##### Brett-Lantz Machine Learning with R
# traduccion y adaptacion Luis A. George
########################################################
#Capitulo 6: Metodos basados en Regresion -------------------
#### Parte 1: Regresion Linear -------------------
setwd("C:\\Users\\Luis\\Desktop\\Brett-Lantz\\chapter_6")
## Ejemplo: La data del Trasbordador Challenger ----
launch <- read.csv("challenger.csv")
# estimacion de beta (manual)
b <- cov(launch$temperature, launch$distress_ct) / var(launch$temperature)
b
## [1] -0.04753968
# estimacion de alfa manual
a <- mean(launch$distress_ct) - b * mean(launch$temperature)
a
## [1] 3.698413
# calculo de la correlacion de la data de lanzamiento
r <- cov(launch$temperature, launch$distress_ct) /
(sd(launch$temperature) * sd(launch$distress_ct))
r
## [1] -0.5111264
cor(launch$temperature, launch$distress_ct)
## [1] -0.5111264
# computo de la pendiente usando la correlacion
r * (sd(launch$distress_ct) / sd(launch$temperature))
## [1] -0.04753968
# confirmacion de la linea de regresion
# usando la funcion lm
model <- lm(distress_ct ~ temperature, data = launch)
model
##
## Call:
## lm(formula = distress_ct ~ temperature, data = launch)
##
## Coefficients:
## (Intercept) temperature
## 3.69841 -0.04754
summary(model)
##
## Call:
## lm(formula = distress_ct ~ temperature, data = launch)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5608 -0.3944 -0.0854 0.1056 1.8671
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.69841 1.21951 3.033 0.00633 **
## temperature -0.04754 0.01744 -2.725 0.01268 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5774 on 21 degrees of freedom
## Multiple R-squared: 0.2613, Adjusted R-squared: 0.2261
## F-statistic: 7.426 on 1 and 21 DF, p-value: 0.01268
# creando una funcion para realizar la regresion multiple
reg <- function(y, x) {
x <- as.matrix(x)
x <- cbind(Intercept = 1, x)
b <- solve(t(x) %*% x) %*% t(x) %*% y
colnames(b) <- "estimate"
print(b)
}
# examinamos la data de lanzamiento
str(launch)
## 'data.frame': 23 obs. of 4 variables:
## $ distress_ct : int 0 1 0 0 0 0 0 0 1 1 ...
## $ temperature : int 66 70 69 68 67 72 73 70 57 63 ...
## $ field_check_pressure: int 50 50 50 50 50 50 100 100 200 200 ...
## $ flight_num : int 1 2 3 4 5 6 7 8 9 10 ...
# probando el modelo de regresion lineal
reg(y = launch$distress_ct, x = launch[2])
## estimate
## Intercept 3.69841270
## temperature -0.04753968
# usando un modelo de regresion multiple
reg(y = launch$distress_ct, x = launch[2:4])
## estimate
## Intercept 3.527093383
## temperature -0.051385940
## field_check_pressure 0.001757009
## flight_num 0.014292843
# confirmando los resultados de la regresion multiple
# usando la funcion lm
model <- lm(launch$distress_ct ~ launch$temperature + launch$field_check_pressure + launch$flight_num, data = launch)
model
##
## Call:
## lm(formula = launch$distress_ct ~ launch$temperature + launch$field_check_pressure +
## launch$flight_num, data = launch)
##
## Coefficients:
## (Intercept) launch$temperature
## 3.527093 -0.051386
## launch$field_check_pressure launch$flight_num
## 0.001757 0.014293
## Ejemplo: Prediccion de Gastos Medicos ----
## Paso 2: Explorando y preparando la data ----
insurance <- read.csv("insurance.csv", stringsAsFactors = TRUE)
str(insurance)
## 'data.frame': 1338 obs. of 7 variables:
## $ age : int 19 18 28 33 32 31 46 37 37 60 ...
## $ sex : Factor w/ 2 levels "female","male": 1 2 2 2 2 1 1 1 2 1 ...
## $ bmi : num 27.9 33.8 33 22.7 28.9 25.7 33.4 27.7 29.8 25.8 ...
## $ children: int 0 1 3 0 0 0 1 3 2 0 ...
## $ smoker : Factor w/ 2 levels "no","yes": 2 1 1 1 1 1 1 1 1 1 ...
## $ region : Factor w/ 4 levels "northeast","northwest",..: 4 3 3 2 2 3 3 2 1 2 ...
## $ expenses: num 16885 1726 4449 21984 3867 ...
# summarize the charges variable
summary(insurance$expenses)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1122 4740 9382 13270 16640 63770
# histograma de los gastos de suguro
hist(insurance$expenses)
# tabla de region
table(insurance$region)
##
## northeast northwest southeast southwest
## 324 325 364 325
# explorando la relacion entre las
# variables: correlation matrix
cor(insurance[c("age", "bmi", "children", "expenses")])
## age bmi children expenses
## age 1.0000000 0.10934101 0.04246900 0.29900819
## bmi 0.1093410 1.00000000 0.01264471 0.19857626
## children 0.0424690 0.01264471 1.00000000 0.06799823
## expenses 0.2990082 0.19857626 0.06799823 1.00000000
# visualizado la relacion entre las variables
# : scatterplot matrix
pairs(insurance[c("age", "bmi", "children", "expenses")])
# un grafico mas informativo que la scatterplot matrix
library(psych)
pairs.panels(insurance[c("age", "bmi", "children", "expenses")])
## Paso 3: Entrenando el modelo en la data ----
ins_model <- lm(expenses ~ age + children + bmi + sex + smoker + region,
data = insurance)
ins_model <- lm(expenses ~ ., data = insurance) # this is equivalent to above
# vemos los coeficientes estimados de beta
ins_model
##
## Call:
## lm(formula = expenses ~ ., data = insurance)
##
## Coefficients:
## (Intercept) age sexmale bmi
## -11941.6 256.8 -131.4 339.3
## children smokeryes regionnorthwest regionsoutheast
## 475.7 23847.5 -352.8 -1035.6
## regionsouthwest
## -959.3
## Paso 4: Evaluando el rendimiento del modelo ----
# detalles adicionales del modelo
summary(ins_model)
##
## Call:
## lm(formula = expenses ~ ., data = insurance)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11302.7 -2850.9 -979.6 1383.9 29981.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11941.6 987.8 -12.089 < 2e-16 ***
## age 256.8 11.9 21.586 < 2e-16 ***
## sexmale -131.3 332.9 -0.395 0.693255
## bmi 339.3 28.6 11.864 < 2e-16 ***
## children 475.7 137.8 3.452 0.000574 ***
## smokeryes 23847.5 413.1 57.723 < 2e-16 ***
## regionnorthwest -352.8 476.3 -0.741 0.458976
## regionsoutheast -1035.6 478.7 -2.163 0.030685 *
## regionsouthwest -959.3 477.9 -2.007 0.044921 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6062 on 1329 degrees of freedom
## Multiple R-squared: 0.7509, Adjusted R-squared: 0.7494
## F-statistic: 500.9 on 8 and 1329 DF, p-value: < 2.2e-16
## Paso 5: Mejorando el rendimiento del modelo ----
# añadiendo un termino higher-order "age"
insurance$age2 <- insurance$age^2
# añadiendo un indicador para BMI >= 30
insurance$bmi30 <- ifelse(insurance$bmi >= 30, 1, 0)
# creando el modelo final
ins_model2 <- lm(expenses ~ age + age2 + children + bmi + sex +
bmi30*smoker + region, data = insurance)
summary(ins_model2)
##
## Call:
## lm(formula = expenses ~ age + age2 + children + bmi + sex + bmi30 *
## smoker + region, data = insurance)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17297.1 -1656.0 -1262.7 -727.8 24161.6
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 139.0053 1363.1359 0.102 0.918792
## age -32.6181 59.8250 -0.545 0.585690
## age2 3.7307 0.7463 4.999 6.54e-07 ***
## children 678.6017 105.8855 6.409 2.03e-10 ***
## bmi 119.7715 34.2796 3.494 0.000492 ***
## sexmale -496.7690 244.3713 -2.033 0.042267 *
## bmi30 -997.9355 422.9607 -2.359 0.018449 *
## smokeryes 13404.5952 439.9591 30.468 < 2e-16 ***
## regionnorthwest -279.1661 349.2826 -0.799 0.424285
## regionsoutheast -828.0345 351.6484 -2.355 0.018682 *
## regionsouthwest -1222.1619 350.5314 -3.487 0.000505 ***
## bmi30:smokeryes 19810.1534 604.6769 32.762 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4445 on 1326 degrees of freedom
## Multiple R-squared: 0.8664, Adjusted R-squared: 0.8653
## F-statistic: 781.7 on 11 and 1326 DF, p-value: < 2.2e-16
#### Parte 2: Arboles de regresion and Modelos de arboles -------------------
## Entendiendo los arboles de regresion y modelos de arboles ----
## Ejemplo: Calculando el SDR ----
# a continuacion la data
tee <- c(1, 1, 1, 2, 2, 3, 4, 5, 5, 6, 6, 7, 7, 7, 7)
at1 <- c(1, 1, 1, 2, 2, 3, 4, 5, 5)
at2 <- c(6, 6, 7, 7, 7, 7)
bt1 <- c(1, 1, 1, 2, 2, 3, 4)
bt2 <- c(5, 5, 6, 6, 7, 7, 7, 7)
# computo del SDR
sdr_a <- sd(tee) - (length(at1) / length(tee) * sd(at1) + length(at2) / length(tee) * sd(at2))
sdr_b <- sd(tee) - (length(bt1) / length(tee) * sd(bt1) + length(bt2) / length(tee) * sd(bt2))
# comparamos el SDR para cada nodo
sdr_a
## [1] 1.202815
sdr_b
## [1] 1.392751
## Ejemplo: Estimando la calidad de un vino ----
## Step 2: Obteniendo y explorando la data ----
wine <- read.csv("whitewines.csv")
# examinamos la data wine
str(wine)
## 'data.frame': 4898 obs. of 12 variables:
## $ fixed.acidity : num 6.7 5.7 5.9 5.3 6.4 7 7.9 6.6 7 6.5 ...
## $ volatile.acidity : num 0.62 0.22 0.19 0.47 0.29 0.14 0.12 0.38 0.16 0.37 ...
## $ citric.acid : num 0.24 0.2 0.26 0.1 0.21 0.41 0.49 0.28 0.3 0.33 ...
## $ residual.sugar : num 1.1 16 7.4 1.3 9.65 0.9 5.2 2.8 2.6 3.9 ...
## $ chlorides : num 0.039 0.044 0.034 0.036 0.041 0.037 0.049 0.043 0.043 0.027 ...
## $ free.sulfur.dioxide : num 6 41 33 11 36 22 33 17 34 40 ...
## $ total.sulfur.dioxide: num 62 113 123 74 119 95 152 67 90 130 ...
## $ density : num 0.993 0.999 0.995 0.991 0.993 ...
## $ pH : num 3.41 3.22 3.49 3.48 2.99 3.25 3.18 3.21 2.88 3.28 ...
## $ sulphates : num 0.32 0.46 0.42 0.54 0.34 0.43 0.47 0.47 0.47 0.39 ...
## $ alcohol : num 10.4 8.9 10.1 11.2 10.9 ...
## $ quality : int 5 6 6 4 6 6 6 6 6 7 ...
# la distribucion del rating de calidad (quality)
hist(wine$quality)
# summario de estadisticas de la data wine
summary(wine)
## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. : 3.800 Min. :0.0800 Min. :0.0000 Min. : 0.600
## 1st Qu.: 6.300 1st Qu.:0.2100 1st Qu.:0.2700 1st Qu.: 1.700
## Median : 6.800 Median :0.2600 Median :0.3200 Median : 5.200
## Mean : 6.855 Mean :0.2782 Mean :0.3342 Mean : 6.391
## 3rd Qu.: 7.300 3rd Qu.:0.3200 3rd Qu.:0.3900 3rd Qu.: 9.900
## Max. :14.200 Max. :1.1000 Max. :1.6600 Max. :65.800
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## Min. :0.00900 Min. : 2.00 Min. : 9.0
## 1st Qu.:0.03600 1st Qu.: 23.00 1st Qu.:108.0
## Median :0.04300 Median : 34.00 Median :134.0
## Mean :0.04577 Mean : 35.31 Mean :138.4
## 3rd Qu.:0.05000 3rd Qu.: 46.00 3rd Qu.:167.0
## Max. :0.34600 Max. :289.00 Max. :440.0
## density pH sulphates alcohol
## Min. :0.9871 Min. :2.720 Min. :0.2200 Min. : 8.00
## 1st Qu.:0.9917 1st Qu.:3.090 1st Qu.:0.4100 1st Qu.: 9.50
## Median :0.9937 Median :3.180 Median :0.4700 Median :10.40
## Mean :0.9940 Mean :3.188 Mean :0.4898 Mean :10.51
## 3rd Qu.:0.9961 3rd Qu.:3.280 3rd Qu.:0.5500 3rd Qu.:11.40
## Max. :1.0390 Max. :3.820 Max. :1.0800 Max. :14.20
## quality
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.878
## 3rd Qu.:6.000
## Max. :9.000
# Creamos la particion de la data entre entrenamiento
# (train) y prueba (test)
wine_train <- wine[1:3750, ]
wine_test <- wine[3751:4898, ]
## Paso 3: Entrenando el modelo en la data ----
# arbol de regresion usando la libreria rpart
library(rpart)
m.rpart <- rpart(quality ~ ., data = wine_train)
# revisamos la informacion basica a cerca del arbol
m.rpart
## n= 3750
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 3750 2945.53200 5.870933
## 2) alcohol< 10.85 2372 1418.86100 5.604975
## 4) volatile.acidity>=0.2275 1611 821.30730 5.432030
## 8) volatile.acidity>=0.3025 688 278.97670 5.255814 *
## 9) volatile.acidity< 0.3025 923 505.04230 5.563380 *
## 5) volatile.acidity< 0.2275 761 447.36400 5.971091 *
## 3) alcohol>=10.85 1378 1070.08200 6.328737
## 6) free.sulfur.dioxide< 10.5 84 95.55952 5.369048 *
## 7) free.sulfur.dioxide>=10.5 1294 892.13600 6.391036
## 14) alcohol< 11.76667 629 430.11130 6.173291
## 28) volatile.acidity>=0.465 11 10.72727 4.545455 *
## 29) volatile.acidity< 0.465 618 389.71680 6.202265 *
## 15) alcohol>=11.76667 665 403.99400 6.596992 *
# para obtener informacion mas sobre el arbol generado
summary(m.rpart)
## Call:
## rpart(formula = quality ~ ., data = wine_train)
## n= 3750
##
## CP nsplit rel error xerror xstd
## 1 0.15501053 0 1.0000000 1.0004889 0.02445917
## 2 0.05098911 1 0.8449895 0.8506566 0.02343744
## 3 0.02796998 2 0.7940004 0.8054548 0.02280410
## 4 0.01970128 3 0.7660304 0.7837084 0.02173762
## 5 0.01265926 4 0.7463291 0.7603372 0.02082953
## 6 0.01007193 5 0.7336698 0.7500661 0.02068249
## 7 0.01000000 6 0.7235979 0.7496347 0.02068898
##
## Variable importance
## alcohol density volatile.acidity
## 34 21 15
## chlorides total.sulfur.dioxide free.sulfur.dioxide
## 11 7 6
## residual.sugar sulphates citric.acid
## 3 1 1
##
## Node number 1: 3750 observations, complexity param=0.1550105
## mean=5.870933, MSE=0.7854751
## left son=2 (2372 obs) right son=3 (1378 obs)
## Primary splits:
## alcohol < 10.85 to the left, improve=0.15501050, (0 missing)
## density < 0.992035 to the right, improve=0.10915940, (0 missing)
## chlorides < 0.0395 to the right, improve=0.07682258, (0 missing)
## total.sulfur.dioxide < 158.5 to the right, improve=0.04089663, (0 missing)
## citric.acid < 0.235 to the left, improve=0.03636458, (0 missing)
## Surrogate splits:
## density < 0.991995 to the right, agree=0.869, adj=0.644, (0 split)
## chlorides < 0.0375 to the right, agree=0.757, adj=0.339, (0 split)
## total.sulfur.dioxide < 103.5 to the right, agree=0.690, adj=0.155, (0 split)
## residual.sugar < 5.375 to the right, agree=0.667, adj=0.094, (0 split)
## sulphates < 0.345 to the right, agree=0.647, adj=0.038, (0 split)
##
## Node number 2: 2372 observations, complexity param=0.05098911
## mean=5.604975, MSE=0.5981709
## left son=4 (1611 obs) right son=5 (761 obs)
## Primary splits:
## volatile.acidity < 0.2275 to the right, improve=0.10585250, (0 missing)
## free.sulfur.dioxide < 13.5 to the left, improve=0.03390500, (0 missing)
## citric.acid < 0.235 to the left, improve=0.03204075, (0 missing)
## alcohol < 10.11667 to the left, improve=0.03136524, (0 missing)
## chlorides < 0.0585 to the right, improve=0.01633599, (0 missing)
## Surrogate splits:
## pH < 3.485 to the left, agree=0.694, adj=0.047, (0 split)
## sulphates < 0.755 to the left, agree=0.685, adj=0.020, (0 split)
## total.sulfur.dioxide < 105.5 to the right, agree=0.683, adj=0.011, (0 split)
## residual.sugar < 0.75 to the right, agree=0.681, adj=0.007, (0 split)
## chlorides < 0.0285 to the right, agree=0.680, adj=0.003, (0 split)
##
## Node number 3: 1378 observations, complexity param=0.02796998
## mean=6.328737, MSE=0.7765472
## left son=6 (84 obs) right son=7 (1294 obs)
## Primary splits:
## free.sulfur.dioxide < 10.5 to the left, improve=0.07699080, (0 missing)
## alcohol < 11.76667 to the left, improve=0.06210660, (0 missing)
## total.sulfur.dioxide < 67.5 to the left, improve=0.04438619, (0 missing)
## residual.sugar < 1.375 to the left, improve=0.02905351, (0 missing)
## fixed.acidity < 7.35 to the right, improve=0.02613259, (0 missing)
## Surrogate splits:
## total.sulfur.dioxide < 53.5 to the left, agree=0.952, adj=0.214, (0 split)
## volatile.acidity < 0.875 to the right, agree=0.940, adj=0.024, (0 split)
##
## Node number 4: 1611 observations, complexity param=0.01265926
## mean=5.43203, MSE=0.5098121
## left son=8 (688 obs) right son=9 (923 obs)
## Primary splits:
## volatile.acidity < 0.3025 to the right, improve=0.04540111, (0 missing)
## alcohol < 10.05 to the left, improve=0.03874403, (0 missing)
## free.sulfur.dioxide < 13.5 to the left, improve=0.03338886, (0 missing)
## chlorides < 0.0495 to the right, improve=0.02574623, (0 missing)
## citric.acid < 0.195 to the left, improve=0.02327981, (0 missing)
## Surrogate splits:
## citric.acid < 0.215 to the left, agree=0.633, adj=0.141, (0 split)
## free.sulfur.dioxide < 20.5 to the left, agree=0.600, adj=0.062, (0 split)
## chlorides < 0.0595 to the right, agree=0.593, adj=0.047, (0 split)
## residual.sugar < 1.15 to the left, agree=0.583, adj=0.023, (0 split)
## total.sulfur.dioxide < 219.25 to the right, agree=0.582, adj=0.022, (0 split)
##
## Node number 5: 761 observations
## mean=5.971091, MSE=0.5878633
##
## Node number 6: 84 observations
## mean=5.369048, MSE=1.137613
##
## Node number 7: 1294 observations, complexity param=0.01970128
## mean=6.391036, MSE=0.6894405
## left son=14 (629 obs) right son=15 (665 obs)
## Primary splits:
## alcohol < 11.76667 to the left, improve=0.06504696, (0 missing)
## chlorides < 0.0395 to the right, improve=0.02758705, (0 missing)
## fixed.acidity < 7.35 to the right, improve=0.02750932, (0 missing)
## pH < 3.055 to the left, improve=0.02307356, (0 missing)
## total.sulfur.dioxide < 191.5 to the right, improve=0.02186818, (0 missing)
## Surrogate splits:
## density < 0.990885 to the right, agree=0.720, adj=0.424, (0 split)
## volatile.acidity < 0.2675 to the left, agree=0.637, adj=0.253, (0 split)
## chlorides < 0.0365 to the right, agree=0.630, adj=0.238, (0 split)
## residual.sugar < 1.475 to the left, agree=0.575, adj=0.126, (0 split)
## total.sulfur.dioxide < 128.5 to the right, agree=0.574, adj=0.124, (0 split)
##
## Node number 8: 688 observations
## mean=5.255814, MSE=0.4054895
##
## Node number 9: 923 observations
## mean=5.56338, MSE=0.5471747
##
## Node number 14: 629 observations, complexity param=0.01007193
## mean=6.173291, MSE=0.6838017
## left son=28 (11 obs) right son=29 (618 obs)
## Primary splits:
## volatile.acidity < 0.465 to the right, improve=0.06897561, (0 missing)
## total.sulfur.dioxide < 200 to the right, improve=0.04223066, (0 missing)
## residual.sugar < 0.975 to the left, improve=0.03061714, (0 missing)
## fixed.acidity < 7.35 to the right, improve=0.02978501, (0 missing)
## sulphates < 0.575 to the left, improve=0.02165970, (0 missing)
## Surrogate splits:
## citric.acid < 0.045 to the left, agree=0.986, adj=0.182, (0 split)
## total.sulfur.dioxide < 279.25 to the right, agree=0.986, adj=0.182, (0 split)
##
## Node number 15: 665 observations
## mean=6.596992, MSE=0.6075098
##
## Node number 28: 11 observations
## mean=4.545455, MSE=0.9752066
##
## Node number 29: 618 observations
## mean=6.202265, MSE=0.6306098
# usamos el paquete rpart.plot para visualizar
library(rpart.plot)
# un diagrama basico de un arbol de decision
rpart.plot(m.rpart, digits = 3)
# unos pocos ajustes al diagrama
rpart.plot(m.rpart, digits = 4, fallen.leaves = TRUE, type = 3, extra = 101)
## Paso 4: Evaluando el rendimiento del modelo ----
# generamos predicciones para la data de prueba
# del modelo (test)
p.rpart <- predict(m.rpart, wine_test)
# comparamos la distribucion value de prediccion vs. valores actuales
summary(p.rpart)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.545 5.563 5.971 5.893 6.202 6.597
summary(wine_test$quality)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.901 6.000 9.000
# comparamos la correlacion
cor(p.rpart, wine_test$quality)
## [1] 0.5369525
# creamos una funcion para calcular
# el valor absoluto del promedio del error
MAE <- function(actual, predicted) {
mean(abs(actual - predicted))
}
# el MAE entre prediccion y valor actual
MAE(p.rpart, wine_test$quality)
## [1] 0.5872652
# el MAE entre valores actuales y el valor promedio
mean(wine_train$quality) # result = 5.87
## [1] 5.870933
MAE(5.87, wine_test$quality)
## [1] 0.6722474
## Paso 5: Mejorando el rendimiento del modelo ----
# usamos el algoritmo M5' del paquete RWeka
library(RWeka)
m.m5p <- M5P(quality ~ ., data = wine_train)
# el nuevo arbol creado
m.m5p
## M5 pruned model tree:
## (using smoothed linear models)
##
## alcohol <= 10.85 :
## | volatile.acidity <= 0.238 :
## | | fixed.acidity <= 6.85 : LM1 (406/66.024%)
## | | fixed.acidity > 6.85 :
## | | | free.sulfur.dioxide <= 24.5 : LM2 (113/87.697%)
## | | | free.sulfur.dioxide > 24.5 :
## | | | | alcohol <= 9.15 :
## | | | | | citric.acid <= 0.305 :
## | | | | | | residual.sugar <= 14.45 :
## | | | | | | | residual.sugar <= 13.8 :
## | | | | | | | | chlorides <= 0.053 : LM3 (6/77.537%)
## | | | | | | | | chlorides > 0.053 : LM4 (13/0%)
## | | | | | | | residual.sugar > 13.8 : LM5 (11/0%)
## | | | | | | residual.sugar > 14.45 : LM6 (12/0%)
## | | | | | citric.acid > 0.305 :
## | | | | | | total.sulfur.dioxide <= 169.5 :
## | | | | | | | total.sulfur.dioxide <= 161.5 :
## | | | | | | | | pH <= 3.355 :
## | | | | | | | | | volatile.acidity <= 0.215 :
## | | | | | | | | | | free.sulfur.dioxide <= 44 : LM7 (3/53.19%)
## | | | | | | | | | | free.sulfur.dioxide > 44 : LM8 (8/48.858%)
## | | | | | | | | | volatile.acidity > 0.215 : LM9 (3/0%)
## | | | | | | | | pH > 3.355 : LM10 (4/0%)
## | | | | | | | total.sulfur.dioxide > 161.5 : LM11 (6/0%)
## | | | | | | total.sulfur.dioxide > 169.5 :
## | | | | | | | sulphates <= 0.56 :
## | | | | | | | | free.sulfur.dioxide <= 48.5 : LM12 (7/0%)
## | | | | | | | | free.sulfur.dioxide > 48.5 :
## | | | | | | | | | fixed.acidity <= 7.3 : LM13 (5/0%)
## | | | | | | | | | fixed.acidity > 7.3 : LM14 (4/0%)
## | | | | | | | sulphates > 0.56 : LM15 (11/0%)
## | | | | alcohol > 9.15 :
## | | | | | density <= 0.996 :
## | | | | | | sulphates <= 0.395 : LM16 (38/85.791%)
## | | | | | | sulphates > 0.395 : LM17 (120/71.353%)
## | | | | | density > 0.996 :
## | | | | | | residual.sugar <= 14.7 : LM18 (84/45.874%)
## | | | | | | residual.sugar > 14.7 : LM19 (24/62.764%)
## | volatile.acidity > 0.238 :
## | | alcohol <= 10.15 :
## | | | volatile.acidity <= 0.303 :
## | | | | citric.acid <= 0.265 :
## | | | | | free.sulfur.dioxide <= 25.5 : LM20 (39/41.77%)
## | | | | | free.sulfur.dioxide > 25.5 : LM21 (131/61.681%)
## | | | | citric.acid > 0.265 :
## | | | | | citric.acid <= 0.395 : LM22 (213/72.749%)
## | | | | | citric.acid > 0.395 : LM23 (189/62.097%)
## | | | volatile.acidity > 0.303 : LM24 (552/64.09%)
## | | alcohol > 10.15 :
## | | | free.sulfur.dioxide <= 26.5 : LM25 (151/75.998%)
## | | | free.sulfur.dioxide > 26.5 :
## | | | | total.sulfur.dioxide <= 161.5 : LM26 (142/74.4%)
## | | | | total.sulfur.dioxide > 161.5 : LM27 (77/77.736%)
## alcohol > 10.85 :
## | alcohol <= 11.767 :
## | | free.sulfur.dioxide <= 21.5 :
## | | | free.sulfur.dioxide <= 11.5 :
## | | | | density <= 0.992 : LM28 (19/84.403%)
## | | | | density > 0.992 :
## | | | | | fixed.acidity <= 6.85 : LM29 (6/108.029%)
## | | | | | fixed.acidity > 6.85 : LM30 (21/69.935%)
## | | | free.sulfur.dioxide > 11.5 :
## | | | | volatile.acidity <= 0.195 : LM31 (36/61.98%)
## | | | | volatile.acidity > 0.195 :
## | | | | | chlorides <= 0.036 : LM32 (34/115.199%)
## | | | | | chlorides > 0.036 : LM33 (59/78.207%)
## | | free.sulfur.dioxide > 21.5 : LM34 (495/84.229%)
## | alcohol > 11.767 :
## | | free.sulfur.dioxide <= 21.5 : LM35 (181/88.599%)
## | | free.sulfur.dioxide > 21.5 : LM36 (527/81.837%)
##
## LM num: 1
## quality =
## 0.266 * fixed.acidity
## - 2.3082 * volatile.acidity
## - 0.012 * citric.acid
## + 0.0421 * residual.sugar
## + 0.1126 * chlorides
## + 0 * free.sulfur.dioxide
## - 0.0015 * total.sulfur.dioxide
## - 109.8813 * density
## + 0.035 * pH
## + 1.4122 * sulphates
## - 0.0046 * alcohol
## + 113.1021
##
## LM num: 2
## quality =
## -0.2557 * fixed.acidity
## - 0.8082 * volatile.acidity
## - 0.1062 * citric.acid
## + 0.0738 * residual.sugar
## + 0.0973 * chlorides
## + 0.0006 * free.sulfur.dioxide
## + 0.0003 * total.sulfur.dioxide
## - 210.1018 * density
## + 0.0323 * pH
## - 0.9604 * sulphates
## - 0.0231 * alcohol
## + 216.8857
##
## LM num: 3
## quality =
## 0.0725 * fixed.acidity
## - 1.0921 * volatile.acidity
## - 0.6118 * citric.acid
## + 0.0294 * residual.sugar
## + 105.3735 * chlorides
## - 0.0027 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.0323 * pH
## + 0.1199 * sulphates
## - 0.0373 * alcohol
## + 32.2345
##
## LM num: 4
## quality =
## 0.0725 * fixed.acidity
## - 1.0921 * volatile.acidity
## - 0.6118 * citric.acid
## + 0.0294 * residual.sugar
## + 99.4295 * chlorides
## - 0.0027 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.0323 * pH
## + 0.1199 * sulphates
## - 0.0373 * alcohol
## + 32.6786
##
## LM num: 5
## quality =
## 0.0944 * fixed.acidity
## - 1.0921 * volatile.acidity
## - 0.6118 * citric.acid
## + 0.0255 * residual.sugar
## + 95.8527 * chlorides
## - 0.0027 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.0323 * pH
## + 0.1199 * sulphates
## - 0.0373 * alcohol
## + 32.9544
##
## LM num: 6
## quality =
## 0.0012 * fixed.acidity
## - 1.0921 * volatile.acidity
## - 0.6118 * citric.acid
## + 0.0491 * residual.sugar
## + 54.3184 * chlorides
## - 0.0027 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.0323 * pH
## + 0.1199 * sulphates
## - 0.0373 * alcohol
## + 35.4429
##
## LM num: 7
## quality =
## 0.0012 * fixed.acidity
## - 2.7131 * volatile.acidity
## - 1.0049 * citric.acid
## + 0.0297 * residual.sugar
## + 5.7935 * chlorides
## - 0.0147 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.633 * pH
## + 0.1199 * sulphates
## - 0.0373 * alcohol
## + 36.9235
##
## LM num: 8
## quality =
## 0.0012 * fixed.acidity
## - 2.7131 * volatile.acidity
## - 1.0049 * citric.acid
## + 0.0297 * residual.sugar
## + 5.7935 * chlorides
## - 0.0141 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.633 * pH
## + 0.1199 * sulphates
## - 0.0373 * alcohol
## + 36.8808
##
## LM num: 9
## quality =
## 0.0012 * fixed.acidity
## - 3.4336 * volatile.acidity
## - 1.0049 * citric.acid
## + 0.0297 * residual.sugar
## + 5.7935 * chlorides
## - 0.0146 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.633 * pH
## + 0.1199 * sulphates
## - 0.0373 * alcohol
## + 37.0118
##
## LM num: 10
## quality =
## 0.0012 * fixed.acidity
## - 1.0921 * volatile.acidity
## - 1.0049 * citric.acid
## + 0.0297 * residual.sugar
## + 5.7935 * chlorides
## - 0.0065 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.8211 * pH
## + 0.1199 * sulphates
## - 0.0373 * alcohol
## + 35.686
##
## LM num: 11
## quality =
## 0.0012 * fixed.acidity
## - 1.0921 * volatile.acidity
## - 1.0049 * citric.acid
## + 0.0297 * residual.sugar
## + 5.7935 * chlorides
## - 0.0065 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.2757 * pH
## + 0.1199 * sulphates
## - 0.0373 * alcohol
## + 37.5168
##
## LM num: 12
## quality =
## -0.0571 * fixed.acidity
## - 1.0921 * volatile.acidity
## - 1.534 * citric.acid
## + 0.0297 * residual.sugar
## + 5.7935 * chlorides
## - 0.0098 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.2583 * pH
## + 0.3345 * sulphates
## - 0.0373 * alcohol
## + 38.0548
##
## LM num: 13
## quality =
## -0.304 * fixed.acidity
## - 1.0921 * volatile.acidity
## + 0.3698 * citric.acid
## + 0.0297 * residual.sugar
## + 5.7935 * chlorides
## - 0.0097 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.2583 * pH
## + 0.3345 * sulphates
## - 0.0373 * alcohol
## + 39.1208
##
## LM num: 14
## quality =
## -0.317 * fixed.acidity
## - 1.0921 * volatile.acidity
## - 1.5116 * citric.acid
## + 0.0297 * residual.sugar
## + 5.7935 * chlorides
## - 0.0097 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.2583 * pH
## + 0.3345 * sulphates
## - 0.0373 * alcohol
## + 39.9144
##
## LM num: 15
## quality =
## -0.0683 * fixed.acidity
## - 1.0921 * volatile.acidity
## - 1.3217 * citric.acid
## + 0.0297 * residual.sugar
## + 5.7935 * chlorides
## - 0.0088 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 31.5856 * density
## + 0.2583 * pH
## + 0.3758 * sulphates
## - 0.0373 * alcohol
## + 37.9875
##
## LM num: 16
## quality =
## -0.4138 * fixed.acidity
## - 2.4188 * volatile.acidity
## - 0.1001 * citric.acid
## + 0.0519 * residual.sugar
## + 1.2445 * chlorides
## + 0.0002 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## + 146.7811 * density
## + 0.5635 * pH
## + 0.3884 * sulphates
## + 0.7403 * alcohol
## - 145.8266
##
## LM num: 17
## quality =
## 0.2744 * fixed.acidity
## - 3.6766 * volatile.acidity
## - 0.1001 * citric.acid
## + 0.0846 * residual.sugar
## + 0.5477 * chlorides
## + 0.0002 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 239.7241 * density
## + 1.5648 * pH
## + 0.8289 * sulphates
## - 0.0207 * alcohol
## + 237.4198
##
## LM num: 18
## quality =
## 0.0178 * fixed.acidity
## - 1.19 * volatile.acidity
## - 0.1001 * citric.acid
## + 0.041 * residual.sugar
## + 0.0973 * chlorides
## + 0.0002 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 46.7151 * density
## + 0.1443 * pH
## + 0.1669 * sulphates
## - 0.0207 * alcohol
## + 51.8086
##
## LM num: 19
## quality =
## 0.0178 * fixed.acidity
## - 11.6553 * volatile.acidity
## - 0.1001 * citric.acid
## + 0.0199 * residual.sugar
## + 0.0973 * chlorides
## + 0.0002 * free.sulfur.dioxide
## + 0.0044 * total.sulfur.dioxide
## - 46.7151 * density
## + 2.2855 * pH
## + 0.1669 * sulphates
## - 0.0207 * alcohol
## + 46.4726
##
## LM num: 20
## quality =
## -0.0389 * fixed.acidity
## - 0.2704 * volatile.acidity
## + 0.6445 * citric.acid
## + 0.0043 * residual.sugar
## - 11.7525 * chlorides
## + 0.0148 * free.sulfur.dioxide
## + 13.1536 * density
## - 0.2235 * pH
## + 0.0154 * sulphates
## + 0.1335 * alcohol
## - 8.119
##
## LM num: 21
## quality =
## -0.0139 * fixed.acidity
## - 0.2704 * volatile.acidity
## + 2.7911 * citric.acid
## + 0.0043 * residual.sugar
## - 16.394 * chlorides
## - 0.0093 * free.sulfur.dioxide
## - 0.0028 * total.sulfur.dioxide
## + 2.2255 * density
## - 0.088 * pH
## + 0.0154 * sulphates
## + 0.285 * alcohol
## + 1.9775
##
## LM num: 22
## quality =
## 0.0008 * fixed.acidity
## - 3.3571 * volatile.acidity
## - 0.0474 * citric.acid
## + 0.0167 * residual.sugar
## + 0.0002 * free.sulfur.dioxide
## - 0.0001 * total.sulfur.dioxide
## - 2.6496 * density
## + 0.0071 * pH
## + 0.0154 * sulphates
## + 0.0295 * alcohol
## + 8.7127
##
## LM num: 23
## quality =
## 0.0008 * fixed.acidity
## - 0.1682 * volatile.acidity
## - 0.0533 * citric.acid
## + 0.0034 * residual.sugar
## + 0.0112 * free.sulfur.dioxide
## - 0.004 * total.sulfur.dioxide
## - 2.4685 * density
## + 0.0071 * pH
## + 0.0154 * sulphates
## + 0.3099 * alcohol
## + 5.1272
##
## LM num: 24
## quality =
## -0.1011 * fixed.acidity
## - 0.8767 * volatile.acidity
## + 0.0025 * citric.acid
## + 0.0183 * residual.sugar
## - 1.5815 * chlorides
## + 0 * free.sulfur.dioxide
## + 0.0015 * total.sulfur.dioxide
## - 4.1889 * density
## + 0.0195 * pH
## + 0.0154 * sulphates
## + 0.2656 * alcohol
## + 7.556
##
## LM num: 25
## quality =
## 0.1885 * fixed.acidity
## - 1.6681 * volatile.acidity
## + 0.0075 * citric.acid
## + 0.1434 * residual.sugar
## + 0.0181 * free.sulfur.dioxide
## - 438.9263 * density
## + 1.5263 * pH
## + 1.5041 * sulphates
## + 0.0067 * alcohol
## + 434.1083
##
## LM num: 26
## quality =
## 0.3156 * fixed.acidity
## - 0.3103 * volatile.acidity
## + 0.0075 * citric.acid
## + 0.0769 * residual.sugar
## + 0.0157 * free.sulfur.dioxide
## - 0.0006 * total.sulfur.dioxide
## - 224.3886 * density
## + 2.8971 * pH
## + 1.4123 * sulphates
## + 0.0067 * alcohol
## + 215.8849
##
## LM num: 27
## quality =
## 0.0704 * fixed.acidity
## - 1.6931 * volatile.acidity
## + 0.0075 * citric.acid
## + 0.0268 * residual.sugar
## + 0 * free.sulfur.dioxide
## - 0.0058 * total.sulfur.dioxide
## - 69.0546 * density
## + 0.5221 * pH
## + 0.3033 * sulphates
## + 0.0067 * alcohol
## + 73.2245
##
## LM num: 28
## quality =
## -0.0359 * fixed.acidity
## - 2.1355 * volatile.acidity
## + 0.0312 * residual.sugar
## - 0.7007 * chlorides
## + 0.0139 * free.sulfur.dioxide
## - 3.9257 * density
## + 0.1002 * pH
## + 0.0883 * sulphates
## + 0.0057 * alcohol
## + 9.0802
##
## LM num: 29
## quality =
## -0.1622 * fixed.acidity
## - 1.936 * volatile.acidity
## + 0.0312 * residual.sugar
## - 0.7007 * chlorides
## + 0.0139 * free.sulfur.dioxide
## - 8.2054 * density
## + 0.5998 * pH
## + 0.0883 * sulphates
## + 0.0057 * alcohol
## + 13.1705
##
## LM num: 30
## quality =
## -0.1095 * fixed.acidity
## - 1.936 * volatile.acidity
## + 0.0312 * residual.sugar
## - 0.7007 * chlorides
## + 0.0139 * free.sulfur.dioxide
## - 8.2054 * density
## + 0.8708 * pH
## + 0.0883 * sulphates
## + 0.0057 * alcohol
## + 11.7475
##
## LM num: 31
## quality =
## -0.2583 * fixed.acidity
## - 1.4215 * volatile.acidity
## - 1.371 * citric.acid
## + 0.0305 * residual.sugar
## - 3.2137 * chlorides
## + 0.0063 * free.sulfur.dioxide
## - 18.7292 * density
## + 0.1002 * pH
## + 0.0883 * sulphates
## + 0.1232 * alcohol
## + 25.7445
##
## LM num: 32
## quality =
## -0.0968 * fixed.acidity
## - 0.9855 * volatile.acidity
## + 0.0245 * residual.sugar
## - 4.6936 * chlorides
## + 0.0063 * free.sulfur.dioxide
## - 18.7292 * density
## - 0.2017 * pH
## + 0.0883 * sulphates
## + 0.0612 * alcohol
## + 25.5306
##
## LM num: 33
## quality =
## -0.0764 * fixed.acidity
## - 0.9855 * volatile.acidity
## + 0.0461 * residual.sugar
## - 3.7456 * chlorides
## + 0.0063 * free.sulfur.dioxide
## - 18.7292 * density
## - 0.0997 * pH
## + 0.0883 * sulphates
## + 0.4563 * alcohol
## + 20.1476
##
## LM num: 34
## quality =
## 0.0026 * fixed.acidity
## - 1.5467 * volatile.acidity
## + 0.5902 * citric.acid
## + 0.0796 * residual.sugar
## - 7.6293 * chlorides
## + 0.0004 * free.sulfur.dioxide
## - 0.002 * total.sulfur.dioxide
## - 105.9188 * density
## + 0.9409 * pH
## + 1.1632 * sulphates
## + 0.0057 * alcohol
## + 108.0478
##
## LM num: 35
## quality =
## 0.1974 * fixed.acidity
## - 1.5244 * volatile.acidity
## - 1.1342 * citric.acid
## + 0.1108 * residual.sugar
## - 0.5309 * chlorides
## + 0.0345 * free.sulfur.dioxide
## + 0.0002 * total.sulfur.dioxide
## - 306.9205 * density
## + 1.162 * pH
## + 0.0755 * sulphates
## - 0.0054 * alcohol
## + 305.176
##
## LM num: 36
## quality =
## 0.2738 * fixed.acidity
## - 0.0442 * volatile.acidity
## + 0.1664 * residual.sugar
## - 7.6486 * chlorides
## + 0.0005 * free.sulfur.dioxide
## + 0.0001 * total.sulfur.dioxide
## - 350.199 * density
## + 1.7781 * pH
## + 1.0583 * sulphates
## - 0.1722 * alcohol
## + 347.3058
##
## Number of Rules : 36
# obtenemos un sumario del rendimiento de este
# nuevo modelo
summary(m.m5p)
##
## === Summary ===
##
## Correlation coefficient 0.6666
## Mean absolute error 0.5151
## Root mean squared error 0.6614
## Relative absolute error 76.4921 %
## Root relative squared error 74.6259 %
## Total Number of Instances 3750
# generamos predicciones con el modelo
p.m5p <- predict(m.m5p, wine_test)
# sumario estadistico de las predicciones obtenidas
summary(p.m5p)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.389 5.430 5.863 5.874 6.305 7.437
# correlacion entre las predicciones y los valores verdaderos
cor(p.m5p, wine_test$quality)
## [1] 0.6272973
# MAE de predicciones y valores verdaderos
# (usamos la funcion definida arriba)
MAE(wine_test$quality, p.m5p)
## [1] 0.5463023