Variables
- O3: Ozone concentration (parts per million)
- vh: Vandenburg 500 millibar height (in)
- wind: wind speed (mph)
- humidity: humidty (Percent)
- temp: temperature (Celsius)
- dpg: Pressure gradient (mmhg)
- ibt: Inversion base temperature (Fahrenheit)
- vis: visibility (miles)
- doy: day of year
(1) Use the training data set to build a regression tree with ozone (O3) as the outcome.
set.seed(2634)
#Split the data into two parts
ind <- sample(1:dim(train)[1], 200, replace = FALSE)
df.train <- train[ind,]
df.test <- train[-ind,]
# Grow tree with rpart
redwood <- rpart(O3 ~ ., method = "class", data = df.train)
# Grow tree with tree
oak <- tree(O3 ~ ., data = df.train)
pruned.oak <- prune.tree(oak)Visualizing/Analyzing Trees: rpart package
# rpart package
# detailed summary of splits
summary(redwood) ## Call:
## rpart(formula = O3 ~ ., data = df.train, method = "class")
## n= 200
##
## CP nsplit rel error xerror xstd
## 1 0.03314917 0 1.0000000 1.060773 0.01531095
## 2 0.02762431 1 0.9668508 1.066298 0.01435933
## 3 0.02209945 2 0.9392265 1.066298 0.01435933
## 4 0.01841621 4 0.8950276 1.060773 0.01531095
## 5 0.01657459 7 0.8397790 1.066298 0.01435933
## 6 0.01104972 13 0.7403315 1.049724 0.01702877
## 7 0.01000000 15 0.7182320 1.060773 0.01531095
##
## Variable importance
## ibt temp vh ID doy ibh humidity wind
## 19 16 15 11 10 9 8 6
## dpg
## 6
##
## Node number 1: 200 observations, complexity param=0.03314917
## predicted class=4 expected loss=0.905 P(node) =1
## class counts: 2 6 17 19 14 12 13 4 10 10 9 10 5 7 3 6 6 4 5 5 2 3 4 4 2 6 2 3 2 2 2 1
## probabilities: 0.010 0.030 0.085 0.095 0.070 0.060 0.065 0.020 0.050 0.050 0.045 0.050 0.025 0.035 0.015 0.030 0.030 0.020 0.025 0.025 0.010 0.015 0.020 0.020 0.010 0.030 0.010 0.015 0.010 0.010 0.010 0.005
## left son=2 (104 obs) right son=3 (96 obs)
## Primary splits:
## temp < 62.5 to the left, improve=5.206154, (0 missing)
## ibh < 3573.5 to the right, improve=4.603695, (0 missing)
## ibt < 137 to the left, improve=4.291239, (0 missing)
## humidity < 27.5 to the left, improve=3.693333, (0 missing)
## dpg < -19.5 to the left, improve=3.599116, (0 missing)
## Surrogate splits:
## ibt < 159 to the left, agree=0.835, adj=0.656, (0 split)
## vh < 5775 to the left, agree=0.780, adj=0.542, (0 split)
## ibh < 2043.5 to the right, agree=0.750, adj=0.479, (0 split)
## ID < 102.5 to the left, agree=0.705, adj=0.385, (0 split)
## doy < 138.5 to the left, agree=0.705, adj=0.385, (0 split)
##
## Node number 2: 104 observations, complexity param=0.02209945
## predicted class=4 expected loss=0.8269231 P(node) =0.52
## class counts: 2 6 17 18 8 10 12 4 6 5 4 6 3 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.019 0.058 0.163 0.173 0.077 0.096 0.115 0.038 0.058 0.048 0.038 0.058 0.029 0.000 0.010 0.010 0.010 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## left son=4 (8 obs) right son=5 (96 obs)
## Primary splits:
## ibt < 32 to the left, improve=2.549679, (0 missing)
## dpg < -20 to the left, improve=2.312375, (0 missing)
## vis < 75 to the right, improve=2.044748, (0 missing)
## humidity < 29 to the left, improve=2.014957, (0 missing)
## ID < 17.5 to the left, improve=1.995659, (0 missing)
## Surrogate splits:
## vh < 5475 to the left, agree=0.962, adj=0.500, (0 split)
## temp < 35.5 to the left, agree=0.952, adj=0.375, (0 split)
##
## Node number 3: 96 observations, complexity param=0.02762431
## predicted class=14 expected loss=0.9270833 P(node) =0.48
## class counts: 0 0 0 1 6 2 1 0 4 5 5 4 2 7 2 5 5 4 5 5 2 3 4 4 2 6 2 3 2 2 2 1
## probabilities: 0.000 0.000 0.000 0.010 0.062 0.021 0.010 0.000 0.042 0.052 0.052 0.042 0.021 0.073 0.021 0.052 0.052 0.042 0.052 0.052 0.021 0.031 0.042 0.042 0.021 0.062 0.021 0.031 0.021 0.021 0.021 0.010
## left son=6 (20 obs) right son=7 (76 obs)
## Primary splits:
## ibt < 175.5 to the left, improve=2.550000, (0 missing)
## ibh < 3591.5 to the right, improve=2.271073, (0 missing)
## temp < 65.5 to the left, improve=2.234211, (0 missing)
## vh < 5755 to the left, improve=1.887007, (0 missing)
## vis < 145 to the right, improve=1.750000, (0 missing)
## Surrogate splits:
## ibh < 3016 to the right, agree=0.906, adj=0.55, (0 split)
## vh < 5755 to the left, agree=0.885, adj=0.45, (0 split)
## humidity < 20.5 to the left, agree=0.812, adj=0.10, (0 split)
## dpg < 58.5 to the right, agree=0.812, adj=0.10, (0 split)
## ID < 23.5 to the left, agree=0.802, adj=0.05, (0 split)
##
## Node number 4: 8 observations
## predicted class=4 expected loss=0.375 P(node) =0.04
## class counts: 0 0 3 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.000 0.375 0.625 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
##
## Node number 5: 96 observations, complexity param=0.02209945
## predicted class=3 expected loss=0.8541667 P(node) =0.48
## class counts: 2 6 14 13 8 10 12 4 6 5 4 6 3 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.021 0.062 0.146 0.135 0.083 0.104 0.125 0.042 0.062 0.052 0.042 0.062 0.031 0.000 0.010 0.010 0.010 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## left son=10 (31 obs) right son=11 (65 obs)
## Primary splits:
## dpg < -20 to the left, improve=3.141884, (0 missing)
## humidity < 29 to the left, improve=2.947917, (0 missing)
## ID < 272 to the right, improve=2.354167, (0 missing)
## doy < 326 to the right, improve=2.354167, (0 missing)
## vh < 5745 to the right, improve=2.149539, (0 missing)
## Surrogate splits:
## humidity < 26.5 to the left, agree=0.906, adj=0.710, (0 split)
## vh < 5805 to the right, agree=0.781, adj=0.323, (0 split)
## ID < 286.5 to the right, agree=0.771, adj=0.290, (0 split)
## doy < 344.5 to the right, agree=0.771, adj=0.290, (0 split)
## wind < 2.5 to the left, agree=0.740, adj=0.194, (0 split)
##
## Node number 6: 20 observations
## predicted class=5 expected loss=0.7 P(node) =0.1
## class counts: 0 0 0 1 6 0 0 0 1 3 2 1 0 2 0 3 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.000 0.000 0.050 0.300 0.000 0.000 0.000 0.050 0.150 0.100 0.050 0.000 0.100 0.000 0.150 0.000 0.000 0.050 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
##
## Node number 7: 76 observations, complexity param=0.01841621
## predicted class=26 expected loss=0.9210526 P(node) =0.38
## class counts: 0 0 0 0 0 2 1 0 3 2 3 3 2 5 2 2 5 4 4 5 2 3 4 4 2 6 2 3 2 2 2 1
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.026 0.013 0.000 0.039 0.026 0.039 0.039 0.026 0.066 0.026 0.026 0.066 0.053 0.053 0.066 0.026 0.039 0.053 0.053 0.026 0.079 0.026 0.039 0.026 0.026 0.026 0.013
## left son=14 (7 obs) right son=15 (69 obs)
## Primary splits:
## ID < 89.5 to the left, improve=1.791925, (0 missing)
## doy < 125.5 to the left, improve=1.791925, (0 missing)
## temp < 79.5 to the left, improve=1.703228, (0 missing)
## ibh < 539 to the right, improve=1.693443, (0 missing)
## ibt < 233.5 to the left, improve=1.661111, (0 missing)
## Surrogate splits:
## doy < 125.5 to the left, agree=1.000, adj=1.000, (0 split)
## temp < 63.5 to the left, agree=0.947, adj=0.429, (0 split)
## humidity < 35 to the left, agree=0.934, adj=0.286, (0 split)
## ibt < 193 to the left, agree=0.921, adj=0.143, (0 split)
##
## Node number 10: 31 observations, complexity param=0.01657459
## predicted class=3 expected loss=0.6774194 P(node) =0.155
## class counts: 0 1 10 8 4 4 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.032 0.323 0.258 0.129 0.129 0.032 0.032 0.000 0.032 0.032 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## left son=20 (24 obs) right son=21 (7 obs)
## Primary splits:
## vh < 5715 to the right, improve=2.063748, (0 missing)
## ID < 46.5 to the right, improve=1.879765, (0 missing)
## doy < 80.5 to the right, improve=1.879765, (0 missing)
## temp < 50.5 to the right, improve=1.526230, (0 missing)
## dpg < -39 to the left, improve=1.053944, (0 missing)
## Surrogate splits:
## ibt < 98.5 to the right, agree=0.903, adj=0.571, (0 split)
## ID < 317.5 to the left, agree=0.839, adj=0.286, (0 split)
## humidity < 29.5 to the left, agree=0.839, adj=0.286, (0 split)
## doy < 375.5 to the left, agree=0.839, adj=0.286, (0 split)
## dpg < -25.5 to the left, agree=0.806, adj=0.143, (0 split)
##
## Node number 11: 65 observations, complexity param=0.01657459
## predicted class=7 expected loss=0.8307692 P(node) =0.325
## class counts: 2 5 4 5 4 6 11 3 6 4 3 6 3 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.031 0.077 0.062 0.077 0.062 0.092 0.169 0.046 0.092 0.062 0.046 0.092 0.046 0.000 0.015 0.015 0.015 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## left son=22 (28 obs) right son=23 (37 obs)
## Primary splits:
## temp < 52 to the left, improve=2.276270, (0 missing)
## humidity < 68.5 to the right, improve=2.098593, (0 missing)
## ibt < 153 to the left, improve=2.065651, (0 missing)
## wind < 7.5 to the right, improve=1.968321, (0 missing)
## vh < 5575 to the left, improve=1.830390, (0 missing)
## Surrogate splits:
## vh < 5685 to the left, agree=0.800, adj=0.536, (0 split)
## ibt < 86.5 to the left, agree=0.785, adj=0.500, (0 split)
## ID < 283 to the right, agree=0.646, adj=0.179, (0 split)
## wind < 8.5 to the right, agree=0.646, adj=0.179, (0 split)
## doy < 341 to the right, agree=0.646, adj=0.179, (0 split)
##
## Node number 14: 7 observations
## predicted class=9 expected loss=0.5714286 P(node) =0.035
## class counts: 0 0 0 0 0 0 0 0 3 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.429 0.143 0.143 0.143 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.143 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
##
## Node number 15: 69 observations, complexity param=0.01841621
## predicted class=26 expected loss=0.9130435 P(node) =0.345
## class counts: 0 0 0 0 0 2 1 0 0 1 2 2 2 5 2 2 5 4 4 5 2 3 4 3 2 6 2 3 2 2 2 1
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.029 0.014 0.000 0.000 0.014 0.029 0.029 0.029 0.072 0.029 0.029 0.072 0.058 0.058 0.072 0.029 0.043 0.058 0.043 0.029 0.087 0.029 0.043 0.029 0.029 0.029 0.014
## left son=30 (58 obs) right son=31 (11 obs)
## Primary splits:
## ibh < 537.5 to the right, improve=1.888101, (0 missing)
## ibt < 233.5 to the left, improve=1.756814, (0 missing)
## temp < 79.5 to the left, improve=1.651424, (0 missing)
## ID < 255 to the right, improve=1.588259, (0 missing)
## doy < 309 to the right, improve=1.588259, (0 missing)
## Surrogate splits:
## dpg < -30.5 to the right, agree=0.870, adj=0.182, (0 split)
## vh < 5915 to the left, agree=0.855, adj=0.091, (0 split)
## humidity < 39.5 to the right, agree=0.855, adj=0.091, (0 split)
## ibt < 295.5 to the left, agree=0.855, adj=0.091, (0 split)
##
## Node number 20: 24 observations, complexity param=0.01104972
## predicted class=3 expected loss=0.5833333 P(node) =0.12
## class counts: 0 1 10 5 3 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.042 0.417 0.208 0.125 0.042 0.042 0.042 0.000 0.042 0.042 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## left son=40 (12 obs) right son=41 (12 obs)
## Primary splits:
## ID < 294.5 to the right, improve=2.166667, (0 missing)
## doy < 352.5 to the right, improve=2.166667, (0 missing)
## ibt < 178.5 to the left, improve=1.416667, (0 missing)
## temp < 57.5 to the left, improve=1.393557, (0 missing)
## ibh < 1648 to the right, improve=1.158263, (0 missing)
## Surrogate splits:
## doy < 352.5 to the right, agree=1.000, adj=1.000, (0 split)
## temp < 53.5 to the left, agree=0.875, adj=0.750, (0 split)
## wind < 4.5 to the left, agree=0.750, adj=0.500, (0 split)
## humidity < 20 to the left, agree=0.667, adj=0.333, (0 split)
## ibt < 173 to the left, agree=0.667, adj=0.333, (0 split)
##
## Node number 21: 7 observations
## predicted class=4 expected loss=0.5714286 P(node) =0.035
## class counts: 0 0 0 3 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.000 0.000 0.429 0.143 0.429 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
##
## Node number 22: 28 observations, complexity param=0.01657459
## predicted class=7 expected loss=0.75 P(node) =0.14
## class counts: 2 4 3 1 1 3 7 3 0 0 3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.071 0.143 0.107 0.036 0.036 0.107 0.250 0.107 0.000 0.000 0.107 0.000 0.036 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## left son=44 (13 obs) right son=45 (15 obs)
## Primary splits:
## humidity < 60 to the right, improve=2.419780, (0 missing)
## vh < 5575 to the left, improve=1.571429, (0 missing)
## wind < 6.5 to the right, improve=1.476190, (0 missing)
## ibt < 72 to the left, improve=1.476190, (0 missing)
## ID < 60.5 to the left, improve=1.464495, (0 missing)
## Surrogate splits:
## ID < 58 to the left, agree=0.750, adj=0.462, (0 split)
## doy < 93.5 to the left, agree=0.750, adj=0.462, (0 split)
## vh < 5575 to the left, agree=0.643, adj=0.231, (0 split)
## wind < 8 to the right, agree=0.643, adj=0.231, (0 split)
## dpg < -1 to the right, agree=0.643, adj=0.231, (0 split)
##
## Node number 23: 37 observations, complexity param=0.01657459
## predicted class=9 expected loss=0.8378378 P(node) =0.185
## class counts: 0 1 1 4 3 3 4 0 6 4 0 6 2 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.027 0.027 0.108 0.081 0.081 0.108 0.000 0.162 0.108 0.000 0.162 0.054 0.000 0.027 0.027 0.027 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## left son=46 (16 obs) right son=47 (21 obs)
## Primary splits:
## wind < 5.5 to the right, improve=2.467503, (0 missing)
## ibt < 153 to the left, improve=1.723323, (0 missing)
## ibh < 3354 to the right, improve=1.438792, (0 missing)
## temp < 55.5 to the left, improve=1.366421, (0 missing)
## humidity < 74.5 to the right, improve=1.354613, (0 missing)
## Surrogate splits:
## ibh < 3026 to the right, agree=0.703, adj=0.313, (0 split)
## ibt < 94.5 to the left, agree=0.676, adj=0.250, (0 split)
## ID < 80.5 to the right, agree=0.649, adj=0.188, (0 split)
## vh < 5695 to the left, agree=0.649, adj=0.188, (0 split)
## humidity < 49.5 to the left, agree=0.649, adj=0.188, (0 split)
##
## Node number 30: 58 observations, complexity param=0.01841621
## predicted class=26 expected loss=0.8965517 P(node) =0.29
## class counts: 0 0 0 0 0 1 1 0 0 1 1 2 2 5 2 2 5 2 4 5 2 2 4 3 2 6 1 0 2 2 0 1
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.017 0.017 0.000 0.000 0.017 0.017 0.034 0.034 0.086 0.034 0.034 0.086 0.034 0.069 0.086 0.034 0.034 0.069 0.052 0.034 0.103 0.017 0.000 0.034 0.034 0.000 0.017
## left son=60 (33 obs) right son=61 (25 obs)
## Primary splits:
## ibt < 233.5 to the left, improve=1.880752, (0 missing)
## humidity < 68.5 to the left, improve=1.780950, (0 missing)
## vh < 5855 to the left, improve=1.724095, (0 missing)
## temp < 79.5 to the left, improve=1.724095, (0 missing)
## ibh < 1157.5 to the right, improve=1.684246, (0 missing)
## Surrogate splits:
## vh < 5845 to the left, agree=0.862, adj=0.68, (0 split)
## temp < 79.5 to the left, agree=0.862, adj=0.68, (0 split)
## ibh < 1115 to the right, agree=0.724, adj=0.36, (0 split)
## humidity < 79.5 to the left, agree=0.638, adj=0.16, (0 split)
## dpg < 40.5 to the right, agree=0.638, adj=0.16, (0 split)
##
## Node number 31: 11 observations
## predicted class=28 expected loss=0.7272727 P(node) =0.055
## class counts: 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 1 3 0 0 2 0
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.091 0.000 0.000 0.000 0.000 0.091 0.000 0.000 0.000 0.000 0.000 0.000 0.182 0.000 0.000 0.000 0.091 0.000 0.000 0.000 0.000 0.091 0.273 0.000 0.000 0.182 0.000
##
## Node number 40: 12 observations
## predicted class=3 expected loss=0.3333333 P(node) =0.06
## class counts: 0 1 8 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.083 0.667 0.083 0.167 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
##
## Node number 41: 12 observations
## predicted class=4 expected loss=0.6666667 P(node) =0.06
## class counts: 0 0 2 4 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.000 0.167 0.333 0.083 0.083 0.083 0.083 0.000 0.083 0.083 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
##
## Node number 44: 13 observations
## predicted class=2 expected loss=0.7692308 P(node) =0.065
## class counts: 2 3 2 0 1 2 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.154 0.231 0.154 0.000 0.077 0.154 0.000 0.000 0.000 0.000 0.154 0.000 0.077 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
##
## Node number 45: 15 observations
## predicted class=7 expected loss=0.5333333 P(node) =0.075
## class counts: 0 1 1 1 0 1 7 3 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.067 0.067 0.067 0.000 0.067 0.467 0.200 0.000 0.000 0.067 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
##
## Node number 46: 16 observations
## predicted class=4 expected loss=0.75 P(node) =0.08
## class counts: 0 0 1 4 1 0 4 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.000 0.062 0.250 0.062 0.000 0.250 0.000 0.188 0.188 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
##
## Node number 47: 21 observations
## predicted class=12 expected loss=0.7142857 P(node) =0.105
## class counts: 0 1 0 0 2 3 0 0 3 1 0 6 2 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.048 0.000 0.000 0.095 0.143 0.000 0.000 0.143 0.048 0.000 0.286 0.095 0.000 0.048 0.048 0.048 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
##
## Node number 60: 33 observations, complexity param=0.01657459
## predicted class=14 expected loss=0.8787879 P(node) =0.165
## class counts: 0 0 0 0 0 1 1 0 0 1 1 2 2 4 1 2 4 2 2 4 1 1 1 0 1 0 0 0 2 0 0 0
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.030 0.030 0.000 0.000 0.030 0.030 0.061 0.061 0.121 0.030 0.061 0.121 0.061 0.061 0.121 0.030 0.030 0.030 0.000 0.030 0.000 0.000 0.000 0.061 0.000 0.000 0.000
## left son=120 (26 obs) right son=121 (7 obs)
## Primary splits:
## ibt < 223 to the left, improve=1.633367, (0 missing)
## dpg < 28.5 to the left, improve=1.474026, (0 missing)
## vh < 5815 to the right, improve=1.380041, (0 missing)
## humidity < 67.5 to the left, improve=1.361631, (0 missing)
## ID < 212.5 to the right, improve=1.336759, (0 missing)
## Surrogate splits:
## ibh < 868.5 to the right, agree=0.818, adj=0.143, (0 split)
##
## Node number 61: 25 observations, complexity param=0.01104972
## predicted class=26 expected loss=0.76 P(node) =0.125
## class counts: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 2 1 1 1 3 3 1 6 1 0 0 2 0 1
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.040 0.040 0.000 0.040 0.000 0.080 0.040 0.040 0.040 0.120 0.120 0.040 0.240 0.040 0.000 0.000 0.080 0.000 0.040
## left son=122 (10 obs) right son=123 (15 obs)
## Primary splits:
## temp < 83.5 to the right, improve=1.693333, (0 missing)
## ibh < 1059 to the right, improve=1.525079, (0 missing)
## ibt < 260.5 to the left, improve=1.523636, (0 missing)
## dpg < 25.5 to the right, improve=1.382222, (0 missing)
## vh < 5875 to the left, improve=1.377949, (0 missing)
## Surrogate splits:
## ibt < 263.5 to the right, agree=0.76, adj=0.4, (0 split)
## ibh < 1136 to the right, agree=0.72, adj=0.3, (0 split)
## vh < 5865 to the right, agree=0.68, adj=0.2, (0 split)
## wind < 6.5 to the right, agree=0.68, adj=0.2, (0 split)
## dpg < 45.5 to the right, agree=0.68, adj=0.2, (0 split)
##
## Node number 120: 26 observations, complexity param=0.01657459
## predicted class=14 expected loss=0.8461538 P(node) =0.13
## class counts: 0 0 0 0 0 1 1 0 0 0 1 1 2 4 1 2 4 2 2 1 1 1 1 0 0 0 0 0 1 0 0 0
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.038 0.038 0.000 0.000 0.000 0.038 0.038 0.077 0.154 0.038 0.077 0.154 0.077 0.077 0.038 0.038 0.038 0.038 0.000 0.000 0.000 0.000 0.000 0.038 0.000 0.000 0.000
## left son=240 (14 obs) right son=241 (12 obs)
## Primary splits:
## vh < 5815 to the right, improve=1.578755, (0 missing)
## humidity < 67.5 to the left, improve=1.563170, (0 missing)
## ibh < 1190.5 to the left, improve=1.369231, (0 missing)
## temp < 72.5 to the left, improve=1.307692, (0 missing)
## dpg < 28 to the left, improve=1.242915, (0 missing)
## Surrogate splits:
## ibh < 1190.5 to the right, agree=0.769, adj=0.500, (0 split)
## ID < 154.5 to the right, agree=0.731, adj=0.417, (0 split)
## temp < 72.5 to the right, agree=0.731, adj=0.417, (0 split)
## ibt < 202 to the right, agree=0.731, adj=0.417, (0 split)
## doy < 194.5 to the right, agree=0.731, adj=0.417, (0 split)
##
## Node number 121: 7 observations
## predicted class=20 expected loss=0.5714286 P(node) =0.035
## class counts: 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 3 0 0 0 0 1 0 0 0 1 0 0 0
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.143 0.000 0.143 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.429 0.000 0.000 0.000 0.000 0.143 0.000 0.000 0.000 0.143 0.000 0.000 0.000
##
## Node number 122: 10 observations
## predicted class=19 expected loss=0.8 P(node) =0.05
## class counts: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 1 2 1 1 0 0 0 0 1 0 1
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.100 0.000 0.000 0.000 0.000 0.200 0.000 0.000 0.100 0.200 0.100 0.100 0.000 0.000 0.000 0.000 0.100 0.000 0.100
##
## Node number 123: 15 observations
## predicted class=26 expected loss=0.6 P(node) =0.075
## class counts: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 2 0 6 1 0 0 1 0 0
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.067 0.000 0.067 0.000 0.000 0.067 0.067 0.000 0.067 0.133 0.000 0.400 0.067 0.000 0.000 0.067 0.000 0.000
##
## Node number 240: 14 observations
## predicted class=14 expected loss=0.7142857 P(node) =0.07
## class counts: 0 0 0 0 0 1 0 0 0 0 1 1 0 4 0 2 1 2 1 0 0 0 0 0 0 0 0 0 1 0 0 0
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.071 0.000 0.000 0.000 0.000 0.071 0.071 0.000 0.286 0.000 0.143 0.071 0.143 0.071 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.071 0.000 0.000 0.000
##
## Node number 241: 12 observations
## predicted class=17 expected loss=0.75 P(node) =0.06
## class counts: 0 0 0 0 0 0 1 0 0 0 0 0 2 0 1 0 3 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0
## probabilities: 0.000 0.000 0.000 0.000 0.000 0.000 0.083 0.000 0.000 0.000 0.000 0.000 0.167 0.000 0.083 0.000 0.250 0.000 0.083 0.083 0.083 0.083 0.083 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000# display the results
printcp(redwood) ##
## Classification tree:
## rpart(formula = O3 ~ ., data = df.train, method = "class")
##
## Variables actually used in tree construction:
## [1] dpg humidity ibh ibt ID temp vh wind
##
## Root node error: 181/200 = 0.905
##
## n= 200
##
## CP nsplit rel error xerror xstd
## 1 0.033149 0 1.00000 1.0608 0.015311
## 2 0.027624 1 0.96685 1.0663 0.014359
## 3 0.022099 2 0.93923 1.0663 0.014359
## 4 0.018416 4 0.89503 1.0608 0.015311
## 5 0.016575 7 0.83978 1.0663 0.014359
## 6 0.011050 13 0.74033 1.0497 0.017029
## 7 0.010000 15 0.71823 1.0608 0.015311plotcp(redwood, col = "red", lty = 1, upper = "size") 
plotcp(redwood, col = "red", lty = 1, upper = "splits") 
rpart.plot(redwood, box.palette = "RdBu", shadow.col = "gray", nn = TRUE)
plot(redwood, uniform = TRUE, main = "Classification Tree for O3")
text(redwood, all = FALSE, cex = .8)
plot(redwood, uniform = FALSE, main = "Classification Tree for O3")
text(redwood, all = FALSE, cex = .8)
plot(redwood, uniform = TRUE, main = "Classification Tree for O3", branch = 0.5, compress = TRUE)
text(redwood, all = FALSE, cex = .8)
prp(redwood)
prp(redwood, varlen = 3)
prp(redwood)
fancyRpartPlot(redwood, main = "Classification Tree for O3", type = 1)
fancyRpartPlot(redwood, main = "Classification Tree for O3", type = 2)
draw.tree(redwood)
Visualizing/Analyzing Trees: tree package
# tree package
summary(oak)##
## Regression tree:
## tree(formula = O3 ~ ., data = df.train)
## Variables actually used in tree construction:
## [1] "temp" "ibh" "dpg" "ibt" "humidity"
## Number of terminal nodes: 9
## Residual mean deviance: 13.55 = 2587 / 191
## Distribution of residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -12.250 -2.235 -0.325 0.000 2.045 11.600cv.tree(oak, FUN = prune.tree)## $size
## [1] 9 8 7 6 5 4 3 2 1
##
## $dev
## [1] 5095.894 5094.726 5666.017 5593.034 5372.997 5197.395 6053.768
## [8] 6513.781 13289.561
##
## $k
## [1] -Inf 159.9671 240.6667 272.1132 296.3526 403.8372 612.8978
## [8] 949.2013 7599.2870
##
## $method
## [1] "deviance"
##
## attr(,"class")
## [1] "prune" "tree.sequence"deviance(oak, detail = TRUE)## [1] 13121.5000 2368.9924 1265.8594 176.9524 685.0698 142.9565
## [7] 270.0000 490.2353 3153.2206 793.4667 108.8000 444.0000
## [13] 1410.5526 365.5000 748.7000 239.4286 349.3043plot.tree.sequence(x = pruned.oak, order = "decreasing")
plot(oak, type = "uni")
text(oak, all=TRUE, cex=.8)
plot(oak, type = "prop")
text(oak, all = TRUE, cex = .8)
draw.tree(oak)
(2) Use the tree you built to predict the missing values of ozone based on the observed factors.
set.seed(2634)
redwood.pred <- predict(redwood, type = "vector")
oak.pred <- predict(oak, type = "vector")
# MSE
redwood.mse <- mean((redwood.pred - train$O3)^2); redwood.mse## Warning in redwood.pred - train$O3: longer object length is not a multiple
## of shorter object length## [1] 125.1294oak.mse <- mean((oak.pred - train$O3)^2); oak.mse## Warning in oak.pred - train$O3: longer object length is not a multiple of
## shorter object length## [1] 112.0374Use CART and random forest modeling to predict the mssing ozone values. Whoever’s prediction minimize mean squared error (MSE) wins a prize or something.
set.seed(2634)
forest <- randomForest(O3 ~.,
data = train,
ntree = 1000,
nodesize = 5,
maxnodes = 10,
importance = TRUE,
localImp = TRUE,
nPerm = 2,
proximity = TRUE,
norm.votes = TRUE,
do.trace = TRUE,
keep.forest = TRUE,
corr.bias = FALSE)## | Out-of-bag |
## Tree | MSE %Var(y) |
## 1 | 25.1 41.58 |
## 2 | 24.66 40.85 |
## 3 | 22.66 37.54 |
## 4 | 22.43 37.16 |
## 5 | 23.48 38.90 |
## 6 | 22.9 37.94 |
## 7 | 22.39 37.10 |
## 8 | 20.95 34.71 |
## 9 | 20.29 33.62 |
## 10 | 19.5 32.30 |
## 11 | 18.82 31.18 |
## 12 | 18.01 29.83 |
## 13 | 17.95 29.73 |
## 14 | 17.82 29.52 |
## 15 | 17.6 29.16 |
## 16 | 17.66 29.26 |
## 17 | 17.3 28.66 |
## 18 | 17.47 28.95 |
## 19 | 17.46 28.93 |
## 20 | 17.62 29.20 |
## 21 | 17.32 28.70 |
## 22 | 16.99 28.14 |
## 23 | 17.09 28.32 |
## 24 | 17.21 28.51 |
## 25 | 17.15 28.41 |
## 26 | 16.97 28.11 |
## 27 | 16.75 27.75 |
## 28 | 16.63 27.55 |
## 29 | 16.48 27.30 |
## 30 | 16.46 27.27 |
## 31 | 16.39 27.16 |
## 32 | 16.57 27.45 |
## 33 | 16.65 27.58 |
## 34 | 16.74 27.73 |
## 35 | 16.69 27.64 |
## 36 | 16.58 27.48 |
## 37 | 16.71 27.68 |
## 38 | 16.83 27.88 |
## 39 | 16.78 27.80 |
## 40 | 16.75 27.75 |
## 41 | 16.83 27.89 |
## 42 | 16.76 27.76 |
## 43 | 16.82 27.86 |
## 44 | 16.78 27.80 |
## 45 | 16.72 27.70 |
## 46 | 16.72 27.70 |
## 47 | 16.68 27.63 |
## 48 | 16.68 27.64 |
## 49 | 16.63 27.55 |
## 50 | 16.62 27.53 |
## 51 | 16.6 27.50 |
## 52 | 16.66 27.60 |
## 53 | 16.7 27.67 |
## 54 | 16.73 27.71 |
## 55 | 16.69 27.65 |
## 56 | 16.72 27.70 |
## 57 | 16.72 27.69 |
## 58 | 16.65 27.59 |
## 59 | 16.71 27.69 |
## 60 | 16.63 27.55 |
## 61 | 16.64 27.57 |
## 62 | 16.65 27.59 |
## 63 | 16.64 27.57 |
## 64 | 16.69 27.64 |
## 65 | 16.65 27.58 |
## 66 | 16.61 27.52 |
## 67 | 16.61 27.52 |
## 68 | 16.58 27.47 |
## 69 | 16.63 27.56 |
## 70 | 16.59 27.49 |
## 71 | 16.6 27.50 |
## 72 | 16.61 27.51 |
## 73 | 16.66 27.61 |
## 74 | 16.72 27.70 |
## 75 | 16.72 27.70 |
## 76 | 16.65 27.59 |
## 77 | 16.57 27.44 |
## 78 | 16.54 27.41 |
## 79 | 16.6 27.50 |
## 80 | 16.53 27.39 |
## 81 | 16.55 27.43 |
## 82 | 16.55 27.42 |
## 83 | 16.53 27.38 |
## 84 | 16.55 27.42 |
## 85 | 16.54 27.40 |
## 86 | 16.56 27.43 |
## 87 | 16.53 27.39 |
## 88 | 16.55 27.43 |
## 89 | 16.58 27.47 |
## 90 | 16.63 27.56 |
## 91 | 16.64 27.56 |
## 92 | 16.68 27.64 |
## 93 | 16.65 27.59 |
## 94 | 16.63 27.56 |
## 95 | 16.64 27.57 |
## 96 | 16.7 27.66 |
## 97 | 16.63 27.56 |
## 98 | 16.65 27.59 |
## 99 | 16.66 27.60 |
## 100 | 16.69 27.64 |
## 101 | 16.67 27.62 |
## 102 | 16.66 27.59 |
## 103 | 16.66 27.60 |
## 104 | 16.66 27.59 |
## 105 | 16.68 27.63 |
## 106 | 16.72 27.71 |
## 107 | 16.72 27.70 |
## 108 | 16.69 27.66 |
## 109 | 16.7 27.67 |
## 110 | 16.7 27.67 |
## 111 | 16.71 27.69 |
## 112 | 16.74 27.73 |
## 113 | 16.74 27.73 |
## 114 | 16.73 27.72 |
## 115 | 16.69 27.65 |
## 116 | 16.68 27.63 |
## 117 | 16.71 27.68 |
## 118 | 16.74 27.73 |
## 119 | 16.75 27.74 |
## 120 | 16.75 27.74 |
## 121 | 16.81 27.85 |
## 122 | 16.82 27.87 |
## 123 | 16.79 27.82 |
## 124 | 16.8 27.83 |
## 125 | 16.81 27.84 |
## 126 | 16.83 27.88 |
## 127 | 16.86 27.93 |
## 128 | 16.84 27.91 |
## 129 | 16.86 27.93 |
## 130 | 16.88 27.96 |
## 131 | 16.93 28.05 |
## 132 | 16.92 28.03 |
## 133 | 16.89 27.99 |
## 134 | 16.88 27.96 |
## 135 | 16.87 27.95 |
## 136 | 16.88 27.97 |
## 137 | 16.87 27.94 |
## 138 | 16.88 27.96 |
## 139 | 16.91 28.02 |
## 140 | 16.91 28.01 |
## 141 | 16.9 27.99 |
## 142 | 16.93 28.04 |
## 143 | 16.92 28.03 |
## 144 | 16.91 28.02 |
## 145 | 16.92 28.03 |
## 146 | 16.91 28.02 |
## 147 | 16.94 28.07 |
## 148 | 16.93 28.05 |
## 149 | 16.93 28.05 |
## 150 | 16.92 28.04 |
## 151 | 16.92 28.04 |
## 152 | 16.9 28.01 |
## 153 | 16.92 28.03 |
## 154 | 16.93 28.06 |
## 155 | 16.89 27.99 |
## 156 | 16.9 28.01 |
## 157 | 16.91 28.02 |
## 158 | 16.93 28.05 |
## 159 | 16.95 28.08 |
## 160 | 16.96 28.10 |
## 161 | 16.96 28.10 |
## 162 | 16.95 28.08 |
## 163 | 16.96 28.10 |
## 164 | 16.94 28.07 |
## 165 | 16.94 28.06 |
## 166 | 16.9 28.00 |
## 167 | 16.92 28.03 |
## 168 | 16.93 28.04 |
## 169 | 16.94 28.07 |
## 170 | 16.93 28.04 |
## 171 | 16.92 28.03 |
## 172 | 16.92 28.03 |
## 173 | 16.91 28.01 |
## 174 | 16.92 28.03 |
## 175 | 16.94 28.07 |
## 176 | 16.93 28.05 |
## 177 | 16.93 28.05 |
## 178 | 16.93 28.04 |
## 179 | 16.94 28.07 |
## 180 | 16.92 28.03 |
## 181 | 16.9 28.00 |
## 182 | 16.91 28.02 |
## 183 | 16.93 28.04 |
## 184 | 16.93 28.05 |
## 185 | 16.93 28.06 |
## 186 | 16.94 28.07 |
## 187 | 16.94 28.07 |
## 188 | 16.92 28.03 |
## 189 | 16.94 28.07 |
## 190 | 16.97 28.12 |
## 191 | 16.98 28.14 |
## 192 | 16.98 28.14 |
## 193 | 16.98 28.13 |
## 194 | 16.97 28.11 |
## 195 | 16.96 28.09 |
## 196 | 16.92 28.03 |
## 197 | 16.92 28.04 |
## 198 | 16.94 28.07 |
## 199 | 16.94 28.07 |
## 200 | 16.95 28.08 |
## 201 | 16.92 28.04 |
## 202 | 16.93 28.05 |
## 203 | 16.9 28.00 |
## 204 | 16.87 27.94 |
## 205 | 16.89 27.98 |
## 206 | 16.91 28.02 |
## 207 | 16.89 27.98 |
## 208 | 16.88 27.96 |
## 209 | 16.9 28.00 |
## 210 | 16.9 27.99 |
## 211 | 16.89 27.99 |
## 212 | 16.91 28.01 |
## 213 | 16.92 28.03 |
## 214 | 16.93 28.04 |
## 215 | 16.9 27.99 |
## 216 | 16.89 27.98 |
## 217 | 16.89 27.99 |
## 218 | 16.86 27.93 |
## 219 | 16.87 27.94 |
## 220 | 16.84 27.91 |
## 221 | 16.84 27.90 |
## 222 | 16.84 27.89 |
## 223 | 16.82 27.86 |
## 224 | 16.82 27.87 |
## 225 | 16.83 27.88 |
## 226 | 16.84 27.90 |
## 227 | 16.82 27.87 |
## 228 | 16.82 27.86 |
## 229 | 16.8 27.84 |
## 230 | 16.76 27.76 |
## 231 | 16.74 27.73 |
## 232 | 16.73 27.73 |
## 233 | 16.74 27.74 |
## 234 | 16.75 27.74 |
## 235 | 16.73 27.72 |
## 236 | 16.73 27.72 |
## 237 | 16.74 27.74 |
## 238 | 16.76 27.76 |
## 239 | 16.77 27.78 |
## 240 | 16.76 27.77 |
## 241 | 16.77 27.78 |
## 242 | 16.77 27.78 |
## 243 | 16.77 27.78 |
## 244 | 16.79 27.82 |
## 245 | 16.78 27.80 |
## 246 | 16.77 27.78 |
## 247 | 16.77 27.78 |
## 248 | 16.76 27.76 |
## 249 | 16.77 27.78 |
## 250 | 16.76 27.76 |
## 251 | 16.75 27.76 |
## 252 | 16.75 27.75 |
## 253 | 16.76 27.77 |
## 254 | 16.78 27.80 |
## 255 | 16.77 27.79 |
## 256 | 16.78 27.79 |
## 257 | 16.76 27.77 |
## 258 | 16.76 27.76 |
## 259 | 16.74 27.73 |
## 260 | 16.73 27.72 |
## 261 | 16.76 27.76 |
## 262 | 16.74 27.74 |
## 263 | 16.74 27.74 |
## 264 | 16.75 27.76 |
## 265 | 16.75 27.75 |
## 266 | 16.76 27.77 |
## 267 | 16.77 27.79 |
## 268 | 16.77 27.78 |
## 269 | 16.78 27.80 |
## 270 | 16.78 27.80 |
## 271 | 16.78 27.81 |
## 272 | 16.77 27.79 |
## 273 | 16.78 27.79 |
## 274 | 16.77 27.78 |
## 275 | 16.77 27.78 |
## 276 | 16.78 27.79 |
## 277 | 16.78 27.79 |
## 278 | 16.76 27.76 |
## 279 | 16.76 27.76 |
## 280 | 16.76 27.76 |
## 281 | 16.76 27.76 |
## 282 | 16.78 27.79 |
## 283 | 16.78 27.81 |
## 284 | 16.78 27.81 |
## 285 | 16.79 27.82 |
## 286 | 16.78 27.80 |
## 287 | 16.76 27.77 |
## 288 | 16.74 27.73 |
## 289 | 16.74 27.73 |
## 290 | 16.76 27.77 |
## 291 | 16.76 27.76 |
## 292 | 16.76 27.77 |
## 293 | 16.79 27.81 |
## 294 | 16.79 27.81 |
## 295 | 16.78 27.80 |
## 296 | 16.78 27.80 |
## 297 | 16.79 27.81 |
## 298 | 16.76 27.77 |
## 299 | 16.78 27.80 |
## 300 | 16.76 27.76 |
## 301 | 16.75 27.75 |
## 302 | 16.73 27.72 |
## 303 | 16.72 27.69 |
## 304 | 16.7 27.67 |
## 305 | 16.71 27.68 |
## 306 | 16.7 27.66 |
## 307 | 16.71 27.68 |
## 308 | 16.7 27.67 |
## 309 | 16.69 27.65 |
## 310 | 16.71 27.69 |
## 311 | 16.7 27.67 |
## 312 | 16.7 27.66 |
## 313 | 16.7 27.67 |
## 314 | 16.71 27.68 |
## 315 | 16.71 27.68 |
## 316 | 16.7 27.67 |
## 317 | 16.71 27.68 |
## 318 | 16.72 27.70 |
## 319 | 16.72 27.70 |
## 320 | 16.71 27.69 |
## 321 | 16.71 27.68 |
## 322 | 16.71 27.68 |
## 323 | 16.71 27.69 |
## 324 | 16.73 27.72 |
## 325 | 16.75 27.75 |
## 326 | 16.75 27.74 |
## 327 | 16.75 27.75 |
## 328 | 16.75 27.75 |
## 329 | 16.74 27.73 |
## 330 | 16.74 27.73 |
## 331 | 16.72 27.70 |
## 332 | 16.72 27.69 |
## 333 | 16.7 27.67 |
## 334 | 16.72 27.70 |
## 335 | 16.73 27.72 |
## 336 | 16.71 27.69 |
## 337 | 16.72 27.69 |
## 338 | 16.72 27.70 |
## 339 | 16.72 27.70 |
## 340 | 16.71 27.69 |
## 341 | 16.71 27.68 |
## 342 | 16.71 27.69 |
## 343 | 16.72 27.70 |
## 344 | 16.73 27.72 |
## 345 | 16.73 27.72 |
## 346 | 16.74 27.73 |
## 347 | 16.74 27.73 |
## 348 | 16.72 27.70 |
## 349 | 16.73 27.71 |
## 350 | 16.72 27.70 |
## 351 | 16.73 27.71 |
## 352 | 16.72 27.70 |
## 353 | 16.71 27.68 |
## 354 | 16.7 27.67 |
## 355 | 16.71 27.68 |
## 356 | 16.71 27.69 |
## 357 | 16.71 27.68 |
## 358 | 16.71 27.68 |
## 359 | 16.72 27.70 |
## 360 | 16.72 27.71 |
## 361 | 16.72 27.71 |
## 362 | 16.72 27.70 |
## 363 | 16.71 27.68 |
## 364 | 16.71 27.68 |
## 365 | 16.72 27.70 |
## 366 | 16.71 27.69 |
## 367 | 16.72 27.70 |
## 368 | 16.72 27.70 |
## 369 | 16.73 27.71 |
## 370 | 16.71 27.68 |
## 371 | 16.7 27.67 |
## 372 | 16.7 27.67 |
## 373 | 16.7 27.67 |
## 374 | 16.71 27.68 |
## 375 | 16.71 27.68 |
## 376 | 16.71 27.68 |
## 377 | 16.71 27.69 |
## 378 | 16.71 27.69 |
## 379 | 16.71 27.69 |
## 380 | 16.72 27.70 |
## 381 | 16.72 27.70 |
## 382 | 16.72 27.70 |
## 383 | 16.71 27.69 |
## 384 | 16.71 27.69 |
## 385 | 16.72 27.70 |
## 386 | 16.73 27.71 |
## 387 | 16.73 27.72 |
## 388 | 16.73 27.72 |
## 389 | 16.72 27.71 |
## 390 | 16.71 27.68 |
## 391 | 16.7 27.66 |
## 392 | 16.69 27.65 |
## 393 | 16.69 27.66 |
## 394 | 16.71 27.68 |
## 395 | 16.71 27.69 |
## 396 | 16.71 27.68 |
## 397 | 16.7 27.67 |
## 398 | 16.7 27.67 |
## 399 | 16.7 27.67 |
## 400 | 16.7 27.67 |
## 401 | 16.72 27.70 |
## 402 | 16.73 27.72 |
## 403 | 16.72 27.70 |
## 404 | 16.72 27.70 |
## 405 | 16.73 27.71 |
## 406 | 16.73 27.72 |
## 407 | 16.74 27.73 |
## 408 | 16.73 27.72 |
## 409 | 16.74 27.74 |
## 410 | 16.73 27.72 |
## 411 | 16.73 27.73 |
## 412 | 16.73 27.72 |
## 413 | 16.73 27.72 |
## 414 | 16.74 27.74 |
## 415 | 16.75 27.75 |
## 416 | 16.74 27.73 |
## 417 | 16.74 27.74 |
## 418 | 16.75 27.74 |
## 419 | 16.75 27.75 |
## 420 | 16.74 27.73 |
## 421 | 16.75 27.75 |
## 422 | 16.73 27.72 |
## 423 | 16.74 27.73 |
## 424 | 16.74 27.73 |
## 425 | 16.73 27.72 |
## 426 | 16.73 27.72 |
## 427 | 16.75 27.75 |
## 428 | 16.76 27.77 |
## 429 | 16.75 27.76 |
## 430 | 16.74 27.73 |
## 431 | 16.74 27.73 |
## 432 | 16.73 27.72 |
## 433 | 16.74 27.73 |
## 434 | 16.73 27.72 |
## 435 | 16.73 27.71 |
## 436 | 16.72 27.70 |
## 437 | 16.72 27.71 |
## 438 | 16.72 27.70 |
## 439 | 16.71 27.68 |
## 440 | 16.73 27.72 |
## 441 | 16.74 27.73 |
## 442 | 16.73 27.72 |
## 443 | 16.74 27.73 |
## 444 | 16.73 27.72 |
## 445 | 16.73 27.72 |
## 446 | 16.73 27.72 |
## 447 | 16.72 27.70 |
## 448 | 16.73 27.72 |
## 449 | 16.74 27.73 |
## 450 | 16.73 27.71 |
## 451 | 16.72 27.70 |
## 452 | 16.72 27.71 |
## 453 | 16.72 27.71 |
## 454 | 16.73 27.72 |
## 455 | 16.73 27.72 |
## 456 | 16.72 27.71 |
## 457 | 16.72 27.70 |
## 458 | 16.72 27.70 |
## 459 | 16.74 27.73 |
## 460 | 16.74 27.73 |
## 461 | 16.73 27.73 |
## 462 | 16.73 27.72 |
## 463 | 16.74 27.73 |
## 464 | 16.74 27.74 |
## 465 | 16.75 27.75 |
## 466 | 16.75 27.75 |
## 467 | 16.74 27.73 |
## 468 | 16.73 27.72 |
## 469 | 16.72 27.71 |
## 470 | 16.73 27.71 |
## 471 | 16.72 27.70 |
## 472 | 16.72 27.70 |
## 473 | 16.72 27.70 |
## 474 | 16.72 27.70 |
## 475 | 16.71 27.69 |
## 476 | 16.7 27.67 |
## 477 | 16.69 27.65 |
## 478 | 16.69 27.65 |
## 479 | 16.7 27.66 |
## 480 | 16.69 27.64 |
## 481 | 16.68 27.64 |
## 482 | 16.68 27.64 |
## 483 | 16.68 27.63 |
## 484 | 16.68 27.64 |
## 485 | 16.68 27.63 |
## 486 | 16.67 27.62 |
## 487 | 16.68 27.63 |
## 488 | 16.66 27.61 |
## 489 | 16.67 27.61 |
## 490 | 16.67 27.62 |
## 491 | 16.67 27.62 |
## 492 | 16.68 27.63 |
## 493 | 16.69 27.65 |
## 494 | 16.69 27.66 |
## 495 | 16.69 27.66 |
## 496 | 16.68 27.64 |
## 497 | 16.69 27.65 |
## 498 | 16.69 27.66 |
## 499 | 16.7 27.68 |
## 500 | 16.7 27.67 |
## 501 | 16.71 27.68 |
## 502 | 16.69 27.66 |
## 503 | 16.7 27.66 |
## 504 | 16.69 27.65 |
## 505 | 16.7 27.66 |
## 506 | 16.69 27.65 |
## 507 | 16.69 27.65 |
## 508 | 16.68 27.64 |
## 509 | 16.68 27.64 |
## 510 | 16.68 27.64 |
## 511 | 16.68 27.64 |
## 512 | 16.68 27.64 |
## 513 | 16.68 27.63 |
## 514 | 16.68 27.64 |
## 515 | 16.69 27.65 |
## 516 | 16.69 27.64 |
## 517 | 16.69 27.64 |
## 518 | 16.69 27.65 |
## 519 | 16.69 27.65 |
## 520 | 16.68 27.63 |
## 521 | 16.68 27.64 |
## 522 | 16.68 27.63 |
## 523 | 16.68 27.64 |
## 524 | 16.69 27.65 |
## 525 | 16.69 27.66 |
## 526 | 16.7 27.67 |
## 527 | 16.71 27.69 |
## 528 | 16.71 27.68 |
## 529 | 16.7 27.67 |
## 530 | 16.71 27.68 |
## 531 | 16.7 27.67 |
## 532 | 16.71 27.68 |
## 533 | 16.72 27.70 |
## 534 | 16.72 27.70 |
## 535 | 16.72 27.70 |
## 536 | 16.71 27.69 |
## 537 | 16.72 27.70 |
## 538 | 16.74 27.73 |
## 539 | 16.74 27.74 |
## 540 | 16.74 27.73 |
## 541 | 16.74 27.74 |
## 542 | 16.75 27.75 |
## 543 | 16.75 27.74 |
## 544 | 16.75 27.74 |
## 545 | 16.74 27.74 |
## 546 | 16.74 27.73 |
## 547 | 16.73 27.72 |
## 548 | 16.72 27.70 |
## 549 | 16.71 27.68 |
## 550 | 16.71 27.68 |
## 551 | 16.71 27.69 |
## 552 | 16.71 27.68 |
## 553 | 16.71 27.68 |
## 554 | 16.71 27.69 |
## 555 | 16.71 27.69 |
## 556 | 16.72 27.70 |
## 557 | 16.72 27.70 |
## 558 | 16.72 27.71 |
## 559 | 16.72 27.71 |
## 560 | 16.73 27.71 |
## 561 | 16.73 27.72 |
## 562 | 16.73 27.72 |
## 563 | 16.74 27.74 |
## 564 | 16.74 27.73 |
## 565 | 16.73 27.71 |
## 566 | 16.72 27.70 |
## 567 | 16.73 27.71 |
## 568 | 16.73 27.71 |
## 569 | 16.73 27.72 |
## 570 | 16.72 27.71 |
## 571 | 16.71 27.69 |
## 572 | 16.72 27.69 |
## 573 | 16.72 27.70 |
## 574 | 16.71 27.69 |
## 575 | 16.72 27.70 |
## 576 | 16.72 27.69 |
## 577 | 16.72 27.71 |
## 578 | 16.73 27.71 |
## 579 | 16.73 27.72 |
## 580 | 16.72 27.71 |
## 581 | 16.72 27.70 |
## 582 | 16.72 27.70 |
## 583 | 16.72 27.71 |
## 584 | 16.72 27.71 |
## 585 | 16.72 27.70 |
## 586 | 16.72 27.71 |
## 587 | 16.73 27.71 |
## 588 | 16.72 27.70 |
## 589 | 16.71 27.69 |
## 590 | 16.72 27.69 |
## 591 | 16.72 27.70 |
## 592 | 16.72 27.70 |
## 593 | 16.72 27.70 |
## 594 | 16.73 27.71 |
## 595 | 16.73 27.71 |
## 596 | 16.72 27.71 |
## 597 | 16.72 27.71 |
## 598 | 16.73 27.71 |
## 599 | 16.74 27.73 |
## 600 | 16.73 27.71 |
## 601 | 16.72 27.70 |
## 602 | 16.73 27.71 |
## 603 | 16.72 27.70 |
## 604 | 16.71 27.69 |
## 605 | 16.71 27.69 |
## 606 | 16.7 27.67 |
## 607 | 16.71 27.68 |
## 608 | 16.7 27.67 |
## 609 | 16.7 27.67 |
## 610 | 16.7 27.67 |
## 611 | 16.7 27.67 |
## 612 | 16.7 27.67 |
## 613 | 16.71 27.68 |
## 614 | 16.71 27.68 |
## 615 | 16.72 27.70 |
## 616 | 16.72 27.71 |
## 617 | 16.73 27.71 |
## 618 | 16.73 27.72 |
## 619 | 16.73 27.72 |
## 620 | 16.74 27.73 |
## 621 | 16.74 27.73 |
## 622 | 16.73 27.72 |
## 623 | 16.74 27.73 |
## 624 | 16.75 27.75 |
## 625 | 16.75 27.75 |
## 626 | 16.75 27.75 |
## 627 | 16.74 27.74 |
## 628 | 16.74 27.74 |
## 629 | 16.74 27.74 |
## 630 | 16.75 27.75 |
## 631 | 16.75 27.75 |
## 632 | 16.74 27.74 |
## 633 | 16.74 27.73 |
## 634 | 16.74 27.74 |
## 635 | 16.74 27.73 |
## 636 | 16.73 27.72 |
## 637 | 16.74 27.74 |
## 638 | 16.74 27.73 |
## 639 | 16.73 27.72 |
## 640 | 16.73 27.71 |
## 641 | 16.72 27.70 |
## 642 | 16.72 27.70 |
## 643 | 16.71 27.68 |
## 644 | 16.71 27.69 |
## 645 | 16.71 27.69 |
## 646 | 16.72 27.69 |
## 647 | 16.72 27.70 |
## 648 | 16.72 27.71 |
## 649 | 16.72 27.70 |
## 650 | 16.72 27.70 |
## 651 | 16.72 27.71 |
## 652 | 16.73 27.71 |
## 653 | 16.74 27.74 |
## 654 | 16.74 27.73 |
## 655 | 16.73 27.72 |
## 656 | 16.73 27.71 |
## 657 | 16.73 27.72 |
## 658 | 16.73 27.71 |
## 659 | 16.72 27.71 |
## 660 | 16.73 27.72 |
## 661 | 16.73 27.72 |
## 662 | 16.73 27.72 |
## 663 | 16.73 27.72 |
## 664 | 16.74 27.73 |
## 665 | 16.74 27.73 |
## 666 | 16.74 27.73 |
## 667 | 16.74 27.73 |
## 668 | 16.74 27.74 |
## 669 | 16.75 27.75 |
## 670 | 16.75 27.75 |
## 671 | 16.75 27.74 |
## 672 | 16.75 27.74 |
## 673 | 16.74 27.74 |
## 674 | 16.75 27.75 |
## 675 | 16.74 27.73 |
## 676 | 16.73 27.72 |
## 677 | 16.72 27.70 |
## 678 | 16.73 27.71 |
## 679 | 16.72 27.71 |
## 680 | 16.72 27.71 |
## 681 | 16.73 27.71 |
## 682 | 16.72 27.71 |
## 683 | 16.72 27.71 |
## 684 | 16.72 27.71 |
## 685 | 16.72 27.71 |
## 686 | 16.72 27.70 |
## 687 | 16.72 27.70 |
## 688 | 16.71 27.69 |
## 689 | 16.71 27.68 |
## 690 | 16.71 27.68 |
## 691 | 16.7 27.67 |
## 692 | 16.7 27.67 |
## 693 | 16.69 27.66 |
## 694 | 16.69 27.65 |
## 695 | 16.69 27.65 |
## 696 | 16.7 27.66 |
## 697 | 16.7 27.66 |
## 698 | 16.7 27.67 |
## 699 | 16.7 27.67 |
## 700 | 16.7 27.67 |
## 701 | 16.71 27.68 |
## 702 | 16.7 27.67 |
## 703 | 16.71 27.68 |
## 704 | 16.7 27.67 |
## 705 | 16.7 27.66 |
## 706 | 16.69 27.65 |
## 707 | 16.69 27.65 |
## 708 | 16.69 27.66 |
## 709 | 16.7 27.67 |
## 710 | 16.71 27.68 |
## 711 | 16.7 27.67 |
## 712 | 16.71 27.68 |
## 713 | 16.71 27.68 |
## 714 | 16.7 27.67 |
## 715 | 16.7 27.67 |
## 716 | 16.7 27.66 |
## 717 | 16.69 27.65 |
## 718 | 16.69 27.65 |
## 719 | 16.7 27.67 |
## 720 | 16.71 27.68 |
## 721 | 16.71 27.68 |
## 722 | 16.71 27.68 |
## 723 | 16.71 27.68 |
## 724 | 16.71 27.69 |
## 725 | 16.71 27.69 |
## 726 | 16.71 27.69 |
## 727 | 16.71 27.68 |
## 728 | 16.71 27.68 |
## 729 | 16.71 27.69 |
## 730 | 16.72 27.70 |
## 731 | 16.72 27.71 |
## 732 | 16.73 27.72 |
## 733 | 16.73 27.71 |
## 734 | 16.72 27.71 |
## 735 | 16.72 27.70 |
## 736 | 16.72 27.71 |
## 737 | 16.73 27.71 |
## 738 | 16.73 27.72 |
## 739 | 16.74 27.73 |
## 740 | 16.73 27.73 |
## 741 | 16.73 27.72 |
## 742 | 16.74 27.73 |
## 743 | 16.74 27.73 |
## 744 | 16.74 27.74 |
## 745 | 16.74 27.74 |
## 746 | 16.75 27.75 |
## 747 | 16.75 27.74 |
## 748 | 16.74 27.73 |
## 749 | 16.73 27.72 |
## 750 | 16.74 27.73 |
## 751 | 16.74 27.73 |
## 752 | 16.74 27.74 |
## 753 | 16.74 27.74 |
## 754 | 16.74 27.74 |
## 755 | 16.74 27.74 |
## 756 | 16.74 27.74 |
## 757 | 16.75 27.74 |
## 758 | 16.75 27.75 |
## 759 | 16.75 27.75 |
## 760 | 16.75 27.75 |
## 761 | 16.74 27.74 |
## 762 | 16.74 27.74 |
## 763 | 16.75 27.76 |
## 764 | 16.76 27.76 |
## 765 | 16.76 27.76 |
## 766 | 16.76 27.76 |
## 767 | 16.76 27.77 |
## 768 | 16.76 27.77 |
## 769 | 16.75 27.76 |
## 770 | 16.76 27.76 |
## 771 | 16.76 27.77 |
## 772 | 16.76 27.77 |
## 773 | 16.76 27.77 |
## 774 | 16.76 27.77 |
## 775 | 16.76 27.77 |
## 776 | 16.76 27.76 |
## 777 | 16.76 27.76 |
## 778 | 16.76 27.77 |
## 779 | 16.76 27.77 |
## 780 | 16.76 27.77 |
## 781 | 16.76 27.77 |
## 782 | 16.77 27.78 |
## 783 | 16.77 27.79 |
## 784 | 16.78 27.80 |
## 785 | 16.78 27.80 |
## 786 | 16.78 27.80 |
## 787 | 16.78 27.80 |
## 788 | 16.79 27.81 |
## 789 | 16.79 27.81 |
## 790 | 16.79 27.81 |
## 791 | 16.79 27.82 |
## 792 | 16.79 27.81 |
## 793 | 16.79 27.81 |
## 794 | 16.79 27.82 |
## 795 | 16.79 27.81 |
## 796 | 16.79 27.81 |
## 797 | 16.78 27.81 |
## 798 | 16.78 27.80 |
## 799 | 16.77 27.79 |
## 800 | 16.77 27.78 |
## 801 | 16.77 27.78 |
## 802 | 16.77 27.78 |
## 803 | 16.77 27.78 |
## 804 | 16.77 27.78 |
## 805 | 16.76 27.77 |
## 806 | 16.77 27.78 |
## 807 | 16.78 27.79 |
## 808 | 16.78 27.80 |
## 809 | 16.78 27.80 |
## 810 | 16.78 27.80 |
## 811 | 16.78 27.80 |
## 812 | 16.78 27.81 |
## 813 | 16.78 27.80 |
## 814 | 16.77 27.79 |
## 815 | 16.77 27.79 |
## 816 | 16.78 27.80 |
## 817 | 16.78 27.80 |
## 818 | 16.77 27.79 |
## 819 | 16.77 27.79 |
## 820 | 16.77 27.79 |
## 821 | 16.77 27.79 |
## 822 | 16.77 27.79 |
## 823 | 16.77 27.79 |
## 824 | 16.77 27.78 |
## 825 | 16.76 27.77 |
## 826 | 16.76 27.77 |
## 827 | 16.76 27.77 |
## 828 | 16.76 27.77 |
## 829 | 16.75 27.76 |
## 830 | 16.75 27.76 |
## 831 | 16.76 27.77 |
## 832 | 16.76 27.77 |
## 833 | 16.76 27.77 |
## 834 | 16.76 27.77 |
## 835 | 16.77 27.78 |
## 836 | 16.77 27.78 |
## 837 | 16.76 27.77 |
## 838 | 16.77 27.78 |
## 839 | 16.77 27.78 |
## 840 | 16.76 27.77 |
## 841 | 16.77 27.78 |
## 842 | 16.77 27.78 |
## 843 | 16.77 27.79 |
## 844 | 16.77 27.79 |
## 845 | 16.77 27.78 |
## 846 | 16.77 27.78 |
## 847 | 16.77 27.79 |
## 848 | 16.77 27.78 |
## 849 | 16.77 27.79 |
## 850 | 16.78 27.79 |
## 851 | 16.77 27.79 |
## 852 | 16.77 27.78 |
## 853 | 16.76 27.77 |
## 854 | 16.75 27.75 |
## 855 | 16.75 27.75 |
## 856 | 16.76 27.77 |
## 857 | 16.76 27.76 |
## 858 | 16.76 27.77 |
## 859 | 16.76 27.77 |
## 860 | 16.77 27.78 |
## 861 | 16.77 27.78 |
## 862 | 16.77 27.78 |
## 863 | 16.76 27.77 |
## 864 | 16.77 27.78 |
## 865 | 16.77 27.78 |
## 866 | 16.77 27.79 |
## 867 | 16.78 27.80 |
## 868 | 16.78 27.80 |
## 869 | 16.78 27.80 |
## 870 | 16.78 27.81 |
## 871 | 16.79 27.81 |
## 872 | 16.8 27.83 |
## 873 | 16.79 27.82 |
## 874 | 16.79 27.82 |
## 875 | 16.79 27.82 |
## 876 | 16.79 27.82 |
## 877 | 16.79 27.81 |
## 878 | 16.78 27.81 |
## 879 | 16.79 27.81 |
## 880 | 16.79 27.82 |
## 881 | 16.79 27.81 |
## 882 | 16.79 27.81 |
## 883 | 16.79 27.82 |
## 884 | 16.79 27.82 |
## 885 | 16.79 27.82 |
## 886 | 16.79 27.82 |
## 887 | 16.79 27.82 |
## 888 | 16.79 27.81 |
## 889 | 16.79 27.82 |
## 890 | 16.8 27.83 |
## 891 | 16.8 27.84 |
## 892 | 16.8 27.83 |
## 893 | 16.8 27.84 |
## 894 | 16.81 27.85 |
## 895 | 16.81 27.85 |
## 896 | 16.81 27.85 |
## 897 | 16.81 27.84 |
## 898 | 16.8 27.84 |
## 899 | 16.8 27.83 |
## 900 | 16.8 27.83 |
## 901 | 16.79 27.82 |
## 902 | 16.8 27.83 |
## 903 | 16.79 27.82 |
## 904 | 16.79 27.82 |
## 905 | 16.79 27.82 |
## 906 | 16.78 27.81 |
## 907 | 16.79 27.81 |
## 908 | 16.79 27.82 |
## 909 | 16.79 27.81 |
## 910 | 16.79 27.81 |
## 911 | 16.78 27.81 |
## 912 | 16.78 27.80 |
## 913 | 16.78 27.80 |
## 914 | 16.78 27.80 |
## 915 | 16.78 27.81 |
## 916 | 16.79 27.81 |
## 917 | 16.78 27.80 |
## 918 | 16.79 27.81 |
## 919 | 16.79 27.81 |
## 920 | 16.79 27.81 |
## 921 | 16.79 27.81 |
## 922 | 16.79 27.82 |
## 923 | 16.79 27.82 |
## 924 | 16.8 27.83 |
## 925 | 16.8 27.83 |
## 926 | 16.8 27.83 |
## 927 | 16.8 27.83 |
## 928 | 16.8 27.83 |
## 929 | 16.8 27.83 |
## 930 | 16.79 27.82 |
## 931 | 16.79 27.82 |
## 932 | 16.79 27.82 |
## 933 | 16.79 27.82 |
## 934 | 16.79 27.82 |
## 935 | 16.8 27.83 |
## 936 | 16.8 27.83 |
## 937 | 16.8 27.83 |
## 938 | 16.8 27.84 |
## 939 | 16.8 27.84 |
## 940 | 16.8 27.83 |
## 941 | 16.8 27.84 |
## 942 | 16.81 27.84 |
## 943 | 16.81 27.84 |
## 944 | 16.81 27.85 |
## 945 | 16.81 27.85 |
## 946 | 16.82 27.86 |
## 947 | 16.82 27.87 |
## 948 | 16.82 27.87 |
## 949 | 16.82 27.87 |
## 950 | 16.83 27.88 |
## 951 | 16.83 27.89 |
## 952 | 16.84 27.90 |
## 953 | 16.83 27.89 |
## 954 | 16.84 27.90 |
## 955 | 16.84 27.90 |
## 956 | 16.84 27.91 |
## 957 | 16.84 27.90 |
## 958 | 16.84 27.90 |
## 959 | 16.84 27.90 |
## 960 | 16.84 27.90 |
## 961 | 16.84 27.89 |
## 962 | 16.83 27.89 |
## 963 | 16.83 27.89 |
## 964 | 16.83 27.89 |
## 965 | 16.83 27.89 |
## 966 | 16.83 27.88 |
## 967 | 16.82 27.87 |
## 968 | 16.82 27.87 |
## 969 | 16.82 27.87 |
## 970 | 16.82 27.86 |
## 971 | 16.82 27.86 |
## 972 | 16.82 27.86 |
## 973 | 16.83 27.88 |
## 974 | 16.83 27.88 |
## 975 | 16.83 27.88 |
## 976 | 16.83 27.89 |
## 977 | 16.83 27.88 |
## 978 | 16.83 27.88 |
## 979 | 16.83 27.88 |
## 980 | 16.83 27.88 |
## 981 | 16.83 27.88 |
## 982 | 16.83 27.89 |
## 983 | 16.84 27.89 |
## 984 | 16.83 27.89 |
## 985 | 16.83 27.88 |
## 986 | 16.83 27.88 |
## 987 | 16.83 27.88 |
## 988 | 16.83 27.89 |
## 989 | 16.83 27.89 |
## 990 | 16.83 27.88 |
## 991 | 16.82 27.87 |
## 992 | 16.83 27.88 |
## 993 | 16.83 27.88 |
## 994 | 16.83 27.89 |
## 995 | 16.83 27.89 |
## 996 | 16.83 27.88 |
## 997 | 16.82 27.87 |
## 998 | 16.82 27.87 |
## 999 | 16.82 27.87 |
## 1000 | 16.82 27.87 |forest##
## Call:
## randomForest(formula = O3 ~ ., data = train, ntree = 1000, nodesize = 5, maxnodes = 10, importance = TRUE, localImp = TRUE, nPerm = 2, proximity = TRUE, norm.votes = TRUE, do.trace = TRUE, keep.forest = TRUE, corr.bias = FALSE)
## Type of random forest: regression
## Number of trees: 1000
## No. of variables tried at each split: 3
##
## Mean of squared residuals: 16.82176
## % Var explained: 72.13varImpPlot(x = forest, sort = TRUE, main = "Variable Importance Relative to O3", scale = TRUE)
varImpPlot(x = forest, sort = TRUE, main = "Variable Importance Relative to O3", scale = FALSE)
min_depth_frame <- min_depth_distribution(forest)## Warning: Factor `split var` contains implicit NA, consider using
## `forcats::fct_explicit_na`save(min_depth_frame, file = "min_depth_frame.rda")
load("min_depth_frame.rda")
head(min_depth_frame, n = 10)## tree variable minimal_depth
## 1 1 dpg 2
## 2 1 ibt 0
## 3 1 ID 2
## 4 1 temp 1
## 5 1 vis 3
## 6 2 dpg 0
## 7 2 ibt 1
## 8 2 temp 2
## 9 2 vis 2
## 10 2 doy 2Cool stuff I found while trying to visualize trees
data(chiroptera)
groupInfo <- split(chiroptera$tip.label, gsub("_\\w+", "", chiroptera$tip.label))
chiroptera <- groupOTU(chiroptera, groupInfo)
ggtree(chiroptera, aes(color = group), layout = 'circular') + geom_tiplab(size = 1, aes(angle = angle))
#rpart.predict(redwood)
#ggtree(redwood, aes(color = group), layout = 'circular') + geom_tiplab(size = 1, aes(angle = angle))