launch <- read.csv("challenger.csv")
b <- cov(launch$temperature, launch$distress_ct) / var(launch$temperature)
b
## [1] -0.04753968
a <- mean(launch$distress_ct) - b * mean(launch$temperature)
a
## [1] 3.698413
r <- cov(launch$temperature, launch$distress_ct) /(sd(launch$temperature) * sd(launch$distress_ct))
r
## [1] -0.5111264
cor(launch$temperature, launch$distress_ct)
## [1] -0.5111264
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 ...
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)
}
reg(y = launch$distress_ct, x = launch[2])
## estimate
## Intercept 3.69841270
## temperature -0.04753968
reg(y = launch$distress_ct, x = launch[2:4])
## estimate
## Intercept 3.527093383
## temperature -0.051385940
## field_check_pressure 0.001757009
## flight_num 0.014292843
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 ...
summary(insurance$expenses)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1122 4740 9382 13270 16640 63770
hist(insurance$expenses)
table(insurance$region)
##
## northeast northwest southeast southwest
## 324 325 364 325
cor(insurance[c("age", "bmi", "children", "expenses")])
## age bmi children expenses
## age 1.0000000 0.10934101 0.04246900 0.29900819
## bmi 0.1093410 1.00000000 0.01264471 0.19857626
## children 0.0424690 0.01264471 1.00000000 0.06799823
## expenses 0.2990082 0.19857626 0.06799823 1.00000000
pairs(insurance[c("age", "bmi", "children", "expenses")])
library(psych)
pairs.panels(insurance[c("age", "bmi", "children", "expenses")])
ins_model <- lm(expenses ~ age + children + bmi + sex + smoker + region, data = insurance)
ins_model <- lm(expenses ~ ., data = insurance)
ins_model
##
## Call:
## lm(formula = expenses ~ ., data = insurance)
##
## Coefficients:
## (Intercept) age sexmale bmi
## -11941.6 256.8 -131.4 339.3
## children smokeryes regionnorthwest regionsoutheast
## 475.7 23847.5 -352.8 -1035.6
## regionsouthwest
## -959.3
summary(ins_model)
##
## Call:
## lm(formula = expenses ~ ., data = insurance)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11302.7 -2850.9 -979.6 1383.9 29981.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11941.6 987.8 -12.089 < 2e-16 ***
## age 256.8 11.9 21.586 < 2e-16 ***
## sexmale -131.3 332.9 -0.395 0.693255
## bmi 339.3 28.6 11.864 < 2e-16 ***
## children 475.7 137.8 3.452 0.000574 ***
## smokeryes 23847.5 413.1 57.723 < 2e-16 ***
## regionnorthwest -352.8 476.3 -0.741 0.458976
## regionsoutheast -1035.6 478.7 -2.163 0.030685 *
## regionsouthwest -959.3 477.9 -2.007 0.044921 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6062 on 1329 degrees of freedom
## Multiple R-squared: 0.7509, Adjusted R-squared: 0.7494
## F-statistic: 500.9 on 8 and 1329 DF, p-value: < 2.2e-16
insurance$age2 <- insurance$age^2
insurance$bmi30 <- ifelse(insurance$bmi >= 30, 1, 0)
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
wine <- read.csv("whitewines.csv")
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 ...
hist(wine$quality)
wine_train <- wine[1:3750, ]
wine_test <- wine[3751:4898, ]
library(rpart)
m.rpart <- rpart(quality ~ ., data = wine_train)
m.rpart
## n= 3750
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 3750 2945.53200 5.870933
## 2) alcohol< 10.85 2372 1418.86100 5.604975
## 4) volatile.acidity>=0.2275 1611 821.30730 5.432030
## 8) volatile.acidity>=0.3025 688 278.97670 5.255814 *
## 9) volatile.acidity< 0.3025 923 505.04230 5.563380 *
## 5) volatile.acidity< 0.2275 761 447.36400 5.971091 *
## 3) alcohol>=10.85 1378 1070.08200 6.328737
## 6) free.sulfur.dioxide< 10.5 84 95.55952 5.369048 *
## 7) free.sulfur.dioxide>=10.5 1294 892.13600 6.391036
## 14) alcohol< 11.76667 629 430.11130 6.173291
## 28) volatile.acidity>=0.465 11 10.72727 4.545455 *
## 29) volatile.acidity< 0.465 618 389.71680 6.202265 *
## 15) alcohol>=11.76667 665 403.99400 6.596992 *
library(rpart.plot)
rpart.plot(m.rpart, digits = 3)
rpart.plot(m.rpart, digits = 4, fallen.leaves = TRUE, type = 3, extra = 101)
p.rpart <- predict(m.rpart, wine_test)
summary(p.rpart)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.545 5.563 5.971 5.893 6.202 6.597
summary(wine_test$quality)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.901 6.000 9.000
cor(p.rpart, wine_test$quality)
## [1] 0.5369525
MAE <- function(actual, predicted) {
mean(abs(actual - predicted))
}
MAE(p.rpart, wine_test$quality)
## [1] 0.5872652
mean(wine_train$quality)
## [1] 5.870933
MAE(5.87, wine_test$quality)
## [1] 0.6722474
library(RWeka)
m.m5p <- M5P(quality ~ ., data = wine_train)
m.m5p
## M5 pruned model tree:
## (using smoothed linear models)
##
## alcohol <= 10.85 :
## | volatile.acidity <= 0.237 :
## | | 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 <= 0.052 : LM3 (6/77.537%)
## | | | | | | | | chlorides > 0.052 : 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 > 0.237 :
## | | alcohol <= 10.15 :
## | | | volatile.acidity <= 0.302 :
## | | | | 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 > 0.302 : 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
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
p.m5p <- predict(m.m5p, wine_test)
summary(p.m5p)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.389 5.430 5.863 5.874 6.305 7.437
cor(p.m5p, wine_test$quality)
## [1] 0.6272973
MAE(wine_test$quality, p.m5p)
## [1] 0.5463023