Arboles de Regresión Temperaturas de NY
Rubén Pizarro Gurrola
12/6/2021
Objetivo
Construir un modelo de árbol de regresión con datos atmosféricos de la cd. de NY con la finalidad de valorar la variable explicativa temperatura y realizar predicciones.
Librerías
library(readr)
library(ggplot2)
library(rpart) # Para crear arboles
library(tree) # Para crear arboles
library(rpart.plot) # Para visualizar arbolDatos
datos <- read.csv("https://raw.githubusercontent.com/rpizarrog/Industrias-4.0/main/datos/temperatura%20condiciones%20NY.csv")
datos## X Ozono Radiacion Vel.viento Temperatura Mes Dia
## 1 1 41.0 190 7.4 67 5 1
## 2 2 36.0 118 8.0 72 5 2
## 3 3 12.0 149 12.6 74 5 3
## 4 4 18.0 313 11.5 62 5 4
## 5 5 31.5 205 14.3 56 5 5
## 6 6 28.0 205 14.9 66 5 6
## 7 7 23.0 299 8.6 65 5 7
## 8 8 19.0 99 13.8 59 5 8
## 9 9 8.0 19 20.1 61 5 9
## 10 10 31.5 194 8.6 69 5 10
## 11 11 7.0 205 6.9 74 5 11
## 12 12 16.0 256 9.7 69 5 12
## 13 13 11.0 290 9.2 66 5 13
## 14 14 14.0 274 10.9 68 5 14
## 15 15 18.0 65 13.2 58 5 15
## 16 16 14.0 334 11.5 64 5 16
## 17 17 34.0 307 12.0 66 5 17
## 18 18 6.0 78 18.4 57 5 18
## 19 19 30.0 322 11.5 68 5 19
## 20 20 11.0 44 9.7 62 5 20
## 21 21 1.0 8 9.7 59 5 21
## 22 22 11.0 320 16.6 73 5 22
## 23 23 4.0 25 9.7 61 5 23
## 24 24 32.0 92 12.0 61 5 24
## 25 25 31.5 66 16.6 57 5 25
## 26 26 31.5 266 14.9 58 5 26
## 27 27 31.5 205 8.0 57 5 27
## 28 28 23.0 13 12.0 67 5 28
## 29 29 45.0 252 14.9 81 5 29
## 30 30 115.0 223 5.7 79 5 30
## 31 31 37.0 279 7.4 76 5 31
## 32 32 31.5 286 8.6 78 6 1
## 33 33 31.5 287 9.7 74 6 2
## 34 34 31.5 242 16.1 67 6 3
## 35 35 31.5 186 9.2 84 6 4
## 36 36 31.5 220 8.6 85 6 5
## 37 37 31.5 264 14.3 79 6 6
## 38 38 29.0 127 9.7 82 6 7
## 39 39 31.5 273 6.9 87 6 8
## 40 40 71.0 291 13.8 90 6 9
## 41 41 39.0 323 11.5 87 6 10
## 42 42 31.5 259 10.9 93 6 11
## 43 43 31.5 250 9.2 92 6 12
## 44 44 23.0 148 8.0 82 6 13
## 45 45 31.5 332 13.8 80 6 14
## 46 46 31.5 322 11.5 79 6 15
## 47 47 21.0 191 14.9 77 6 16
## 48 48 37.0 284 20.7 72 6 17
## 49 49 20.0 37 9.2 65 6 18
## 50 50 12.0 120 11.5 73 6 19
## 51 51 13.0 137 10.3 76 6 20
## 52 52 31.5 150 6.3 77 6 21
## 53 53 31.5 59 1.7 76 6 22
## 54 54 31.5 91 4.6 76 6 23
## 55 55 31.5 250 6.3 76 6 24
## 56 56 31.5 135 8.0 75 6 25
## 57 57 31.5 127 8.0 78 6 26
## 58 58 31.5 47 10.3 73 6 27
## 59 59 31.5 98 11.5 80 6 28
## 60 60 31.5 31 14.9 77 6 29
## 61 61 31.5 138 8.0 83 6 30
## 62 62 135.0 269 4.1 84 7 1
## 63 63 49.0 248 9.2 85 7 2
## 64 64 32.0 236 9.2 81 7 3
## 65 65 31.5 101 10.9 84 7 4
## 66 66 64.0 175 4.6 83 7 5
## 67 67 40.0 314 10.9 83 7 6
## 68 68 77.0 276 5.1 88 7 7
## 69 69 97.0 267 6.3 92 7 8
## 70 70 97.0 272 5.7 92 7 9
## 71 71 85.0 175 7.4 89 7 10
## 72 72 31.5 139 8.6 82 7 11
## 73 73 10.0 264 14.3 73 7 12
## 74 74 27.0 175 14.9 81 7 13
## 75 75 31.5 291 14.9 91 7 14
## 76 76 7.0 48 14.3 80 7 15
## 77 77 48.0 260 6.9 81 7 16
## 78 78 35.0 274 10.3 82 7 17
## 79 79 61.0 285 6.3 84 7 18
## 80 80 79.0 187 5.1 87 7 19
## 81 81 63.0 220 11.5 85 7 20
## 82 82 16.0 7 6.9 74 7 21
## 83 83 31.5 258 9.7 81 7 22
## 84 84 31.5 295 11.5 82 7 23
## 85 85 80.0 294 8.6 86 7 24
## 86 86 108.0 223 8.0 85 7 25
## 87 87 20.0 81 8.6 82 7 26
## 88 88 52.0 82 12.0 86 7 27
## 89 89 82.0 213 7.4 88 7 28
## 90 90 50.0 275 7.4 86 7 29
## 91 91 64.0 253 7.4 83 7 30
## 92 92 59.0 254 9.2 81 7 31
## 93 93 39.0 83 6.9 81 8 1
## 94 94 9.0 24 13.8 81 8 2
## 95 95 16.0 77 7.4 82 8 3
## 96 96 78.0 205 6.9 86 8 4
## 97 97 35.0 205 7.4 85 8 5
## 98 98 66.0 205 4.6 87 8 6
## 99 99 122.0 255 4.0 89 8 7
## 100 100 89.0 229 10.3 90 8 8
## 101 101 110.0 207 8.0 90 8 9
## 102 102 31.5 222 8.6 92 8 10
## 103 103 31.5 137 11.5 86 8 11
## 104 104 44.0 192 11.5 86 8 12
## 105 105 28.0 273 11.5 82 8 13
## 106 106 65.0 157 9.7 80 8 14
## 107 107 31.5 64 11.5 79 8 15
## 108 108 22.0 71 10.3 77 8 16
## 109 109 59.0 51 6.3 79 8 17
## 110 110 23.0 115 7.4 76 8 18
## 111 111 31.0 244 10.9 78 8 19
## 112 112 44.0 190 10.3 78 8 20
## 113 113 21.0 259 15.5 77 8 21
## 114 114 9.0 36 14.3 72 8 22
## 115 115 31.5 255 12.6 75 8 23
## 116 116 45.0 212 9.7 79 8 24
## 117 117 168.0 238 3.4 81 8 25
## 118 118 73.0 215 8.0 86 8 26
## 119 119 31.5 153 5.7 88 8 27
## 120 120 76.0 203 9.7 97 8 28
## 121 121 118.0 225 2.3 94 8 29
## 122 122 84.0 237 6.3 96 8 30
## 123 123 85.0 188 6.3 94 8 31
## 124 124 96.0 167 6.9 91 9 1
## 125 125 78.0 197 5.1 92 9 2
## 126 126 73.0 183 2.8 93 9 3
## 127 127 91.0 189 4.6 93 9 4
## 128 128 47.0 95 7.4 87 9 5
## 129 129 32.0 92 15.5 84 9 6
## 130 130 20.0 252 10.9 80 9 7
## 131 131 23.0 220 10.3 78 9 8
## 132 132 21.0 230 10.9 75 9 9
## 133 133 24.0 259 9.7 73 9 10
## 134 134 44.0 236 14.9 81 9 11
## 135 135 21.0 259 15.5 76 9 12
## 136 136 28.0 238 6.3 77 9 13
## 137 137 9.0 24 10.9 71 9 14
## 138 138 13.0 112 11.5 71 9 15
## 139 139 46.0 237 6.9 78 9 16
## 140 140 18.0 224 13.8 67 9 17
## 141 141 13.0 27 10.3 76 9 18
## 142 142 24.0 238 10.3 68 9 19
## 143 143 16.0 201 8.0 82 9 20
## 144 144 13.0 238 12.6 64 9 21
## 145 145 23.0 14 9.2 71 9 22
## 146 146 36.0 139 10.3 81 9 23
## 147 147 7.0 49 10.3 69 9 24
## 148 148 14.0 20 16.6 63 9 25
## 149 149 30.0 193 6.9 70 9 26
## 150 150 31.5 145 13.2 77 9 27
## 151 151 14.0 191 14.3 75 9 28
## 152 152 18.0 131 8.0 76 9 29
## 153 153 20.0 223 11.5 68 9 30Se cargan los datos de las condiciones del ambiente de la cd. de NY.
Se describen los datos con summary() y str()
summary(datos)## X Ozono Radiacion Vel.viento
## Min. : 1 Min. : 1.00 Min. : 7.0 Min. : 1.700
## 1st Qu.: 39 1st Qu.: 21.00 1st Qu.:120.0 1st Qu.: 7.400
## Median : 77 Median : 31.50 Median :205.0 Median : 9.700
## Mean : 77 Mean : 39.56 Mean :186.8 Mean : 9.958
## 3rd Qu.:115 3rd Qu.: 46.00 3rd Qu.:256.0 3rd Qu.:11.500
## Max. :153 Max. :168.00 Max. :334.0 Max. :20.700
## Temperatura Mes Dia
## Min. :56.00 Min. :5.000 Min. : 1.0
## 1st Qu.:72.00 1st Qu.:6.000 1st Qu.: 8.0
## Median :79.00 Median :7.000 Median :16.0
## Mean :77.88 Mean :6.993 Mean :15.8
## 3rd Qu.:85.00 3rd Qu.:8.000 3rd Qu.:23.0
## Max. :97.00 Max. :9.000 Max. :31.0str(datos)## 'data.frame': 153 obs. of 7 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Ozono : num 41 36 12 18 31.5 28 23 19 8 31.5 ...
## $ Radiacion : int 190 118 149 313 205 205 299 99 19 194 ...
## $ Vel.viento : num 7.4 8 12.6 11.5 14.3 14.9 8.6 13.8 20.1 8.6 ...
## $ Temperatura: int 67 72 74 62 56 66 65 59 61 69 ...
## $ Mes : int 5 5 5 5 5 5 5 5 5 5 ...
## $ Dia : int 1 2 3 4 5 6 7 8 9 10 ...Construir modelo de árbol de regresión
modelo <- rpart(data=datos, formula = Temperatura ~ Ozono + Radiacion + Vel.viento + Mes)
# modelo
sm <- summary(modelo)## Call:
## rpart(formula = Temperatura ~ Ozono + Radiacion + Vel.viento +
## Mes, data = datos)
## n= 153
##
## CP nsplit rel error xerror xstd
## 1 0.43429937 0 1.0000000 1.0072851 0.10212141
## 2 0.17012108 1 0.5657006 0.5712855 0.05934825
## 3 0.07642747 2 0.3955795 0.4614733 0.04783078
## 4 0.03100834 3 0.3191521 0.3714267 0.04001974
## 5 0.01566744 4 0.2881437 0.3905500 0.04289275
## 6 0.01000000 5 0.2724763 0.3829833 0.04210009
##
## Variable importance
## Mes Ozono Vel.viento Radiacion
## 49 32 11 8
##
## Node number 1: 153 observations, complexity param=0.4342994
## mean=77.88235, MSE=89.00577
## left son=2 (31 obs) right son=3 (122 obs)
## Primary splits:
## Mes < 5.5 to the left, improve=0.4342994, (0 missing)
## Ozono < 46.5 to the left, improve=0.3322210, (0 missing)
## Vel.viento < 8.9 to the right, improve=0.1498241, (0 missing)
## Radiacion < 79.5 to the left, improve=0.1405230, (0 missing)
## Surrogate splits:
## Ozono < 6.5 to the left, agree=0.817, adj=0.097, (0 split)
## Radiacion < 297 to the right, agree=0.810, adj=0.065, (0 split)
## Vel.viento < 16.35 to the right, agree=0.810, adj=0.065, (0 split)
##
## Node number 2: 31 observations, complexity param=0.03100834
## mean=65.54839, MSE=45.47347
## left son=4 (10 obs) right son=5 (21 obs)
## Primary splits:
## Radiacion < 108.5 to the left, improve=0.2995493, (0 missing)
## Ozono < 31.75 to the left, improve=0.2438493, (0 missing)
## Vel.viento < 8.9 to the right, improve=0.1431859, (0 missing)
## Surrogate splits:
## Ozono < 6.5 to the left, agree=0.774, adj=0.3, (0 split)
## Vel.viento < 15.75 to the right, agree=0.742, adj=0.2, (0 split)
##
## Node number 3: 122 observations, complexity param=0.1701211
## mean=81.01639, MSE=51.5899
## left son=6 (97 obs) right son=7 (25 obs)
## Primary splits:
## Ozono < 65.5 to the left, improve=0.3680809, (0 missing)
## Vel.viento < 8.9 to the right, improve=0.1509717, (0 missing)
## Radiacion < 50 to the left, improve=0.1474241, (0 missing)
## Mes < 8.5 to the right, improve=0.1071032, (0 missing)
## Surrogate splits:
## Vel.viento < 5.4 to the right, agree=0.852, adj=0.28, (0 split)
##
## Node number 4: 10 observations
## mean=60.2, MSE=7.96
##
## Node number 5: 21 observations
## mean=68.09524, MSE=43.22902
##
## Node number 6: 97 observations, complexity param=0.07642747
## mean=78.80412, MSE=37.27091
## left son=12 (33 obs) right son=13 (64 obs)
## Primary splits:
## Ozono < 25.5 to the left, improve=0.2878838, (0 missing)
## Mes < 8.5 to the right, improve=0.1787796, (0 missing)
## Radiacion < 50 to the left, improve=0.1426820, (0 missing)
## Vel.viento < 12.3 to the right, improve=0.0680503, (0 missing)
## Surrogate splits:
## Mes < 8.5 to the right, agree=0.763, adj=0.303, (0 split)
## Radiacion < 50 to the left, agree=0.742, adj=0.242, (0 split)
## Vel.viento < 13.5 to the right, agree=0.670, adj=0.030, (0 split)
##
## Node number 7: 25 observations
## mean=89.6, MSE=14.48
##
## Node number 12: 33 observations, complexity param=0.01566744
## mean=74.24242, MSE=27.94123
## left son=24 (26 obs) right son=25 (7 obs)
## Primary splits:
## Vel.viento < 8.9 to the right, improve=0.23139180, (0 missing)
## Mes < 8.5 to the right, improve=0.14754940, (0 missing)
## Radiacion < 42.5 to the left, improve=0.07846079, (0 missing)
## Ozono < 15 to the left, improve=0.06158346, (0 missing)
##
## Node number 13: 64 observations
## mean=81.15625, MSE=25.81934
##
## Node number 24: 26 observations
## mean=72.92308, MSE=24.22485
##
## Node number 25: 7 observations
## mean=79.14286, MSE=11.26531sm## n= 153
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 153 13617.88000 77.88235
## 2) Mes< 5.5 31 1409.67700 65.54839
## 4) Radiacion< 108.5 10 79.60000 60.20000 *
## 5) Radiacion>=108.5 21 907.80950 68.09524 *
## 3) Mes>=5.5 122 6293.96700 81.01639
## 6) Ozono< 65.5 97 3615.27800 78.80412
## 12) Ozono< 25.5 33 922.06060 74.24242
## 24) Vel.viento>=8.9 26 629.84620 72.92308 *
## 25) Vel.viento< 8.9 7 78.85714 79.14286 *
## 13) Ozono>=25.5 64 1652.43800 81.15625 *
## 7) Ozono>=65.5 25 362.00000 89.60000 *Visualización del árbol
Se muestra un árbol de regresión
prp(modelo, main="Arbol de regresión",
nn = TRUE, # display the node numbers
fallen.leaves = TRUE, # put the leaves on the bottom of the page
shadow.col = "gray", # shadows under the leaves
branch.lty = 3, # draw branches using dotted lines
branch = .5, # change angle of branch lines
faclen = 0, # faclen = 0 to print full factor names
trace = 1, # print the auto calculated cex, xlim, ylim
split.cex = 1.2, # make the split text larger than the node text
split.prefix = "is ", # put "is " before split text
split.suffix = "?", # put "?" after split text
split.box.col = "lightblue", # lightgray split boxes (default is white)
split.border.col = "darkgray", # darkgray border on split boxes
split.round = 0.5) # round the split box corners a tad## cex 1 xlim c(-0.2, 1.2) ylim c(0, 1)
Predecir resultados
Se predicen temperaturas con nuevos datos de las variables independientes.
ozono <- 60
radiacion <- 80
velocidad.viento <- 90
mes <- 4
ozono; radiacion; velocidad.viento; mes## [1] 60## [1] 80## [1] 90## [1] 4La predicción:
predict(object = modelo, newdata = data.frame(Ozono = ozono, Radiacion = radiacion, Vel.viento = velocidad.viento, Mes = mes))## 1
## 60.2La temperatura es en grados Fareingeith
Cuales serían las condicioens de temperatura para varios nuevos registros:
ozono <- c(60,70,90,100)
radiacion <- c(80,100, 150, 200)
velocidad.viento <- c(90, 60, 50, 40)
mes <- c(4, 4, 5, 6)
ozono; radiacion; velocidad.viento; mes## [1] 60 70 90 100## [1] 80 100 150 200## [1] 90 60 50 40## [1] 4 4 5 6Se generan las predicciones:
predicciones <- predict(object = modelo, newdata = data.frame(Ozono = ozono, Radiacion = radiacion, Vel.viento = velocidad.viento, Mes = mes))
predicciones## 1 2 3 4
## 60.20000 60.20000 68.09524 89.60000Formar un nuevo conjunto de datos mostrando los valores nuevos y las predicciones:
las.predicciones <- data.frame(Ozono = ozono, Radiacion = radiacion, Vel.viento = velocidad.viento, Mes = mes)
las.predicciones <- cbind(las.predicciones, predicciones)
las.predicciones## Ozono Radiacion Vel.viento Mes predicciones
## 1 60 80 90 4 60.20000
## 2 70 100 60 4 60.20000
## 3 90 150 50 5 68.09524
## 4 100 200 40 6 89.60000FALTA VALORAR LA EFICIENCIA DEL MODELO O EL GRADO DE EXPLICACIÓN QUE TIENEN LAS VARIABES INDEPENDIENTE CON RESPECTO A LA TEMPERATURA.
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