Caso 4. Arbol de regresiOn con datos Adverstising
Alfredo Flores Garcia
2022-10-06
Objetivo
Crear y evaluar un modelo de Ć”rbol de regresiĆ³n para predecir las ventas con datos simulados de una empresa dependiendo de las inversiones realizadas en publicidad.
DescripciĆ³n
- Cargar librerĆas y datos
- Limpiar datos si es necesario
- Explorar datos
- Partir los datos en datos de entrenamiento y datos de validaciĆ³n 70% y 30%
- Crear modelo de Ć”rbol de regresiĆ³n con los datos de entrenamiento
- Hacer Predicciones con datos de validaciĆ³n
- Evaluar predicciones
- Determinar el estadĆstico rmse para evaluar con respecto a otros modelos
- Interpretar el caso
Fundamento teĆ³rico
Los algoritmos de aprendizaje basados en Ć”rbol se consideran uno de los mejores y mĆ”s utilizados mĆ©todos de aprendizaje supervisado. Potencian modelos predictivos con alta precisiĆ³n, estabilidad y facilidad de interpretaciĆ³n.
Los Ć”rboles de clasificaciĆ³n y regresiĆ³n son mĆ©todos que proporcionan modelos que satisfacen objetivos tanto predictivos como explicativos.
Algunas ventajas son su sencillez y la representaciĆ³n grĆ”fica mediante Ć”rboles y, por otro, la definiciĆ³n de reglas de asociaciĆ³n entre variables que incluye expresiones de condiciĆ³n que permiten explicar las predicciones.
Se pueden usar para regresiones con variables dependientes que tienen valores numĆ©ricos continuos o para clasificaciones con variables categĆ³ricas.
Utilizar un Ć”rbol de regresiĆ³n para crear un modelo explicativo y predictivo para una variable cuantitativa dependiente basada en variables explicativas independientes cuantitativas y cualitativas [@xlstatbyaddinsoft].
Un Ć”rbol de regresiĆ³n consiste en hacer preguntas de tipo \(Āæx_k < c?\) para cada una de las covariables, de esta forma el espacio de las covariables es divido en hiper-rectĆ”ngulos (con el resultado de las condicionales) de las observaciones que queden dentro de un hiper-rectĆ”ngulo tendrĆ”n el mismo valor estimado \(\hat{y}\) o \(Y\) .[@hernĆ”ndez2021]
Por otra parte, bajo el paradigma divide y vencerĆ”s, usando Ć”rboles de regresiĆ³n y decisiĆ³n y correspondientes reglas, el Ć”rbol representa el modelo similar a un diagrama de flujo en el que los nodos de decisiĆ³n, los nodos de hoja y las ramas definen una serie de decisiones que se pueden usar para generar predicciones. Siguiendo las reglas se encuentran predicciones en la hoja final. [@lantz2013].
Desarrollo
Cargar librerĆas
library(readr) # Para importar datos
library(dplyr) # Para filtrar
library(knitr) # Para datos tabulares
library(ggplot2) # Para visualizar
library(plotly)
library(caret) # Para particionar
library(Metrics) # Para determinar rmse
library(rpart) # Para Ɣrbol
library(rpart.plot) # Para ƔrbolCargar datos
datos <- read.csv("https://raw.githubusercontent.com/rpizarrog/Analisis-Inteligente-de-datos/main/datos/Advertising_Web.csv")Explorar datos
Son 200 registros tres variables independientes y una variable dependiente.
La variable dependiente o variable objetivo es Sales que deberĆ” estar en funciĆ³n de la inversiĆ³n que se hace en TV, Radio, Newspaper o Web.
str(datos)## 'data.frame': 200 obs. of 7 variables:
## $ X.1 : int 1 2 3 4 5 6 7 8 9 10 ...
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ TV : num 230.1 44.5 17.2 151.5 180.8 ...
## $ Radio : num 37.8 39.3 45.9 41.3 10.8 48.9 32.8 19.6 2.1 2.6 ...
## $ Newspaper: num 69.2 45.1 69.3 58.5 58.4 75 23.5 11.6 1 21.2 ...
## $ Web : num 306.6 302.7 49.5 257.8 195.7 ...
## $ Sales : num 22.1 10.4 9.3 18.5 12.9 7.2 11.8 13.2 4.8 10.6 ...summary(datos)## X.1 X TV Radio
## Min. : 1.00 Min. : 1.00 Min. : 0.70 Min. : 0.000
## 1st Qu.: 50.75 1st Qu.: 50.75 1st Qu.: 74.38 1st Qu.: 9.975
## Median :100.50 Median :100.50 Median :149.75 Median :22.900
## Mean :100.50 Mean :100.50 Mean :147.04 Mean :23.264
## 3rd Qu.:150.25 3rd Qu.:150.25 3rd Qu.:218.82 3rd Qu.:36.525
## Max. :200.00 Max. :200.00 Max. :296.40 Max. :49.600
## Newspaper Web Sales
## Min. : 0.30 Min. : 4.308 Min. : 1.60
## 1st Qu.: 12.75 1st Qu.: 99.049 1st Qu.:10.38
## Median : 25.75 Median :156.862 Median :12.90
## Mean : 30.55 Mean :159.587 Mean :14.02
## 3rd Qu.: 45.10 3rd Qu.:212.312 3rd Qu.:17.40
## Max. :114.00 Max. :358.247 Max. :27.00Limpiar datos
Quitar las primeras columnas
datos <- select(datos, TV, Radio, Newspaper, Web, Sales)head(datos)
kable(head(datos, 20), caption = "Primeros 20 registros")| TV | Radio | Newspaper | Web | Sales |
|---|---|---|---|---|
| 230.1 | 37.8 | 69.2 | 306.63475 | 22.1 |
| 44.5 | 39.3 | 45.1 | 302.65307 | 10.4 |
| 17.2 | 45.9 | 69.3 | 49.49891 | 9.3 |
| 151.5 | 41.3 | 58.5 | 257.81689 | 18.5 |
| 180.8 | 10.8 | 58.4 | 195.66008 | 12.9 |
| 8.7 | 48.9 | 75.0 | 22.07240 | 7.2 |
| 57.5 | 32.8 | 23.5 | 246.81160 | 11.8 |
| 120.2 | 19.6 | 11.6 | 229.97146 | 13.2 |
| 8.6 | 2.1 | 1.0 | 144.61739 | 4.8 |
| 199.8 | 2.6 | 21.2 | 111.27226 | 10.6 |
| 66.1 | 5.8 | 24.2 | 45.35903 | 8.6 |
| 214.7 | 24.0 | 4.0 | 164.97176 | 17.4 |
| 23.8 | 35.1 | 65.9 | 87.92109 | 9.2 |
| 97.5 | 7.6 | 7.2 | 173.65804 | 9.7 |
| 204.1 | 32.9 | 46.0 | 245.77496 | 19.0 |
| 195.4 | 47.7 | 52.9 | 148.09513 | 22.4 |
| 67.8 | 36.6 | 114.0 | 202.63890 | 12.5 |
| 281.4 | 39.6 | 55.8 | 41.75531 | 24.4 |
| 69.2 | 20.5 | 18.3 | 210.48991 | 11.3 |
| 147.3 | 23.9 | 19.1 | 268.73538 | 14.6 |
tail(datos)
kable(tail(datos, 20), caption = "Ćltimos 20 registros")| TV | Radio | Newspaper | Web | Sales | |
|---|---|---|---|---|---|
| 181 | 156.6 | 2.6 | 8.3 | 122.11647 | 10.5 |
| 182 | 218.5 | 5.4 | 27.4 | 162.38749 | 12.2 |
| 183 | 56.2 | 5.7 | 29.7 | 42.19929 | 8.7 |
| 184 | 287.6 | 43.0 | 71.8 | 154.30972 | 26.2 |
| 185 | 253.8 | 21.3 | 30.0 | 181.57905 | 17.6 |
| 186 | 205.0 | 45.1 | 19.6 | 208.69269 | 22.6 |
| 187 | 139.5 | 2.1 | 26.6 | 236.74404 | 10.3 |
| 188 | 191.1 | 28.7 | 18.2 | 239.27571 | 17.3 |
| 189 | 286.0 | 13.9 | 3.7 | 151.99073 | 15.9 |
| 190 | 18.7 | 12.1 | 23.4 | 222.90695 | 6.7 |
| 191 | 39.5 | 41.1 | 5.8 | 219.89058 | 10.8 |
| 192 | 75.5 | 10.8 | 6.0 | 301.48119 | 9.9 |
| 193 | 17.2 | 4.1 | 31.6 | 265.02864 | 5.9 |
| 194 | 166.8 | 42.0 | 3.6 | 192.24621 | 19.6 |
| 195 | 149.7 | 35.6 | 6.0 | 99.57998 | 17.3 |
| 196 | 38.2 | 3.7 | 13.8 | 248.84107 | 7.6 |
| 197 | 94.2 | 4.9 | 8.1 | 118.04186 | 9.7 |
| 198 | 177.0 | 9.3 | 6.4 | 213.27467 | 12.8 |
| 199 | 283.6 | 42.0 | 66.2 | 237.49806 | 25.5 |
| 200 | 232.1 | 8.6 | 8.7 | 151.99073 | 13.4 |
Datos de entrenamiento y validaciĆ³n
Datos de entrenamiento
n <- nrow(datos)
# Modificar la semilla estableciendo como parĆ”metro los Ćŗtimos cuatro dĆgitos de su no de control.
# Ej. set.seed(0732), o set.seed(1023)
# set.seed(2022)
set.seed(1804)De manera aleatoria se construyen los datos de entrenamiento y los datos de validaciĆ³n.
En la variable entrena se generan los registros que van a ser los datos de entrenamiento, de tal forma que los datos de validaciĆ³n serĆ”n los que no sena de entrenamiento [-entrena].
entrena <- createDataPartition(y = datos$Sales, p = 0.70, list = FALSE, times = 1)
# Datos entrenamiento
datos.entrenamiento <- datos[entrena, ] # [renglones, columna]
# Datos validaciĆ³n
datos.validacion <- datos[-entrena, ]head()
kable(head(datos.entrenamiento, 20), caption = "Datos de Entrenamiento. Primeros 20 registros")| TV | Radio | Newspaper | Web | Sales | |
|---|---|---|---|---|---|
| 2 | 44.5 | 39.3 | 45.1 | 302.65307 | 10.4 |
| 5 | 180.8 | 10.8 | 58.4 | 195.66008 | 12.9 |
| 7 | 57.5 | 32.8 | 23.5 | 246.81160 | 11.8 |
| 8 | 120.2 | 19.6 | 11.6 | 229.97146 | 13.2 |
| 9 | 8.6 | 2.1 | 1.0 | 144.61739 | 4.8 |
| 10 | 199.8 | 2.6 | 21.2 | 111.27226 | 10.6 |
| 11 | 66.1 | 5.8 | 24.2 | 45.35903 | 8.6 |
| 12 | 214.7 | 24.0 | 4.0 | 164.97176 | 17.4 |
| 13 | 23.8 | 35.1 | 65.9 | 87.92109 | 9.2 |
| 14 | 97.5 | 7.6 | 7.2 | 173.65804 | 9.7 |
| 18 | 281.4 | 39.6 | 55.8 | 41.75531 | 24.4 |
| 19 | 69.2 | 20.5 | 18.3 | 210.48991 | 11.3 |
| 20 | 147.3 | 23.9 | 19.1 | 268.73538 | 14.6 |
| 21 | 218.4 | 27.7 | 53.4 | 59.96055 | 18.0 |
| 22 | 237.4 | 5.1 | 23.5 | 296.95207 | 12.5 |
| 23 | 13.2 | 15.9 | 49.6 | 219.88278 | 5.6 |
| 25 | 62.3 | 12.6 | 18.3 | 256.96524 | 9.7 |
| 26 | 262.9 | 3.5 | 19.5 | 160.56286 | 12.0 |
| 27 | 142.9 | 29.3 | 12.6 | 275.51248 | 15.0 |
| 28 | 240.1 | 16.7 | 22.9 | 228.15744 | 15.9 |
tail()
kable(tail(datos.entrenamiento, 20), caption = "Datos de entrenamiento Ć¼ltimos 20 registros")| TV | Radio | Newspaper | Web | Sales | |
|---|---|---|---|---|---|
| 170 | 284.3 | 10.6 | 6.4 | 157.90011 | 15.0 |
| 171 | 50.0 | 11.6 | 18.4 | 64.01480 | 8.4 |
| 172 | 164.5 | 20.9 | 47.4 | 96.18039 | 14.5 |
| 174 | 168.4 | 7.1 | 12.8 | 218.18083 | 11.7 |
| 177 | 248.4 | 30.2 | 20.3 | 163.85204 | 20.2 |
| 178 | 170.2 | 7.8 | 35.2 | 104.91734 | 11.7 |
| 179 | 276.7 | 2.3 | 23.7 | 137.32377 | 11.8 |
| 180 | 165.6 | 10.0 | 17.6 | 151.99073 | 12.6 |
| 182 | 218.5 | 5.4 | 27.4 | 162.38749 | 12.2 |
| 183 | 56.2 | 5.7 | 29.7 | 42.19929 | 8.7 |
| 185 | 253.8 | 21.3 | 30.0 | 181.57905 | 17.6 |
| 188 | 191.1 | 28.7 | 18.2 | 239.27571 | 17.3 |
| 189 | 286.0 | 13.9 | 3.7 | 151.99073 | 15.9 |
| 190 | 18.7 | 12.1 | 23.4 | 222.90695 | 6.7 |
| 191 | 39.5 | 41.1 | 5.8 | 219.89058 | 10.8 |
| 192 | 75.5 | 10.8 | 6.0 | 301.48119 | 9.9 |
| 194 | 166.8 | 42.0 | 3.6 | 192.24621 | 19.6 |
| 196 | 38.2 | 3.7 | 13.8 | 248.84107 | 7.6 |
| 199 | 283.6 | 42.0 | 66.2 | 237.49806 | 25.5 |
| 200 | 232.1 | 8.6 | 8.7 | 151.99073 | 13.4 |
Datos de validaciĆ³n
Los datos de validaciĆ³n deben ser diferentes a los datos den entrenamiento.
head()
kable(head(datos.validacion, 20), caption = "Datos de ValidaciĆ³n Primeros 20 registros")| TV | Radio | Newspaper | Web | Sales | |
|---|---|---|---|---|---|
| 1 | 230.1 | 37.8 | 69.2 | 306.63475 | 22.1 |
| 3 | 17.2 | 45.9 | 69.3 | 49.49891 | 9.3 |
| 4 | 151.5 | 41.3 | 58.5 | 257.81689 | 18.5 |
| 6 | 8.7 | 48.9 | 75.0 | 22.07240 | 7.2 |
| 15 | 204.1 | 32.9 | 46.0 | 245.77496 | 19.0 |
| 16 | 195.4 | 47.7 | 52.9 | 148.09513 | 22.4 |
| 17 | 67.8 | 36.6 | 114.0 | 202.63890 | 12.5 |
| 24 | 228.3 | 16.9 | 26.2 | 51.17007 | 15.5 |
| 37 | 266.9 | 43.8 | 5.0 | 96.31683 | 25.4 |
| 44 | 206.9 | 8.4 | 26.4 | 213.60961 | 12.9 |
| 49 | 227.2 | 15.8 | 49.9 | 75.26918 | 14.8 |
| 52 | 100.4 | 9.6 | 3.6 | 41.33526 | 10.7 |
| 56 | 198.9 | 49.4 | 60.0 | 204.41893 | 23.7 |
| 65 | 131.1 | 42.8 | 28.9 | 124.38223 | 18.0 |
| 66 | 69.0 | 9.3 | 0.9 | 205.99349 | 9.3 |
| 67 | 31.5 | 24.6 | 2.2 | 216.47140 | 9.5 |
| 69 | 237.4 | 27.5 | 11.0 | 291.54860 | 18.9 |
| 74 | 129.4 | 5.7 | 31.3 | 61.30619 | 11.0 |
| 76 | 16.9 | 43.7 | 89.4 | 70.23428 | 8.7 |
| 77 | 27.5 | 1.6 | 20.7 | 117.10193 | 6.9 |
tail()
kable(tail(datos.validacion, 20), caption = "Datos de validaciĆ³ Ćŗltimos 20 registros")| TV | Radio | Newspaper | Web | Sales | |
|---|---|---|---|---|---|
| 144 | 104.6 | 5.7 | 34.4 | 336.57109 | 10.4 |
| 146 | 140.3 | 1.9 | 9.0 | 231.88339 | 10.3 |
| 148 | 243.2 | 49.0 | 44.3 | 151.99073 | 25.4 |
| 157 | 93.9 | 43.5 | 50.5 | 74.36194 | 15.3 |
| 158 | 149.8 | 1.3 | 24.3 | 145.80321 | 10.1 |
| 161 | 172.5 | 18.1 | 30.7 | 207.49680 | 14.4 |
| 162 | 85.7 | 35.8 | 49.3 | 188.93353 | 13.3 |
| 165 | 117.2 | 14.7 | 5.4 | 109.00876 | 11.9 |
| 166 | 234.5 | 3.4 | 84.8 | 135.02491 | 11.9 |
| 173 | 19.6 | 20.1 | 17.0 | 155.58366 | 7.6 |
| 175 | 222.4 | 3.4 | 13.1 | 144.52566 | 11.5 |
| 176 | 276.9 | 48.9 | 41.8 | 151.99073 | 27.0 |
| 181 | 156.6 | 2.6 | 8.3 | 122.11647 | 10.5 |
| 184 | 287.6 | 43.0 | 71.8 | 154.30972 | 26.2 |
| 186 | 205.0 | 45.1 | 19.6 | 208.69269 | 22.6 |
| 187 | 139.5 | 2.1 | 26.6 | 236.74404 | 10.3 |
| 193 | 17.2 | 4.1 | 31.6 | 265.02864 | 5.9 |
| 195 | 149.7 | 35.6 | 6.0 | 99.57998 | 17.3 |
| 197 | 94.2 | 4.9 | 8.1 | 118.04186 | 9.7 |
| 198 | 177.0 | 9.3 | 6.4 | 213.27467 | 12.8 |
Construir el modelo
Se construye el modelo con la funciĆ³n rpart
modelo_ar <- rpart(data = datos.entrenamiento,formula = Sales ~ TV + Radio + Newspaper )
modelo_ar## n= 142
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 142 3635.499000 14.016900
## 2) TV< 122.05 57 360.939300 9.503509
## 4) TV< 33.3 18 45.711110 6.822222 *
## 5) TV>=33.3 39 126.094400 10.741030
## 10) Radio< 13.45 19 18.761050 9.468421 *
## 11) Radio>=13.45 20 47.330000 11.950000 *
## 3) TV>=122.05 85 1334.789000 17.043530
## 6) Radio< 26.85 45 174.752000 14.020000
## 12) Radio< 10.3 18 7.945000 12.116670 *
## 13) Radio>=10.3 27 58.126670 15.288890 *
## 7) Radio>=26.85 40 285.859000 20.445000
## 14) TV< 210.75 15 47.297330 18.086670 *
## 15) TV>=210.75 25 105.080000 21.860000
## 30) Radio< 34.9 11 8.647273 19.945450 *
## 31) Radio>=34.9 14 24.432140 23.364290 *resumen del modelo
summary(modelo_ar)## Call:
## rpart(formula = Sales ~ TV + Radio + Newspaper, data = datos.entrenamiento)
## n= 142
##
## CP nsplit rel error xerror xstd
## 1 0.53356388 0 1.00000000 1.0190004 0.10024366
## 2 0.24045608 1 0.46643612 0.4963230 0.05073521
## 3 0.05202417 2 0.22598004 0.2538805 0.02887406
## 4 0.03671618 3 0.17395587 0.2255442 0.02577819
## 5 0.02989420 4 0.13723969 0.1854665 0.02046758
## 6 0.01980487 5 0.10734549 0.1609072 0.01756799
## 7 0.01650483 6 0.08754062 0.1355591 0.01648750
## 8 0.01000000 7 0.07103579 0.1136658 0.01524298
##
## Variable importance
## TV Radio Newspaper
## 57 33 10
##
## Node number 1: 142 observations, complexity param=0.5335639
## mean=14.0169, MSE=25.60211
## left son=2 (57 obs) right son=3 (85 obs)
## Primary splits:
## TV < 122.05 to the left, improve=0.5335639, (0 missing)
## Radio < 26.75 to the left, improve=0.3101329, (0 missing)
## Newspaper < 50.9 to the left, improve=0.1446599, (0 missing)
## Surrogate splits:
## Radio < 2.2 to the left, agree=0.662, adj=0.158, (0 split)
##
## Node number 2: 57 observations, complexity param=0.05202417
## mean=9.503509, MSE=6.332268
## left son=4 (18 obs) right son=5 (39 obs)
## Primary splits:
## TV < 33.3 to the left, improve=0.5240045, (0 missing)
## Radio < 16.5 to the left, improve=0.1142287, (0 missing)
## Newspaper < 7.9 to the left, improve=0.0753710, (0 missing)
## Surrogate splits:
## Newspaper < 5.75 to the left, agree=0.737, adj=0.167, (0 split)
##
## Node number 3: 85 observations, complexity param=0.2404561
## mean=17.04353, MSE=15.7034
## left son=6 (45 obs) right son=7 (40 obs)
## Primary splits:
## Radio < 26.85 to the left, improve=0.6549185, (0 missing)
## Newspaper < 37.35 to the left, improve=0.1603000, (0 missing)
## TV < 210.15 to the left, improve=0.1513591, (0 missing)
## Surrogate splits:
## Newspaper < 37.35 to the left, agree=0.706, adj=0.375, (0 split)
## TV < 210.15 to the left, agree=0.588, adj=0.125, (0 split)
##
## Node number 4: 18 observations
## mean=6.822222, MSE=2.539506
##
## Node number 5: 39 observations, complexity param=0.01650483
## mean=10.74103, MSE=3.233189
## left son=10 (19 obs) right son=11 (20 obs)
## Primary splits:
## Radio < 13.45 to the left, improve=0.4758604, (0 missing)
## TV < 100.1 to the left, improve=0.3070722, (0 missing)
## Newspaper < 41.95 to the left, improve=0.2231540, (0 missing)
## Surrogate splits:
## Newspaper < 30.85 to the left, agree=0.667, adj=0.316, (0 split)
## TV < 47.35 to the right, agree=0.590, adj=0.158, (0 split)
##
## Node number 6: 45 observations, complexity param=0.0298942
## mean=14.02, MSE=3.883378
## left son=12 (18 obs) right son=13 (27 obs)
## Primary splits:
## Radio < 10.3 to the left, improve=0.62191180, (0 missing)
## Newspaper < 14.9 to the right, improve=0.06674602, (0 missing)
## TV < 201.15 to the left, improve=0.04630562, (0 missing)
## Surrogate splits:
## TV < 216.95 to the right, agree=0.689, adj=0.222, (0 split)
##
## Node number 7: 40 observations, complexity param=0.03671618
## mean=20.445, MSE=7.146475
## left son=14 (15 obs) right son=15 (25 obs)
## Primary splits:
## TV < 210.75 to the left, improve=0.4669493, (0 missing)
## Radio < 37.3 to the left, improve=0.3178088, (0 missing)
## Newspaper < 18.35 to the left, improve=0.1026163, (0 missing)
## Surrogate splits:
## Newspaper < 14.25 to the left, agree=0.7, adj=0.2, (0 split)
##
## Node number 10: 19 observations
## mean=9.468421, MSE=0.9874238
##
## Node number 11: 20 observations
## mean=11.95, MSE=2.3665
##
## Node number 12: 18 observations
## mean=12.11667, MSE=0.4413889
##
## Node number 13: 27 observations
## mean=15.28889, MSE=2.15284
##
## Node number 14: 15 observations
## mean=18.08667, MSE=3.153156
##
## Node number 15: 25 observations, complexity param=0.01980487
## mean=21.86, MSE=4.2032
## left son=30 (11 obs) right son=31 (14 obs)
## Primary splits:
## Radio < 34.9 to the left, improve=0.6851978, (0 missing)
## TV < 258.35 to the left, improve=0.1541742, (0 missing)
## Newspaper < 54.05 to the left, improve=0.1084895, (0 missing)
## Surrogate splits:
## Newspaper < 23.05 to the left, agree=0.68, adj=0.273, (0 split)
## TV < 217.6 to the right, agree=0.60, adj=0.091, (0 split)
##
## Node number 30: 11 observations
## mean=19.94545, MSE=0.7861157
##
## Node number 31: 14 observations
## mean=23.36429, MSE=1.745153Representar visualmente el Ć”rbol de regresiĆ³n
rpart.plot(modelo_ar)
Predecir valores con datos de validaciĆ³n
predicciones <- predict(object = modelo_ar, newdata = datos.validacion)Construir un data frame para comparar y luego evaluar
comparaciones <- data.frame(datos.validacion, predicciones)
comparaciones## TV Radio Newspaper Web Sales predicciones
## 1 230.1 37.8 69.2 306.634752 22.1 23.364286
## 3 17.2 45.9 69.3 49.498908 9.3 6.822222
## 4 151.5 41.3 58.5 257.816893 18.5 18.086667
## 6 8.7 48.9 75.0 22.072395 7.2 6.822222
## 15 204.1 32.9 46.0 245.774960 19.0 18.086667
## 16 195.4 47.7 52.9 148.095134 22.4 18.086667
## 17 67.8 36.6 114.0 202.638903 12.5 11.950000
## 24 228.3 16.9 26.2 51.170073 15.5 15.288889
## 37 266.9 43.8 5.0 96.316829 25.4 23.364286
## 44 206.9 8.4 26.4 213.609610 12.9 12.116667
## 49 227.2 15.8 49.9 75.269182 14.8 15.288889
## 52 100.4 9.6 3.6 41.335255 10.7 9.468421
## 56 198.9 49.4 60.0 204.418927 23.7 18.086667
## 65 131.1 42.8 28.9 124.382228 18.0 18.086667
## 66 69.0 9.3 0.9 205.993485 9.3 9.468421
## 67 31.5 24.6 2.2 216.471397 9.5 6.822222
## 69 237.4 27.5 11.0 291.548597 18.9 19.945455
## 74 129.4 5.7 31.3 61.306191 11.0 12.116667
## 76 16.9 43.7 89.4 70.234282 8.7 6.822222
## 77 27.5 1.6 20.7 117.101925 6.9 6.822222
## 78 120.5 28.5 14.2 97.455125 14.2 11.950000
## 79 5.4 29.9 9.4 4.308085 5.3 6.822222
## 84 68.4 44.5 35.6 78.393104 13.6 11.950000
## 87 76.3 27.5 16.0 193.830894 12.0 11.950000
## 90 109.8 47.8 51.4 162.727890 16.7 11.950000
## 91 134.3 4.9 9.3 258.355488 11.2 12.116667
## 93 217.7 33.5 59.0 150.962754 19.4 19.945455
## 95 107.4 14.0 10.9 151.990733 11.5 11.950000
## 96 163.3 31.6 52.9 155.594877 16.9 18.086667
## 98 184.9 21.0 22.0 253.300721 15.5 15.288889
## 103 280.2 10.1 21.4 49.808451 14.8 12.116667
## 105 238.2 34.3 5.3 112.155489 20.7 19.945455
## 111 225.8 8.2 56.5 95.185762 13.4 12.116667
## 115 78.2 46.8 34.5 76.770428 14.6 11.950000
## 131 0.7 39.6 8.7 162.902591 1.6 6.822222
## 135 36.9 38.6 65.6 81.246748 10.8 11.950000
## 136 48.3 47.0 8.5 61.227323 11.6 11.950000
## 139 43.0 25.9 20.5 181.368740 9.6 11.950000
## 144 104.6 5.7 34.4 336.571095 10.4 9.468421
## 146 140.3 1.9 9.0 231.883385 10.3 12.116667
## 148 243.2 49.0 44.3 151.990733 25.4 23.364286
## 157 93.9 43.5 50.5 74.361939 15.3 11.950000
## 158 149.8 1.3 24.3 145.803211 10.1 12.116667
## 161 172.5 18.1 30.7 207.496801 14.4 15.288889
## 162 85.7 35.8 49.3 188.933530 13.3 11.950000
## 165 117.2 14.7 5.4 109.008763 11.9 11.950000
## 166 234.5 3.4 84.8 135.024909 11.9 12.116667
## 173 19.6 20.1 17.0 155.583662 7.6 6.822222
## 175 222.4 3.4 13.1 144.525662 11.5 12.116667
## 176 276.9 48.9 41.8 151.990733 27.0 23.364286
## 181 156.6 2.6 8.3 122.116470 10.5 12.116667
## 184 287.6 43.0 71.8 154.309725 26.2 23.364286
## 186 205.0 45.1 19.6 208.692690 22.6 18.086667
## 187 139.5 2.1 26.6 236.744035 10.3 12.116667
## 193 17.2 4.1 31.6 265.028644 5.9 6.822222
## 195 149.7 35.6 6.0 99.579981 17.3 18.086667
## 197 94.2 4.9 8.1 118.041856 9.7 9.468421
## 198 177.0 9.3 6.4 213.274671 12.8 12.116667rmse Root Mean StƔndard Error (Root-mean-square deviation),
Este valor normalmente se compara contra otro modelo y el que estƩ mas cerca de cero es mejor.
La raiz del Error CuadrĆ”tico Medio (rmse) es una mĆ©trica que dice quĆ© tan lejos estĆ”n los valores predichos de los valores observados o reales en un anĆ”lisis de regresiĆ³n, en promedio. Se calcula como:
\[ rmse = \sqrt{\frac{\sum(predicho_i - real_i)^{2}}{n}} \]
RMSE es una forma Ćŗtil de ver quĆ© tan bien un modelo de regresiĆ³n puede ajustarse a un conjunto de datos.
Cuanto mayor sea el rmse, mayor serĆ” la diferencia entre los valores predichos y reales, lo que significa que peor se ajusta un modelo de regresiĆ³n a los datos. Por el contrario, cuanto mĆ”s pequeƱo sea el rmse, mejor podrĆ” un modelo ajustar los datos.
Se compara este valor de rmse con respecto al modelo de regresiĆ³n mĆŗltiple
Con este modelo de Ć”rbol de regresiĆ³n, los mismos datos, mismas particiones se tuvo un valor de 1.455681 por lo que se puede interpretar que este modelo de regresiĆ³n fuĆ© mejor con respecto a la mĆ©trica rmse con respecto al modelo de regresiĆ³n mĆŗltiple que tuvo un valor de 1.543975.
rmse <- rmse(actual = comparaciones$Sales, predicted = comparaciones$predicciones)
rmse## [1] 2.042057Graficar predicciones contra valores reales
ggplot(data = comparaciones) +
geom_line(aes(x = 1:nrow(comparaciones), y = Sales), col='blue') +
geom_line(aes(x = 1:nrow(comparaciones), y = predicciones), col='yellow') +
ggtitle(label="Valores reales vs predichos Adverstising", subtitle = "Arbol de RegresiĆ³n") 
Predicciones con datos nuevos
TV <- c(140, 160)
Radio <- c(60, 40)
Newspaper <- c(80, 90)
nuevos <- data.frame(TV, Radio, Newspaper)
nuevos## TV Radio Newspaper
## 1 140 60 80
## 2 160 40 90Y.predicciones <- predict(object = modelo_ar, newdata = nuevos)
Y.predicciones## 1 2
## 18.08667 18.08667InterpretaciĆ³n
Con el modelo de arbol de regresion, podemos visualizar de manera logica y visual los nodos de decision a base de las metricas que le indiquemos, en este caso nos describe las variables independientes (TV, Radio, Newspaper) que mas ganancia produjo para la variable dependiente Sales, en la grafica solamente se ven las variables TV y Radio ya que en el contexto de la actualidad, lavariable Newspaper ya no representa un factor para una mayor ganancia en Sales.