2041] "annualPET904.059509277344" "annualPET904.111450195312"
## [2043] "annualPET904.233703613281" "annualPET904.326049804688"
## [2045] "annualPET904.330871582031" "annualPET904.343566894531"
## [2047] "annualPET904.354248046875" "annualPET904.35546875"    
## [2049] "annualPET904.365112304688" "annualPET904.390991210938"
## [2051] "annualPET904.473999023438" "annualPET904.486572265625"
## [2053] "annualPET904.636474609375" "annualPET904.65576171875" 
## [2055] "annualPET904.667907714844" "annualPET904.677917480469"
## [2057] "annualPET904.78662109375"  "annualPET904.847900390625"
## [2059] "annualPET904.851013183594" "annualPET904.93701171875" 
## [2061] "annualPET904.944702148438" "annualPET904.956481933594"
## [2063] "annualPET905.026977539062" "annualPET905.037170410156"
## [2065] "annualPET905.060913085938" "annualPET905.072326660156"
## [2067] "annualPET905.156433105469" "annualPET905.167297363281"
## [2069] "annualPET905.175231933594" "annualPET905.326721191406"
## [2071] "annualPET905.438354492188" "annualPET905.448120117188"
## [2073] "annualPET905.627807617188" "annualPET905.630737304688"
## [2075] "annualPET905.735961914062" "annualPET905.768737792969"
## [2077] "annualPET905.856384277344" "annualPET905.865600585938"
## [2079] "annualPET905.961853027344" "annualPET905.977233886719"
## [2081] "annualPET906.015686035156" "annualPET906.016174316406"
## [2083] "annualPET906.057800292969" "annualPET906.061401367188"
## [2085] "annualPET906.18115234375"  "annualPET906.293518066406"
## [2087] "annualPET906.317932128906" "annualPET906.493103027344"
## [2089] "annualPET906.517395019531" "annualPET906.563537597656"
## [2091] "annualPET906.606140136719" "annualPET906.630065917969"
## [2093] "annualPET906.662536621094" "annualPET906.6669921875"  
## [2095] "annualPET906.667419433594" "annualPET906.729553222656"
## [2097] "annualPET906.775451660156" "annualPET906.851501464844"
## [2099] "annualPET906.863098144531" "annualPET907.081726074219"
## [2101] "annualPET907.082763671875" "annualPET907.162536621094"
## [2103] "annualPET907.17626953125"  "annualPET907.228698730469"
## [2105] "annualPET907.229125976562" "annualPET907.247009277344"
## [2107] "annualPET907.248840332031" "annualPET907.266418457031"
## [2109] "annualPET907.275634765625" "annualPET907.289367675781"
## [2111] "annualPET907.383728027344" "annualPET907.436950683594"
## [2113] "annualPET907.465881347656" "annualPET907.514892578125"
## [2115] "annualPET907.549682617188" "annualPET907.564636230469"
## [2117] "annualPET907.58251953125"  "annualPET907.609191894531"
## [2119] "annualPET907.639343261719" "annualPET907.645263671875"
## [2121] "annualPET907.654602050781" "annualPET907.732971191406"
## [2123] "annualPET907.747375488281" "annualPET907.846618652344"
## [2125] "annualPET907.949768066406" "annualPET907.984680175781"
## [2127] "annualPET908.026184082031" "annualPET908.138122558594"
## [2129] "annualPET908.246398925781" "annualPET908.274963378906"
## [2131] "annualPET908.336791992188" "annualPET908.454772949219"
## [2133] "annualPET908.493041992188" "annualPET908.575622558594"
## [2135] "annualPET908.578674316406" "annualPET908.598388671875"
## [2137] "annualPET908.608581542969" "annualPET908.663696289062"
## [2139] "annualPET908.670959472656" "annualPET908.675537109375"
## [2141] "annualPET908.691955566406" "annualPET908.727783203125"
## [2143] "annualPET908.754211425781" "annualPET909.083862304688"
## [2145] "annualPET909.290222167969" "annualPET909.473022460938"
## [2147] "annualPET909.487182617188" "annualPET909.502136230469"
## [2149] "annualPET909.58642578125"  "annualPET909.58935546875" 
## [2151] "annualPET909.603393554688" "annualPET909.635925292969"
## [2153] "annualPET909.682922363281" "annualPET909.690612792969"
## [2155] "annualPET909.716064453125" "annualPET909.73193359375" 
## [2157] "annualPET909.7822265625"   "annualPET909.7978515625"  
## [2159] "annualPET909.826416015625" "annualPET909.843383789062"
## [2161] "annualPET909.8564453125"   "annualPET909.9169921875"  
## [2163] "annualPET909.923278808594" "annualPET909.961975097656"
## [2165] "annualPET909.998168945312" "annualPET910.035034179688"
## [2167] "annualPET910.042297363281" "annualPET910.084106445312"
## [2169] "annualPET910.087341308594" "annualPET910.097045898438"
## [2171] "annualPET910.114685058594" "annualPET910.157531738281"
## [2173] "annualPET910.310974121094" "annualPET910.337707519531"
## [2175] "annualPET910.490600585938" "annualPET910.5126953125"  
## [2177] "annualPET910.562316894531" "annualPET910.635864257812"
## [2179] "annualPET910.695373535156" "annualPET910.73828125"    
## [2181] "annualPET910.770446777344" "annualPET910.912963867188"
## [2183] "annualPET911.03515625"     "annualPET911.067260742188"
## [2185] "annualPET911.082763671875" "annualPET911.236145019531"
## [2187] "annualPET911.26025390625"  "annualPET911.287902832031"
## [2189] "annualPET911.326171875"    "annualPET911.327514648438"
## [2191] "annualPET911.341430664062" "annualPET911.346252441406"
## [2193] "annualPET911.39013671875"  "annualPET911.392883300781"
## [2195] "annualPET911.398071289062" "annualPET911.421813964844"
## [2197] "annualPET911.450134277344" "annualPET911.480346679688"
## [2199] "annualPET911.704040527344" "annualPET911.745361328125"
## [2201] "annualPET911.785217285156" "annualPET911.790100097656"
## [2203] "annualPET911.798889160156" "annualPET911.945373535156"
## [2205] "annualPET911.996887207031" "annualPET912.017822265625"
## [2207] "annualPET912.102478027344" "annualPET912.142700195312"
## [2209] "annualPET912.224670410156" "annualPET912.228759765625"
## [2211] "annualPET912.232482910156" "annualPET912.245727539062"
## [2213] "annualPET912.306091308594" "annualPET912.495727539062"
## [2215] "annualPET912.62060546875"  "annualPET912.678466796875"
## [2217] "annualPET912.682739257812" "annualPET912.6953125"     
## [2219] "annualPET912.705871582031" "annualPET912.752685546875"
## [2221] "annualPET912.781799316406" "annualPET912.818786621094"
## [2223] "annualPET912.829650878906" "annualPET912.835327148438"
## [2225] "annualPET912.893188476562" "annualPET912.902099609375"
## [2227] "annualPET912.95068359375"  "annualPET913.086669921875"
## [2229] "annualPET913.095275878906" "annualPET913.151977539062"
## [2231] "annualPET913.320251464844" "annualPET913.428161621094"
## [2233] "annualPET913.447387695312" "annualPET913.466552734375"
## [2235] "annualPET913.560424804688" "annualPET913.654846191406"
## [2237] "annualPET913.764587402344" "annualPET913.976379394531"
## [2239] "annualPET913.996032714844" "annualPET914.00439453125" 
## [2241] "annualPET914.025268554688" "annualPET914.045837402344"
## [2243] "annualPET914.0830078125"   "annualPET914.170349121094"
## [2245] "annualPET914.189819335938" "annualPET914.231018066406"
## [2247] "annualPET914.243957519531" "annualPET914.258422851562"
## [2249] "annualPET914.28857421875"  "annualPET914.3076171875"  
## [2251] "annualPET914.359069824219" "annualPET914.428649902344"
## [2253] "annualPET914.456237792969" "annualPET914.471008300781"
## [2255] "annualPET914.506164550781" "annualPET914.55126953125" 
## [2257] "annualPET914.56494140625"  "annualPET914.568176269531"
## [2259] "annualPET914.600952148438" "annualPET914.763244628906"
## [2261] "annualPET914.767333984375" "annualPET914.811279296875"
## [2263] "annualPET914.859252929688" "annualPET914.891784667969"
## [2265] "annualPET914.915954589844" "annualPET914.923095703125"
## [2267] "annualPET914.937316894531" "annualPET914.953186035156"
## [2269] "annualPET915.011169433594" "annualPET915.033020019531"
## [2271] "annualPET915.173645019531" "annualPET915.178283691406"
## [2273] "annualPET915.228271484375" "annualPET915.307189941406"
## [2275] "annualPET915.341979980469" "annualPET915.368103027344"
## [2277] "annualPET915.37255859375"  "annualPET915.377868652344"
## [2279] "annualPET915.416015625"    "annualPET915.505065917969"
## [2281] "annualPET915.56005859375"  "annualPET915.827758789062"
## [2283] "annualPET915.855529785156" "annualPET915.945556640625"
## [2285] "annualPET915.965759277344" "annualPET916.049072265625"
## [2287] "annualPET916.096740722656" "annualPET916.105773925781"
## [2289] "annualPET916.143615722656" "annualPET916.183837890625"
## [2291] "annualPET916.231262207031" "annualPET916.260986328125"
## [2293] "annualPET916.263427734375" "annualPET916.294372558594"
## [2295] "annualPET916.309997558594" "annualPET916.416198730469"
## [2297] "annualPET916.494079589844" "annualPET916.530456542969"
## [2299] "annualPET916.671569824219" "annualPET916.932250976562"
## [2301] "annualPET917.002380371094" "annualPET917.004699707031"
## [2303] "annualPET917.026733398438" "annualPET917.105834960938"
## [2305] "annualPET917.109191894531" "annualPET917.114196777344"
## [2307] "annualPET917.148193359375" "annualPET917.164733886719"
## [2309] "annualPET917.210693359375" "annualPET917.219177246094"
## [2311] "annualPET917.311157226562" "annualPET917.338134765625"
## [2313] "annualPET917.360107421875" "annualPET917.395263671875"
## [2315] "annualPET917.413757324219" "annualPET917.42919921875" 
## [2317] "annualPET917.4345703125"   "annualPET917.451232910156"
## [2319] "annualPET917.477844238281" "annualPET917.497863769531"
## [2321] "annualPET917.619323730469" "annualPET917.716796875"   
## [2323] "annualPET917.738647460938" "annualPET917.860290527344"
## [2325] "annualPET917.8935546875"   "annualPET918.029724121094"
## [2327] "annualPET918.058410644531" "annualPET918.082275390625"
## [2329] "annualPET918.187683105469" "annualPET918.229187011719"
## [2331] "annualPET918.327697753906" "annualPET918.345275878906"
## [2333] "annualPET918.372924804688" "annualPET918.408020019531"
## [2335] "annualPET918.427429199219" "annualPET918.578186035156"
## [2337] "annualPET918.760131835938" "annualPET918.78955078125" 
## [2339] "annualPET918.815856933594" "annualPET918.826171875"   
## [2341] "annualPET918.830810546875" "annualPET918.844299316406"
## [2343] "annualPET918.921569824219" "annualPET918.923400878906"
## [2345] "annualPET918.944946289062" "annualPET918.967834472656"
## [2347] "annualPET918.977416992188" "annualPET919.036987304688"
## [2349] "annualPET919.073486328125" "annualPET919.106750488281"
## [2351] "annualPET919.146911621094" "annualPET919.160522460938"
## [2353] "annualPET919.170288085938" "annualPET919.176879882812"
## [2355] "annualPET919.204040527344" "annualPET919.204711914062"
## [2357] "annualPET919.2099609375"   "annualPET919.21484375"    
## [2359] "annualPET919.386169433594" "annualPET919.469421386719"
## [2361] "annualPET919.511169433594" "annualPET919.564208984375"
## [2363] "annualPET919.627319335938" "annualPET919.690490722656"
## [2365] "annualPET919.81591796875"  "annualPET919.818481445312"
## [2367] "annualPET919.857849121094" "annualPET919.894226074219"
## [2369] "annualPET919.913513183594" "annualPET920.005126953125"
## [2371] "annualPET920.030517578125" "annualPET920.072509765625"
## [2373] "annualPET920.109313964844" "annualPET920.112487792969"
## [2375] "annualPET920.138122558594" "annualPET920.145202636719"
## [2377] "annualPET920.234985351562" "annualPET920.283203125"   
## [2379] "annualPET920.311279296875" "annualPET920.375854492188"
## [2381] "annualPET920.41552734375"  "annualPET920.541259765625"
## [2383] "annualPET920.692810058594" "annualPET920.865112304688"
## [2385] "annualPET920.922180175781" "annualPET920.947082519531"
## [2387] "annualPET920.962646484375" "annualPET921.10498046875" 
## [2389] "annualPET921.161865234375" "annualPET921.165283203125"
## [2391] "annualPET921.3876953125"   "annualPET921.40087890625" 
## [2393] "annualPET921.427551269531" "annualPET921.456237792969"
## [2395] "annualPET921.504638671875" "annualPET921.518981933594"
## [2397] "annualPET921.542358398438" "annualPET921.579711914062"
## [2399] "annualPET921.628112792969" "annualPET921.688110351562"
## [2401] "annualPET921.7626953125"   "annualPET921.821716308594"
## [2403] "annualPET921.880432128906" "annualPET921.894226074219"
## [2405] "annualPET921.903564453125" "annualPET921.932922363281"
## [2407] "annualPET921.956970214844" "annualPET921.9697265625"  
## [2409] "annualPET921.975830078125" "annualPET922.0087890625"  
## [2411] "annualPET922.012634277344" "annualPET922.045043945312"
## [2413] "annualPET922.073120117188" "annualPET922.085266113281"
## [2415] "annualPET922.095153808594" "annualPET922.121520996094"
## [2417] "annualPET922.158752441406" "annualPET922.164489746094"
## [2419] "annualPET922.280151367188" "annualPET922.300537109375"
## [2421] "annualPET922.301086425781" "annualPET922.428344726562"
## [2423] "annualPET922.438415527344" "annualPET922.44189453125" 
## [2425] "annualPET922.468444824219" "annualPET922.498901367188"
## [2427] "annualPET922.505187988281" "annualPET922.615173339844"
## [2429] "annualPET922.75439453125"  "annualPET922.909912109375"
## [2431] "annualPET922.9267578125"   "annualPET922.960266113281"
## [2433] "annualPET922.985534667969" "annualPET923.0244140625"  
## [2435] "annualPET923.111083984375" "annualPET923.164672851562"
## [2437] "annualPET923.198547363281" "annualPET923.401489257812"
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## [6453] "annualPET999.489624023438" "annualPET999.499267578125"
## [6455] "annualPET999.508605957031" "annualPET999.521301269531"
## [6457] "annualPET999.558715820312" "annualPET999.622192382812"
## [6459] "annualPET999.643676757812" "annualPET999.681640625"   
## [6461] "annualPET999.682495117188" "annualPET999.68896484375" 
## [6463] "annualPET999.690185546875" "annualPET999.691467285156"
## [6465] "annualPET999.693969726562" "annualPET999.705078125"   
## [6467] "annualPET999.7265625"      "annualPET999.729675292969"
## [6469] "annualPET999.762268066406" "annualPET999.774597167969"
## [6471] "annualPET999.832275390625" "annualPET999.861328125"   
## [6473] "annualPET999.881225585938" "annualPET999.8857421875"  
## [6475] "annualPET999.900390625"    "annualPET999.9072265625"  
## [6477] "annualPET999.919189453125" "annualPET999.931884765625"
## [6479] "annualPET999.938232421875" "annualPET999.963928222656"
## [6481] "annualPET999.994445800781" "annualPET1000.01263427734"
## [6483] "annualPET1000.02001953125" "annualPET1000.06268310547"
## [6485] "annualPET1000.06524658203" "annualPET1000.06890869141"
## [6487] "annualPET1000.10382080078" "annualPET1000.10650634766"
## [6489] "annualPET1000.14813232422" "annualPET1000.16888427734"
## [6491] "annualPET1000.17584228516" "annualPET1000.22613525391"
## [6493] "annualPET1000.33135986328" "annualPET1000.35443115234"
## [6495] "annualPET1000.35717773438" "annualPET1000.37768554688"
## [6497] "annualPET1000.38421630859" "annualPET1000.41491699219"
## [6499] "annualPET1000.41693115234" "annualPET1000.42602539062"
## [6501] "annualPET1000.4462890625"  "annualPET1000.48278808594"
## [6503] "annualPET1000.48773193359" "annualPET1000.52868652344"
## [6505] "annualPET1000.53338623047" "annualPET1000.65289306641"
## [6507] "annualPET1000.6572265625"  "annualPET1000.66058349609"
## [6509] "annualPET1000.66296386719" "annualPET1000.68743896484"
## [6511] "annualPET1000.69036865234" "annualPET1000.69506835938"
## [6513] "annualPET1000.7060546875"  "annualPET1000.71087646484"
## [6515] "annualPET1000.73303222656" "annualPET1000.73492431641"
## [6517] "annualPET1000.74206542969" "annualPET1000.74395751953"
## [6519] "annualPET1000.7568359375"  "annualPET1000.79669189453"
## [6521] "annualPET1000.79919433594" "annualPET1000.80725097656"
## [6523] "annualPET1000.84265136719" "annualPET1000.85943603516"
## [6525] "annualPET1000.90301513672" "annualPET1000.92510986328"
## [6527] "annualPET1000.93927001953" "annualPET1000.939453125"  
## [6529] "annualPET1000.95007324219" "annualPET1000.96173095703"
## [6531] "annualPET1000.97717285156" "annualPET1000.99401855469"
## [6533] "annualPET1001.01751708984" "annualPET1001.05432128906"
## [6535] "annualPET1001.07019042969" "annualPET1001.08288574219"
## [6537] "annualPET1001.08819580078" "annualPET1001.09167480469"
## [6539] "annualPET1001.13641357422" "annualPET1001.17163085938"
## [6541] "annualPET1001.18890380859" "annualPET1001.21630859375"
## [6543] "annualPET1001.26055908203" "annualPET1001.27331542969"
## [6545] "annualPET1001.28607177734" "annualPET1001.296875"     
## [6547] "annualPET1001.34442138672" "annualPET1001.36145019531"
## [6549] "annualPET1001.36987304688" "annualPET1001.38024902344"
## [6551] "annualPET1001.39904785156" "annualPET1001.40515136719"
## [6553] "annualPET1001.41345214844" "annualPET1001.49749755859"
## [6555] "annualPET1001.50164794922" "annualPET1001.50573730469"
## [6557] "annualPET1001.50793457031" "annualPET1001.51861572266"
## [6559] "annualPET1001.52801513672" "annualPET1001.54974365234"
## [6561] "annualPET1001.55297851562" "annualPET1001.56323242188"
## [6563] "annualPET1001.59729003906" "annualPET1001.62982177734"
## [6565] "annualPET1001.64569091797" "annualPET1001.65771484375"
## [6567] "annualPET1001.74737548828" "annualPET1001.76135253906"
## [6569] "annualPET1001.77978515625" "annualPET1001.82208251953"
## [6571] "annualPET1001.83251953125" "annualPET1001.83825683594"
## [6573] "annualPET1001.87182617188" "annualPET1001.88165283203"
## [6575] "annualPET1001.90710449219" "annualPET1001.91174316406"
## [6577] "annualPET1001.91217041016" "annualPET1001.91650390625"
## [6579] "annualPET1001.91912841797" "annualPET1001.96136474609"
## [6581] "annualPET1001.97839355469" "annualPET1001.97894287109"
## [6583] "annualPET1001.98571777344" "annualPET1001.99798583984"
## [6585] "annualPET1002.017578125"   "annualPET1002.03521728516"
## [6587] "annualPET1002.04162597656" "annualPET1002.04602050781"
## [6589] "annualPET1002.04656982422" "annualPET1002.05169677734"
## [6591] "annualPET1002.05627441406" "annualPET1002.09674072266"
## [6593] "annualPET1002.10211181641" "annualPET1002.12512207031"
## [6595] "annualPET1002.17248535156" "annualPET1002.19525146484"
## [6597] "annualPET1002.22552490234" "annualPET1002.27325439453"
## [6599] "annualPET1002.29425048828" "annualPET1002.30950927734"
## [6601] "annualPET1002.32354736328" "annualPET1002.33459472656"
## [6603] "annualPET1002.34423828125" "annualPET1002.35845947266"
## [6605] "annualPET1002.37719726562" "annualPET1002.40557861328"
## [6607] "annualPET1002.41156005859" "annualPET1002.42120361328"
## [6609] "annualPET1002.42504882812" "annualPET1002.43188476562"
## [6611] "annualPET1002.49731445312" "annualPET1002.51379394531"
## [6613] "annualPET1002.52288818359" "annualPET1002.52319335938"
## [6615] "annualPET1002.54272460938" "annualPET1002.54846191406"
## [6617] "annualPET1002.54858398438" "annualPET1002.55096435547"
## [6619] "annualPET1002.55120849609" "annualPET1002.55883789062"
## [6621] "annualPET1002.56414794922" "annualPET1002.60321044922"
## [6623] "annualPET1002.61743164062" "annualPET1002.61901855469"
## [6625] "annualPET1002.62854003906" "annualPET1002.65643310547"
## [6627] "annualPET1002.70709228516" "annualPET1002.7353515625" 
## [6629] "annualPET1002.73760986328" "annualPET1002.76684570312"
## [6631] "annualPET1002.77301025391" "annualPET1002.77429199219"
## [6633] "annualPET1002.77532958984" "annualPET1002.83856201172"
## [6635] "annualPET1002.85284423828" "annualPET1002.88818359375"
## [6637] "annualPET1002.92132568359" "annualPET1002.92724609375"
## [6639] "annualPET1002.93188476562" "annualPET1002.93432617188"
## [6641] "annualPET1002.93542480469" "annualPET1002.98468017578"
## [6643] "annualPET1003.00817871094" "annualPET1003.00982666016"
## [6645] "annualPET1003.01678466797" "annualPET1003.02697753906"
## [6647] "annualPET1003.04229736328" "annualPET1003.07946777344"
## [6649] "annualPET1003.08013916016" "annualPET1003.08203125"   
## [6651] "annualPET1003.10113525391" "annualPET1003.12994384766"
## [6653] "annualPET1003.15753173828" "annualPET1003.16235351562"
## [6655] "annualPET1003.20745849609" "annualPET1003.21392822266"
## [6657] "annualPET1003.25439453125" "annualPET1003.25653076172"
## [6659] "annualPET1003.32086181641" "annualPET1003.32653808594"
## [6661] "annualPET1003.33728027344" "annualPET1003.42950439453"
## [6663] "annualPET1003.43121337891" "annualPET1003.45910644531"
## [6665] "annualPET1003.48138427734" "annualPET1003.4853515625" 
## [6667] "annualPET1003.52526855469" "annualPET1003.52893066406"
## [6669] "annualPET1003.56726074219" "annualPET1003.57067871094"
## [6671] "annualPET1003.57458496094" "annualPET1003.59167480469"
## [6673] "annualPET1003.60473632812" "annualPET1003.61285400391"
## [6675] "annualPET1003.62701416016" "annualPET1003.634765625"  
## [6677] "annualPET1003.63677978516" "annualPET1003.65014648438"
## [6679] "annualPET1003.68402099609" "annualPET1003.72772216797"
## [6681] "annualPET1003.73492431641" "annualPET1003.76629638672"
## [6683] "annualPET1003.76739501953" "annualPET1003.78247070312"
## [6685] "annualPET1003.78540039062" "annualPET1003.78771972656"
## [6687] "annualPET1003.79028320312" "annualPET1003.79522705078"
## [6689] "annualPET1003.7958984375"  "annualPET1003.82147216797"
## [6691] "annualPET1003.83923339844" "annualPET1003.84503173828"
## [6693] "annualPET1003.86798095703" "annualPET1003.86993408203"
## [6695] "annualPET1003.89135742188" "annualPET1003.93273925781"
## [6697] "annualPET1004.05120849609" "annualPET1004.05328369141"
## [6699] "annualPET1004.07000732422" "annualPET1004.12536621094"
## [6701] "annualPET1004.14361572266" "annualPET1004.19732666016"
## [6703] "annualPET1004.21215820312" "annualPET1004.23370361328"
## [6705] "annualPET1004.24743652344" "annualPET1004.25030517578"
## [6707] "annualPET1004.26776123047" "annualPET1004.29064941406"
## [6709] "annualPET1004.30810546875" "annualPET1004.32214355469"
## [6711] "annualPET1004.32269287109" "annualPET1004.34149169922"
## [6713] "annualPET1004.34442138672" "annualPET1004.34735107422"
## [6715] "annualPET1004.50091552734" "annualPET1004.50689697266"
## [6717] "annualPET1004.50982666016" "annualPET1004.53271484375"
## [6719] "annualPET1004.56787109375" "annualPET1004.60491943359"
## [6721] "annualPET1004.63159179688" "annualPET1004.65582275391"
## [6723] "annualPET1004.69525146484" "annualPET1004.7353515625" 
## [6725] "annualPET1004.76208496094" "annualPET1004.78430175781"
## [6727] "annualPET1004.78631591797" "annualPET1004.80731201172"
## [6729] "annualPET1004.83764648438" "annualPET1004.88214111328"
## [6731] "annualPET1004.88745117188" "annualPET1004.90789794922"
## [6733] "annualPET1004.92486572266" "annualPET1004.9375"       
## [6735] "annualPET1004.94268798828" "annualPET1004.94293212891"
## [6737] "annualPET1004.94805908203" "annualPET1004.96411132812"
## [6739] "annualPET1004.96710205078" "annualPET1004.98394775391"
## [6741] "annualPET1005.005859375"   "annualPET1005.00671386719"
## [6743] "annualPET1005.00708007812" "annualPET1005.06024169922"
## [6745] "annualPET1005.09173583984" "annualPET1005.13055419922"
## [6747] "annualPET1005.17272949219" "annualPET1005.17492675781"
## [6749] "annualPET1005.21508789062" "annualPET1005.25256347656"
## [6751] "annualPET1005.26672363281" "annualPET1005.29351806641"
## [6753] "annualPET1005.31121826172" "annualPET1005.31579589844"
## [6755] "annualPET1005.32531738281" "annualPET1005.32647705078"
## [6757] "annualPET1005.35034179688" "annualPET1005.375"        
## [6759] "annualPET1005.38305664062" "annualPET1005.42120361328"
## [6761] "annualPET1005.44458007812" "annualPET1005.46148681641"
## [6763] "annualPET1005.47210693359" "annualPET1005.51153564453"
## [6765] "annualPET1005.52020263672" "annualPET1005.52593994141"
## [6767] "annualPET1005.56109619141" "annualPET1005.59039306641"
## [6769] "annualPET1005.595703125"   "annualPET1005.60205078125"
## [6771] "annualPET1005.64709472656" "annualPET1005.66119384766"
## [6773] "annualPET1005.66534423828" "annualPET1005.67785644531"
## [6775] "annualPET1005.68896484375" "annualPET1005.69927978516"
## [6777] "annualPET1005.80749511719" "annualPET1005.81506347656"
## [6779] "annualPET1005.82202148438" "annualPET1005.85699462891"
## [6781] "annualPET1005.85900878906" "annualPET1005.86468505859"
## [6783] "annualPET1005.87426757812" "annualPET1005.88690185547"
## [6785] "annualPET1005.89965820312" "annualPET1005.90057373047"
## [6787] "annualPET1005.90130615234" "annualPET1005.91064453125"
## [6789] "annualPET1005.94641113281" "annualPET1005.95220947266"
## [6791] "annualPET1005.96838378906" "annualPET1005.97082519531"
## [6793] "annualPET1005.98211669922" "annualPET1006.01019287109"
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## [6797] "annualPET1006.02935791016" "annualPET1006.03479003906"
## [6799] "annualPET1006.04925537109" "annualPET1006.05383300781"
## [6801] "annualPET1006.05780029297" "annualPET1006.10437011719"
## [6803] "annualPET1006.13513183594" "annualPET1006.18768310547"
## [6805] "annualPET1006.20031738281" "annualPET1006.20458984375"
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## [6811] "annualPET1006.26147460938" "annualPET1006.27239990234"
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## [6815] "annualPET1006.28570556641" "annualPET1006.29052734375"
## [6817] "annualPET1006.30963134766" "annualPET1006.32482910156"
## [6819] "annualPET1006.32659912109" "annualPET1006.33575439453"
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## [6823] "annualPET1006.35076904297" "annualPET1006.37426757812"
## [6825] "annualPET1006.37896728516" "annualPET1006.39617919922"
## [6827] "annualPET1006.40014648438" "annualPET1006.43273925781"
## [6829] "annualPET1006.48852539062" "annualPET1006.50897216797"
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## [6833] "annualPET1006.56860351562" "annualPET1006.57958984375"
## [6835] "annualPET1006.59106445312" "annualPET1006.59173583984"
## [6837] "annualPET1006.60699462891" "annualPET1006.609375"     
## [6839] "annualPET1006.62091064453" "annualPET1006.63562011719"
## [6841] "annualPET1006.67797851562" "annualPET1006.71600341797"
## [6843] "annualPET1006.74731445312" "annualPET1006.75207519531"
## [6845] "annualPET1006.76599121094" "annualPET1006.83483886719"
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## [6849] "annualPET1006.91369628906" "annualPET1006.92034912109"
## [6851] "annualPET1006.93334960938" "annualPET1006.94317626953"
## [6853] "annualPET1007.01538085938" "annualPET1007.015625"     
## [6855] "annualPET1007.03375244141" "annualPET1007.04284667969"
## [6857] "annualPET1007.04626464844" "annualPET1007.05682373047"
## [6859] "annualPET1007.06420898438" "annualPET1007.095703125"  
## [6861] "annualPET1007.10864257812" "annualPET1007.11877441406"
## [6863] "annualPET1007.13061523438" "annualPET1007.15649414062"
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## [6867] "annualPET1007.20166015625" "annualPET1007.22015380859"
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## [6873] "annualPET1007.36212158203" "annualPET1007.37377929688"
## [6875] "annualPET1007.37554931641" "annualPET1007.43011474609"
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## [6879] "annualPET1007.48297119141" "annualPET1007.52252197266"
## [6881] "annualPET1007.53326416016" "annualPET1007.54797363281"
## [6883] "annualPET1007.56530761719" "annualPET1007.60815429688"
## [6885] "annualPET1007.61242675781" "annualPET1007.62713623047"
## [6887] "annualPET1007.63494873047" "annualPET1007.63610839844"
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## [6893] "annualPET1007.73693847656" "annualPET1007.75531005859"
## [6895] "annualPET1007.75854492188" "annualPET1007.80847167969"
## [6897] "annualPET1007.8095703125"  "annualPET1007.82922363281"
## [6899] "annualPET1007.87188720703" "annualPET1007.88763427734"
## [6901] "annualPET1007.92608642578" "annualPET1007.94219970703"
## [6903] "annualPET1007.96307373047" "annualPET1007.96575927734"
## [6905] "annualPET1007.97351074219" "annualPET1007.97448730469"
## [6907] "annualPET1008.03515625"    "annualPET1008.04357910156"
## [6909] "annualPET1008.06488037109" "annualPET1008.07000732422"
## [6911] "annualPET1008.07043457031" "annualPET1008.08148193359"
## [6913] "annualPET1008.10247802734" "annualPET1008.13665771484"
## [6915] "annualPET1008.15057373047" "annualPET1008.15081787109"
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## [6919] "annualPET1008.19476318359" "annualPET1008.20135498047"
## [6921] "annualPET1008.20520019531" "annualPET1008.21496582031"
## [6923] "annualPET1008.2265625"     "annualPET1008.23614501953"
## [6925] "annualPET1008.244140625"   "annualPET1008.24987792969"
## [6927] "annualPET1008.26428222656" "annualPET1008.3076171875" 
## [6929] "annualPET1008.3232421875"  "annualPET1008.34387207031"
## [6931] "annualPET1008.35015869141" "annualPET1008.35314941406"
## [6933] "annualPET1008.42486572266" "annualPET1008.42572021484"
## [6935] "annualPET1008.42736816406" "annualPET1008.458984375"  
## [6937] "annualPET1008.47906494141" "annualPET1008.484375"     
## [6939] "annualPET1008.48822021484" "annualPET1008.49676513672"
## [6941] "annualPET1008.52496337891" "annualPET1008.53021240234"
## [6943] "annualPET1008.54541015625" "annualPET1008.54730224609"
## [6945] "annualPET1008.609375"      "annualPET1008.61004638672"
## [6947] "annualPET1008.6103515625"  "annualPET1008.66235351562"
## [6949] "annualPET1008.67840576172" "annualPET1008.68017578125"
## [6951] "annualPET1008.69287109375" "annualPET1008.75146484375"
## [6953] "annualPET1008.75659179688" "annualPET1008.76751708984"
## [6955] "annualPET1008.82702636719" "annualPET1008.85296630859"
## [6957] "annualPET1008.85510253906" "annualPET1008.86944580078"
## [6959] "annualPET1008.88256835938" "annualPET1008.88659667969"
## [6961] "annualPET1008.91577148438" "annualPET1008.92864990234"
## [6963] "annualPET1008.93389892578" "annualPET1008.93713378906"
## [6965] "annualPET1008.94122314453" "annualPET1008.955078125"  
## [6967] "annualPET1008.95599365234" "annualPET1008.98498535156"
## [6969] "annualPET1009.00671386719" "annualPET1009.01275634766"
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## [7473] "annualPET1018.91656494141" "annualPET1018.95721435547"
## [7475] "annualPET1018.96746826172" "annualPET1018.97241210938"
## [7477] "annualPET1018.98376464844" "annualPET1018.98913574219"
## [7479] "annualPET1019.00219726562" "annualPET1019.00659179688"
## [7481] "annualPET1019.04943847656" "annualPET1019.05102539062"
## [7483] "annualPET1019.09454345703" "annualPET1019.13250732422"
## [7485] "annualPET1019.16986083984" "annualPET1019.20306396484"
## [7487] "annualPET1019.21887207031" "annualPET1019.25457763672"
## [7489] "annualPET1019.3427734375"  "annualPET1019.36944580078"
## [7491] "annualPET1019.39617919922" "annualPET1019.45623779297"
## [7493] "annualPET1019.47680664062" "annualPET1019.47747802734"
## [7495] "annualPET1019.53161621094" "annualPET1019.69622802734"
## [7497] "annualPET1019.74273681641" "annualPET1019.75823974609"
## [7499] "annualPET1019.77423095703" "annualPET1019.85144042969"
## [7501] "annualPET1019.88629150391" "annualPET1019.89471435547"
## [7503] "annualPET1019.93969726562" "annualPET1019.95587158203"
## [7505] "annualPET1019.99792480469" "annualPET1019.99835205078"
## [7507] "annualPET1020.00244140625" "annualPET1020.02709960938"
## [7509] "annualPET1020.03997802734" "annualPET1020.05004882812"
## [7511] "annualPET1020.08221435547" "annualPET1020.08471679688"
## [7513] "annualPET1020.16345214844" "annualPET1020.18908691406"
## [7515] "annualPET1020.24072265625" "annualPET1020.2431640625" 
## [7517] "annualPET1020.24627685547" "annualPET1020.2587890625" 
## [7519] "annualPET1020.32440185547" "annualPET1020.32861328125"
## [7521] "annualPET1020.37567138672" "annualPET1020.37908935547"
## [7523] "annualPET1020.38934326172" "annualPET1020.41448974609"
## [7525] "annualPET1020.41552734375" "annualPET1020.44793701172"
## [7527] "annualPET1020.47601318359" "annualPET1020.49432373047"
## [7529] "annualPET1020.52423095703" "annualPET1020.53948974609"
## [7531] "annualPET1020.57739257812" "annualPET1020.59368896484"
## [7533] "annualPET1020.61376953125" "annualPET1020.63104248047"
## [7535] "annualPET1020.70037841797" "annualPET1020.73767089844"
## [7537] "annualPET1020.7578125"     "annualPET1020.75836181641"
## [7539] "annualPET1020.84515380859" "annualPET1020.85656738281"
## [7541] "annualPET1020.86047363281" "annualPET1020.86572265625"
## [7543] "annualPET1020.90008544922" "annualPET1020.90014648438"
## [7545] "annualPET1020.90325927734" "annualPET1020.91314697266"
## [7547] "annualPET1020.91497802734" "annualPET1020.9296875"    
## [7549] "annualPET1020.93310546875" "annualPET1020.939453125"  
## [7551] "annualPET1020.96954345703" "annualPET1021.01593017578"
## [7553] "annualPET1021.02331542969" "annualPET1021.04455566406"
## [7555] "annualPET1021.04705810547" "annualPET1021.08892822266"
## [7557] "annualPET1021.13427734375" "annualPET1021.17840576172"
## [7559] "annualPET1021.20965576172" "annualPET1021.29406738281"
## [7561] "annualPET1021.29974365234" "annualPET1021.49774169922"
## [7563] "annualPET1021.61737060547" "annualPET1021.62689208984"
## [7565] "annualPET1021.63616943359" "annualPET1021.68096923828"
## [7567] "annualPET1021.68225097656" "annualPET1021.75286865234"
## [7569] "annualPET1021.77124023438" "annualPET1021.77697753906"
## [7571] "annualPET1021.85241699219" "annualPET1021.86047363281"
## [7573] "annualPET1021.87829589844" "annualPET1021.88208007812"
## [7575] "annualPET1021.92755126953" "annualPET1021.93560791016"
## [7577] "annualPET1021.94921875"    "annualPET1021.98675537109"
## [7579] "annualPET1022.00756835938" "annualPET1022.02966308594"
## [7581] "annualPET1022.10113525391" "annualPET1022.10955810547"
## [7583] "annualPET1022.12176513672" "annualPET1022.17523193359"
## [7585] "annualPET1022.20050048828" "annualPET1022.23193359375"
## [7587] "annualPET1022.33636474609" "annualPET1022.42803955078"
## [7589] "annualPET1022.48248291016" "annualPET1022.50482177734"
## [7591] "annualPET1022.50817871094" "annualPET1022.53112792969"
## [7593] "annualPET1022.552734375"   "annualPET1022.60394287109"
## [7595] "annualPET1022.77008056641" "annualPET1022.78747558594"
## [7597] "annualPET1022.8212890625"  "annualPET1022.82421875"   
## [7599] "annualPET1022.94146728516" "annualPET1023.12390136719"
## [7601] "annualPET1023.15484619141" "annualPET1023.17150878906"
## [7603] "annualPET1023.27954101562" "annualPET1023.44799804688"
## [7605] "annualPET1023.46630859375" "annualPET1023.48156738281"
## [7607] "annualPET1023.48590087891" "annualPET1023.50708007812"
## [7609] "annualPET1023.533203125"   "annualPET1023.5419921875" 
## [7611] "annualPET1023.59741210938" "annualPET1023.60302734375"
## [7613] "annualPET1023.63098144531" "annualPET1023.64111328125"
## [7615] "annualPET1023.67492675781" "annualPET1023.78454589844"
## [7617] "annualPET1023.82373046875" "annualPET1023.87274169922"
## [7619] "annualPET1024.03515625"    "annualPET1024.13403320312"
## [7621] "annualPET1024.16516113281" "annualPET1024.19738769531"
## [7623] "annualPET1024.2109375"     "annualPET1024.37829589844"
## [7625] "annualPET1024.38610839844" "annualPET1024.42749023438"
## [7627] "annualPET1024.45959472656" "annualPET1024.4833984375" 
## [7629] "annualPET1024.63269042969" "annualPET1024.71032714844"
## [7631] "annualPET1024.79772949219" "annualPET1024.86767578125"
## [7633] "annualPET1024.90502929688" "annualPET1024.96411132812"
## [7635] "annualPET1024.96630859375" "annualPET1025.02355957031"
## [7637] "annualPET1025.04907226562" "annualPET1025.14477539062"
## [7639] "annualPET1025.17797851562" "annualPET1025.19152832031"
## [7641] "annualPET1025.21179199219" "annualPET1025.21997070312"
## [7643] "annualPET1025.23449707031" "annualPET1025.24816894531"
## [7645] "annualPET1025.29907226562" "annualPET1025.45812988281"
## [7647] "annualPET1025.49560546875" "annualPET1025.58227539062"
## [7649] "annualPET1025.67443847656" "annualPET1025.76574707031"
## [7651] "annualPET1025.8681640625"  "annualPET1025.97509765625"
## [7653] "annualPET1025.98620605469" "annualPET1026.02392578125"
## [7655] "annualPET1026.078125"      "annualPET1026.08850097656"
## [7657] "annualPET1026.16223144531" "annualPET1026.17419433594"
## [7659] "annualPET1026.19055175781" "annualPET1026.28344726562"
## [7661] "annualPET1026.3017578125"  "annualPET1026.30615234375"
## [7663] "annualPET1026.63610839844" "annualPET1026.66870117188"
## [7665] "annualPET1026.79736328125" "annualPET1026.85144042969"
## [7667] "annualPET1026.86096191406" "annualPET1026.86291503906"
## [7669] "annualPET1026.89782714844" "annualPET1026.90991210938"
## [7671] "annualPET1026.947265625"   "annualPET1027.33422851562"
## [7673] "annualPET1027.36596679688" "annualPET1027.39514160156"
## [7675] "annualPET1027.66162109375" "annualPET1027.72668457031"
## [7677] "annualPET1027.78515625"    "annualPET1027.85485839844"
## [7679] "annualPET1028.01135253906" "annualPET1028.14294433594"
## [7681] "annualPET1028.17883300781" "annualPET1028.18273925781"
## [7683] "annualPET1028.24755859375" "annualPET1028.27075195312"
## [7685] "annualPET1028.4951171875"  "annualPET1028.60339355469"
## [7687] "annualPET1028.70190429688" "annualPET1028.79748535156"
## [7689] "annualPET1028.9560546875"  "annualPET1029.12768554688"
## [7691] "annualPET1029.14184570312" "annualPET1029.16333007812"
## [7693] "annualPET1029.28381347656" "annualPET1029.38244628906"
## [7695] "annualPET1029.61877441406" "annualPET1029.67663574219"
## [7697] "annualPET1029.70935058594" "annualPET1029.78625488281"
## [7699] "annualPET1029.9609375"     "annualPET1030.01293945312"
## [7701] "annualPET1030.05419921875" "annualPET1030.05554199219"
## [7703] "annualPET1030.1015625"     "annualPET1030.14758300781"
## [7705] "annualPET1030.15100097656" "annualPET1030.17211914062"
## [7707] "annualPET1030.33935546875" "annualPET1030.42810058594"
## [7709] "annualPET1030.99304199219" "annualPET1031.16845703125"
## [7711] "annualPET1031.20434570312" "annualPET1031.23254394531"
## [7713] "annualPET1031.392578125"   "annualPET1031.45971679688"
## [7715] "annualPET1031.54333496094" "annualPET1031.55114746094"
## [7717] "annualPET1031.69714355469" "annualPET1031.71179199219"
## [7719] "annualPET1031.78894042969" "annualPET1031.88110351562"
## [7721] "annualPET1031.88842773438" "annualPET1031.92102050781"
## [7723] "annualPET1031.97448730469" "annualPET1032.015625"     
## [7725] "annualPET1032.06091308594" "annualPET1032.12622070312"
## [7727] "annualPET1032.46325683594" "annualPET1032.484375"     
## [7729] "annualPET1032.49853515625" "annualPET1032.56372070312"
## [7731] "annualPET1032.58959960938" "annualPET1032.611328125"  
## [7733] "annualPET1032.64318847656" "annualPET1032.70727539062"
## [7735] "annualPET1032.74694824219" "annualPET1032.99377441406"
## [7737] "annualPET1033.06408691406" "annualPET1033.08874511719"
## [7739] "annualPET1033.17724609375" "annualPET1033.24829101562"
## [7741] "annualPET1033.51403808594" "annualPET1033.82666015625"
## [7743] "annualPET1034.13305664062" "annualPET1034.19311523438"
## [7745] "annualPET1034.77819824219" "annualPET1034.8046875"    
## [7747] "annualPET1035.01147460938" "annualPET1035.0537109375" 
## [7749] "annualPET1035.08459472656" "annualPET1035.18420410156"
## [7751] "annualPET1035.44494628906" "annualPET1035.51940917969"
## [7753] "annualPET1035.78784179688" "annualPET1035.82250976562"
## [7755] "annualPET1035.84338378906" "annualPET1036.05212402344"
## [7757] "annualPET1036.06530761719" "annualPET1036.10534667969"
## [7759] "annualPET1036.60107421875" "annualPET1036.72607421875"
## [7761] "annualPET1036.78674316406" "annualPET1036.81372070312"
## [7763] "annualPET1037.29040527344" "annualPET1037.40075683594"
## [7765] "annualPET1037.49597167969" "annualPET1037.51416015625"
## [7767] "annualPET1037.9130859375"  "annualPET1038.03637695312"
## [7769] "annualPET1038.04809570312" "annualPET1038.09997558594"
## [7771] "annualPET1038.17065429688" "annualPET1038.45361328125"
## [7773] "annualPET1038.51892089844" "annualPET1038.52416992188"
## [7775] "annualPET1038.69287109375" "annualPET1038.75854492188"
## [7777] "annualPET1038.76672363281" "annualPET1038.77185058594"
## [7779] "annualPET1038.88757324219" "annualPET1039.12463378906"
## [7781] "annualPET1039.37707519531" "annualPET1039.45129394531"
## [7783] "annualPET1039.45776367188" "annualPET1039.4775390625" 
## [7785] "annualPET1039.80932617188" "annualPET1039.84143066406"
## [7787] "annualPET1040.03063964844" "annualPET1040.03991699219"
## [7789] "annualPET1040.17541503906" "annualPET1040.62670898438"
## [7791] "annualPET1041.09033203125"
# convert annualPET column to dummy, the result is a matrix
# to have one column per category we had to add -1 to the formula
annualPET_dummy <- model.matrix(~annualPET -1, data = nj.SOC@data)
# convert the matrix to a data.frame
annualPET_dummy <- as.data.frame(annualPET_dummy)

nj.SOC@data <- cbind(nj.SOC@data, annualPET_dummy)

nj.SOC@data <- nj.SOC@data[,-(1:2)]
names(nj.SOC@data)
##  [1] "SOC"                      "CRFVOL"                  
##  [3] "OCSKGM"                   "annualPET"               
##  [5] "aridityIndexThornthwaite" "climaticMoistureIndex"   
##  [7] "continentality"           "embergerQ"               
##  [9] "growingDegDays0"          "growingDegDays5"         
## [11] "maxTempColdest"           "meanTempColdest"         
## [13] "meanTempWarmest"          "minTempWarmest"          
## [15] "monthCountByTemp10"       "PETColdestQuarter"       
## [17] "PETDriestQuarter"         "PETseasonality"          
## [19] "PETWarmestQuarter"        "PETWettestQuarter"       
## [21] "thermicityIndex"          "optional"                
## [23] "annualPET.1"
library(e1071)
library(caret)
# Fitting a svm model and parameter tuning

#  Test different values of epsilon and cost
# tuneResult <- tune(svm, OCSKGM ~., data = nj.SOC@data[,c("OCSKGM", names(COV))],
#         ranges = list(epsilon = seq(0.1,0.2,0.02), cost = c(5,7,15,20)))
# 
# 
# plot(tuneResult)