DATA 624 — Applied Predictive Modeling (Kuhn & Johnson) — Problems 3.1–3.2
Sachi Kapoor
March 01, 2026
required_pkgs <- c("tidyverse", "caret", "mlbench", "e1071", "corrplot", "RANN")
to_install <- required_pkgs[!vapply(required_pkgs, requireNamespace, FUN.VALUE = logical(1), quietly = TRUE)]
if (length(to_install) > 0) install.packages(to_install)
invisible(lapply(required_pkgs, library, character.only = TRUE))1 Problem 3.1 (Glass data): explore distributions, outliers, correlations, and transformations
1.1 Load data
data(Glass)
glimpse(Glass)## Rows: 214
## Columns: 10
## $ RI <dbl> 1.52101, 1.51761, 1.51618, 1.51766, 1.51742, 1.51596, 1.51743, 1.…
## $ Na <dbl> 13.64, 13.89, 13.53, 13.21, 13.27, 12.79, 13.30, 13.15, 14.04, 13…
## $ Mg <dbl> 4.49, 3.60, 3.55, 3.69, 3.62, 3.61, 3.60, 3.61, 3.58, 3.60, 3.46,…
## $ Al <dbl> 1.10, 1.36, 1.54, 1.29, 1.24, 1.62, 1.14, 1.05, 1.37, 1.36, 1.56,…
## $ Si <dbl> 71.78, 72.73, 72.99, 72.61, 73.08, 72.97, 73.09, 73.24, 72.08, 72…
## $ K <dbl> 0.06, 0.48, 0.39, 0.57, 0.55, 0.64, 0.58, 0.57, 0.56, 0.57, 0.67,…
## $ Ca <dbl> 8.75, 7.83, 7.78, 8.22, 8.07, 8.07, 8.17, 8.24, 8.30, 8.40, 8.09,…
## $ Ba <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ Fe <dbl> 0.00, 0.00, 0.00, 0.00, 0.00, 0.26, 0.00, 0.00, 0.00, 0.11, 0.24,…
## $ Type <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…The outcome is Type (categorical). The remaining columns
are predictors measured on different scales.
1.2 Pairwise plots and correlations
# Pairwise scatterplot matrix (can be visually busy; keeping it for completeness)
pairs(Glass[, -10], pch = 19, cex = 0.4)
# Correlation among predictors
cor_mat <- cor(Glass[, -10])
cor_mat## RI Na Mg Al Si K
## RI 1.0000000000 -0.19188538 -0.122274039 -0.40732603 -0.54205220 -0.289832711
## Na -0.1918853790 1.00000000 -0.273731961 0.15679367 -0.06980881 -0.266086504
## Mg -0.1222740393 -0.27373196 1.000000000 -0.48179851 -0.16592672 0.005395667
## Al -0.4073260341 0.15679367 -0.481798509 1.00000000 -0.00552372 0.325958446
## Si -0.5420521997 -0.06980881 -0.165926723 -0.00552372 1.00000000 -0.193330854
## K -0.2898327111 -0.26608650 0.005395667 0.32595845 -0.19333085 1.000000000
## Ca 0.8104026963 -0.27544249 -0.443750026 -0.25959201 -0.20873215 -0.317836155
## Ba -0.0003860189 0.32660288 -0.492262118 0.47940390 -0.10215131 -0.042618059
## Fe 0.1430096093 -0.24134641 0.083059529 -0.07440215 -0.09420073 -0.007719049
## Ca Ba Fe
## RI 0.8104027 -0.0003860189 0.143009609
## Na -0.2754425 0.3266028795 -0.241346411
## Mg -0.4437500 -0.4922621178 0.083059529
## Al -0.2595920 0.4794039017 -0.074402151
## Si -0.2087322 -0.1021513105 -0.094200731
## K -0.3178362 -0.0426180594 -0.007719049
## Ca 1.0000000 -0.1128409671 0.124968219
## Ba -0.1128410 1.0000000000 -0.058691755
## Fe 0.1249682 -0.0586917554 1.000000000# Visual correlation map (clustered)
corrplot(cor_mat, order = "hclust", tl.cex = 0.7)
Quick note: Several predictors show moderate correlations, but nothing here automatically implies we must remove variables—this is mainly a diagnostic step before modeling.
1.3 Outliers and skewness
# Boxplots for a quick outlier scan across predictors
boxplot(Glass[, -10], las = 2, main = "Glass predictors: boxplots (outliers + spread)")
# Skewness of each predictor (raw scale)
sk_raw <- apply(Glass[, -10], 2, e1071::skewness)
sk_raw## RI Na Mg Al Si K Ca
## 1.6027151 0.4478343 -1.1364523 0.8946104 -0.7202392 6.4600889 2.0184463
## Ba Fe
## 3.3686800 1.7298107# Look at histograms for a few skewed predictors
par(mfrow = c(1, 3))
hist(Glass$K, main = "K", xlab = "K")
hist(Glass$Ba, main = "Ba", xlab = "Ba")
hist(Glass$Mg, main = "Mg", xlab = "Mg")
par(mfrow = c(1, 1))From the plots, there are predictors with noticeable skewness and
some extreme values (e.g., K and Ba). These
can affect models that assume roughly symmetric distributions or that
are sensitive to large values.
1.4 Box–Cox transformations (reduce skewness)
Box–Cox requires strictly positive values, so we add a tiny constant to any zero-valued columns before estimating transformations.
glass_bc <- Glass
# Add a very small constant to avoid zeros (helps BoxCoxTrans converge)
for (nm in names(glass_bc)[names(glass_bc) != "Type"]) {
if (any(glass_bc[[nm]] <= 0, na.rm = TRUE)) {
glass_bc[[nm]] <- glass_bc[[nm]] + 1e-6
}
}
# Helper: compute skewness after applying an estimated Box-Cox transform
skew_after_boxcox <- function(x) {
bct <- BoxCoxTrans(x)
x_bc <- predict(bct, x)
e1071::skewness(x_bc)
}
sk_bc <- apply(glass_bc[, -10], 2, skew_after_boxcox)
sk_bc## RI Na Mg Al Si K
## 1.56566039 0.03384644 -1.43270870 0.09105899 -0.65090568 -0.78216211
## Ca Ba Fe
## -0.19395573 1.67566612 0.74424403# Compare skewness before vs after
sk_comp <- tibble(
predictor = names(sk_raw),
skew_raw = as.numeric(sk_raw),
skew_boxcox = as.numeric(sk_bc)
) |> arrange(desc(abs(skew_raw)))
sk_comp## # A tibble: 9 × 3
## predictor skew_raw skew_boxcox
## <chr> <dbl> <dbl>
## 1 K 6.46 -0.782
## 2 Ba 3.37 1.68
## 3 Ca 2.02 -0.194
## 4 Fe 1.73 0.744
## 5 RI 1.60 1.57
## 6 Mg -1.14 -1.43
## 7 Al 0.895 0.0911
## 8 Si -0.720 -0.651
## 9 Na 0.448 0.0338Conclusion (3.1): Several predictors show strong skewness and/or outliers. A Box–Cox transformation tends to pull the skewness closer to 0 for many variables, which can make modeling (and distance-based methods in particular) behave more stably. I would typically combine transformation with centering/scaling in a preprocessing recipe (depending on the model family).
2 Problem 3.2 (Soybean data): near-zero variance predictors and missing data
2.1 Load data
data(Soybean)
glimpse(Soybean)## Rows: 683
## Columns: 36
## $ Class <fct> diaporthe-stem-canker, diaporthe-stem-canker, diaporth…
## $ date <fct> 6, 4, 3, 3, 6, 5, 5, 4, 6, 4, 6, 4, 3, 6, 6, 5, 6, 4, …
## $ plant.stand <ord> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ precip <ord> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ temp <ord> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, …
## $ hail <fct> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, …
## $ crop.hist <fct> 1, 2, 1, 1, 2, 3, 2, 1, 3, 2, 1, 1, 1, 3, 1, 3, 0, 2, …
## $ area.dam <fct> 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 2, 3, 3, 3, 2, 2, …
## $ sever <fct> 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, …
## $ seed.tmt <fct> 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, …
## $ germ <ord> 0, 1, 2, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 0, 1, 2, 0, 1, …
## $ plant.growth <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
## $ leaves <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
## $ leaf.halo <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ leaf.marg <fct> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
## $ leaf.size <ord> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
## $ leaf.shread <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ leaf.malf <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ leaf.mild <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ stem <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
## $ lodging <fct> 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, …
## $ stem.cankers <fct> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ canker.lesion <fct> 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, …
## $ fruiting.bodies <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ ext.decay <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ mycelium <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ int.discolor <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, …
## $ sclerotia <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, …
## $ fruit.pods <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ fruit.spots <fct> 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, …
## $ seed <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ mold.growth <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ seed.discolor <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ seed.size <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ shriveling <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ roots <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …The outcome is Class. Many predictors are categorical
and the dataset contains missing values.
2.2 Identify and remove near-zero variance predictors
nzv <- nearZeroVar(Soybean)
length(nzv)## [1] 3colnames(Soybean)[nzv]## [1] "leaf.mild" "mycelium" "sclerotia"Soybean_nzv <- Soybean[, -nzv]
dim(Soybean)## [1] 683 36dim(Soybean_nzv)## [1] 683 33Removing near-zero variance predictors helps because they contribute little information but can add noise and complexity.
2.3 Missing data: how much and where?
na_counts <- sapply(Soybean_nzv, function(x) sum(is.na(x)))
na_counts |> sort(decreasing = TRUE) |> head(15)## hail sever seed.tmt lodging germ
## 121 121 121 121 112
## fruiting.bodies fruit.spots seed.discolor shriveling leaf.shread
## 106 106 106 106 100
## seed mold.growth seed.size leaf.halo leaf.marg
## 92 92 92 84 84# How many rows have at least one missing predictor?
# (use all predictors and exclude the outcome column)
row_has_na <- apply(dplyr::select(Soybean_nzv, -Class), 1, function(x) any(is.na(x)))
table(row_has_na)## row_has_na
## FALSE TRUE
## 562 121# Are missing values concentrated in specific classes?
tab_class_na <- table(Class = Soybean_nzv$Class, HasMissing = row_has_na)
tab_class_na## HasMissing
## Class FALSE TRUE
## 2-4-d-injury 0 16
## alternarialeaf-spot 91 0
## anthracnose 44 0
## bacterial-blight 20 0
## bacterial-pustule 20 0
## brown-spot 92 0
## brown-stem-rot 44 0
## charcoal-rot 20 0
## cyst-nematode 0 14
## diaporthe-pod-&-stem-blight 0 15
## diaporthe-stem-canker 20 0
## downy-mildew 20 0
## frog-eye-leaf-spot 91 0
## herbicide-injury 0 8
## phyllosticta-leaf-spot 20 0
## phytophthora-rot 20 68
## powdery-mildew 20 0
## purple-seed-stain 20 0
## rhizoctonia-root-rot 20 0Conclusion (3.2): After removing near-zero variance predictors, there are still missing values across many predictors, and the missingness is not evenly distributed across classes.
2.4 Example: kNN
imputation via preProcess()
For many models, we need a complete dataset. One common approach is
kNN imputation. For caret::preProcess() with
knnImpute, predictors must be numeric, so we first one-hot
encode the predictors.
# One-hot encode predictors (excluding outcome)
dummies <- dummyVars(Class ~ ., data = Soybean_nzv, fullRank = TRUE)
X <- predict(dummies, newdata = Soybean_nzv) |> as.data.frame()
# Preprocess: center/scale + kNN imputation
pp <- preProcess(X, method = c("center", "scale", "knnImpute"))
X_imp <- predict(pp, X)
# Confirm no missing values remain
sum(is.na(X_imp))## [1] 0At this point, you can bind the outcome back to the processed predictors and proceed to model training:
soy_processed <- bind_cols(Class = Soybean_nzv$Class, as_tibble(X_imp))
glimpse(soy_processed)## Rows: 683
## Columns: 61
## $ Class <fct> diaporthe-stem-canker, diaporthe-stem-canker, diapor…
## $ date.1 <dbl> -0.3512511, -0.3512511, -0.3512511, -0.3512511, -0.3…
## $ date.2 <dbl> -0.3970683, -0.3970683, -0.3970683, -0.3970683, -0.3…
## $ date.3 <dbl> -0.4570701, -0.4570701, 2.1846402, 2.1846402, -0.457…
## $ date.4 <dbl> -0.4872381, 2.0493754, -0.4872381, -0.4872381, -0.48…
## $ date.5 <dbl> -0.5283368, -0.5283368, -0.5283368, -0.5283368, -0.5…
## $ date.6 <dbl> 2.5628369, -0.3896205, -0.3896205, -0.3896205, 2.562…
## $ plant.stand.L <dbl> -0.9090678, -0.9090678, -0.9090678, -0.9090678, -0.9…
## $ precip.L <dbl> 0.5874845, 0.5874845, 0.5874845, 0.5874845, 0.587484…
## $ precip.Q <dbl> 0.4580454, 0.4580454, 0.4580454, 0.4580454, 0.458045…
## $ temp.L <dbl> -0.2900854, -0.2900854, -0.2900854, -0.2900854, -0.2…
## $ temp.Q <dbl> -0.8630451, -0.8630451, -0.8630451, -0.8630451, -0.8…
## $ hail.1 <dbl> -0.5398468, -0.5398468, -0.5398468, -0.5398468, -0.5…
## $ crop.hist.1 <dbl> 1.7429466, -0.5728809, 1.7429466, 1.7429466, -0.5728…
## $ crop.hist.2 <dbl> -0.6986461, 1.4291939, -0.6986461, -0.6986461, 1.429…
## $ crop.hist.3 <dbl> -0.6962726, -0.6962726, -0.6962726, -0.6962726, -0.6…
## $ area.dam.1 <dbl> 1.4147319, -0.7058113, -0.7058113, -0.7058113, -0.70…
## $ area.dam.2 <dbl> -0.5192521, -0.5192521, -0.5192521, -0.5192521, -0.5…
## $ area.dam.3 <dbl> -0.6141855, -0.6141855, -0.6141855, -0.6141855, -0.6…
## $ sever.1 <dbl> 0.8625633, -1.1572724, -1.1572724, -1.1572724, 0.862…
## $ sever.2 <dbl> -0.2947639, 3.3865094, 3.3865094, 3.3865094, -0.2947…
## $ seed.tmt.1 <dbl> -0.8073285, 1.2364491, 1.2364491, -0.8073285, -0.807…
## $ seed.tmt.2 <dbl> -0.2574791, -0.2574791, -0.2574791, -0.2574791, -0.2…
## $ germ.L <dbl> -1.32623673, -0.06199437, 1.20224798, -0.06199437, 1…
## $ germ.Q <dbl> 0.7706686, -1.2953021, 0.7706686, -1.2953021, 0.7706…
## $ plant.growth.1 <dbl> 1.395852, 1.395852, 1.395852, 1.395852, 1.395852, 1.…
## $ leaves.1 <dbl> 0.3561975, 0.3561975, 0.3561975, 0.3561975, 0.356197…
## $ leaf.halo.1 <dbl> -0.2526587, -0.2526587, -0.2526587, -0.2526587, -0.2…
## $ leaf.halo.2 <dbl> -1.152613, -1.152613, -1.152613, -1.152613, -1.15261…
## $ leaf.marg.1 <dbl> -0.1904508, -0.1904508, -0.1904508, -0.1904508, -0.1…
## $ leaf.marg.2 <dbl> 1.306733, 1.306733, 1.306733, 1.306733, 1.306733, 1.…
## $ leaf.size.L <dbl> 1.170838, 1.170838, 1.170838, 1.170838, 1.170838, 1.…
## $ leaf.size.Q <dbl> 1.095536, 1.095536, 1.095536, 1.095536, 1.095536, 1.…
## $ leaf.shread.1 <dbl> -0.443607, -0.443607, -0.443607, -0.443607, -0.44360…
## $ leaf.malf.1 <dbl> -0.2847663, -0.2847663, -0.2847663, -0.2847663, -0.2…
## $ stem.1 <dbl> 0.8925511, 0.8925511, 0.8925511, 0.8925511, 0.892551…
## $ lodging.1 <dbl> 3.5155259, -0.2839463, -0.2839463, -0.2839463, -0.28…
## $ stem.cankers.1 <dbl> -0.253489, -0.253489, -0.253489, -0.253489, -0.25348…
## $ stem.cankers.2 <dbl> -0.2429437, -0.2429437, -0.2429437, -0.2429437, -0.2…
## $ stem.cankers.3 <dbl> 1.5405448, 1.5405448, 1.5405448, 1.5405448, 1.540544…
## $ canker.lesion.1 <dbl> 2.6001128, 2.6001128, -0.3840024, -0.3840024, 2.6001…
## $ canker.lesion.2 <dbl> -0.6145069, -0.6145069, -0.6145069, -0.6145069, -0.6…
## $ canker.lesion.3 <dbl> -0.3345074, -0.3345074, -0.3345074, -0.3345074, -0.3…
## $ fruiting.bodies.1 <dbl> 2.1307732, 2.1307732, 2.1307732, 2.1307732, 2.130773…
## $ ext.decay.1 <dbl> 1.9421433, 1.9421433, 1.9421433, 1.9421433, 1.942143…
## $ ext.decay.2 <dbl> -0.1433099, -0.1433099, -0.1433099, -0.1433099, -0.1…
## $ int.discolor.1 <dbl> -0.2703661, -0.2703661, -0.2703661, -0.2703661, -0.2…
## $ int.discolor.2 <dbl> -0.1787467, -0.1787467, -0.1787467, -0.1787467, -0.1…
## $ fruit.pods.1 <dbl> -0.5260444, -0.5260444, -0.5260444, -0.5260444, -0.5…
## $ fruit.pods.2 <dbl> -0.1545693, -0.1545693, -0.1545693, -0.1545693, -0.1…
## $ fruit.pods.3 <dbl> -0.2949049, -0.2949049, -0.2949049, -0.2949049, -0.2…
## $ fruit.spots.1 <dbl> -0.386191, -0.386191, -0.386191, -0.386191, -0.38619…
## $ fruit.spots.2 <dbl> -0.3307951, -0.3307951, -0.3307951, -0.3307951, -0.3…
## $ fruit.spots.4 <dbl> 2.18214, 2.18214, 2.18214, 2.18214, 2.18214, 2.18214…
## $ seed.1 <dbl> -0.4911088, -0.4911088, -0.4911088, -0.4911088, -0.4…
## $ mold.growth.1 <dbl> -0.3572761, -0.3572761, -0.3572761, -0.3572761, -0.3…
## $ seed.discolor.1 <dbl> -0.3529024, -0.3529024, -0.3529024, -0.3529024, -0.3…
## $ seed.size.1 <dbl> -0.332738, -0.332738, -0.332738, -0.332738, -0.33273…
## $ shriveling.1 <dbl> -0.2652899, -0.2652899, -0.2652899, -0.2652899, -0.2…
## $ roots.1 <dbl> -0.3895002, -0.3895002, -0.3895002, -0.3895002, -0.3…
## $ roots.2 <dbl> -0.1533355, -0.1533355, -0.1533355, -0.1533355, -0.1…3 Session Info
sessionInfo()## R version 4.5.2 (2025-10-31)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.4 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
##
## locale:
## [1] LC_CTYPE=C.UTF-8 LC_NUMERIC=C LC_TIME=C.UTF-8
## [4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
## [7] LC_PAPER=C.UTF-8 LC_NAME=C LC_ADDRESS=C
## [10] LC_TELEPHONE=C LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C
##
## time zone: UTC
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] RANN_2.6.2 corrplot_0.95 e1071_1.7-17 mlbench_2.1-7
## [5] caret_7.0-1 lattice_0.22-7 lubridate_1.9.5 forcats_1.0.1
## [9] stringr_1.6.0 dplyr_1.2.0 purrr_1.2.1 readr_2.2.0
## [13] tidyr_1.3.2 tibble_3.3.1 ggplot2_4.0.2 tidyverse_2.0.0
##
## loaded via a namespace (and not attached):
## [1] tidyselect_1.2.1 timeDate_4052.112 farver_2.1.2
## [4] S7_0.2.1 fastmap_1.2.0 pROC_1.19.0.1
## [7] digest_0.6.39 rpart_4.1.24 timechange_0.4.0
## [10] lifecycle_1.0.5 survival_3.8-3 magrittr_2.0.4
## [13] compiler_4.5.2 rlang_1.1.7 sass_0.4.10
## [16] tools_4.5.2 utf8_1.2.6 yaml_2.3.12
## [19] data.table_1.18.2.1 knitr_1.51 plyr_1.8.9
## [22] RColorBrewer_1.1-3 withr_3.0.2 nnet_7.3-20
## [25] grid_4.5.2 stats4_4.5.2 future_1.69.0
## [28] globals_0.19.0 scales_1.4.0 iterators_1.0.14
## [31] MASS_7.3-65 cli_3.6.5 rmarkdown_2.30
## [34] generics_0.1.4 rstudioapi_0.18.0 future.apply_1.20.2
## [37] reshape2_1.4.5 tzdb_0.5.0 cachem_1.1.0
## [40] proxy_0.4-29 splines_4.5.2 parallel_4.5.2
## [43] vctrs_0.7.1 hardhat_1.4.2 Matrix_1.7-4
## [46] jsonlite_2.0.0 hms_1.1.4 listenv_0.10.0
## [49] foreach_1.5.2 gower_1.0.2 jquerylib_0.1.4
## [52] recipes_1.3.1 glue_1.8.0 parallelly_1.46.1
## [55] codetools_0.2-20 stringi_1.8.7 gtable_0.3.6
## [58] pillar_1.11.1 htmltools_0.5.9 ipred_0.9-15
## [61] lava_1.8.2 R6_2.6.1 evaluate_1.0.5
## [64] bslib_0.10.0 class_7.3-23 Rcpp_1.1.1
## [67] nlme_3.1-168 prodlim_2025.04.28 xfun_0.56
## [70] ModelMetrics_1.2.2.2 pkgconfig_2.0.3