Homework 1
Lynx
2023-02-01
R Markdown
Part 1: Association Analysis
- Load the bob_ross csv file into R. This data contains information about various paintings done by Bob Ross. Bob Ross was an American artist know for his TV show called The Joy of Painting. This dataset lists possible elements of each painting, such as a barn or tree, and whether they were present or absent.
library(readr)
bobross <- read_csv("C:/Users/Lynx/Documents/MSDA/MSDA 622 - Big Data/Homework 1/bob_ross.csv")## Rows: 403 Columns: 69
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (2): EPISODE, TITLE
## dbl (67): APPLE_FRAME, AURORA_BOREALIS, BARN, BEACH, BOAT, BRIDGE, BUILDING,...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.- To perform association analysis on this dataset, we need to first remove all non-binary columns from the dataset, and then convert the dataset into a matrix of transactions. Do this in R.
library(arules)## Loading required package: Matrix##
## Attaching package: 'arules'## The following objects are masked from 'package:base':
##
## abbreviate, writestr(bobross)## spc_tbl_ [403 × 69] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ EPISODE : chr [1:403] "S01E01" "S01E02" "S01E03" "S01E04" ...
## $ TITLE : chr [1:403] "\"A WALK IN THE WOODS\"" "\"MT. MCKINLEY\"" "\"EBONY SUNSET\"" "\"WINTER MIST\"" ...
## $ APPLE_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ AURORA_BOREALIS : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ BARN : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ BEACH : num [1:403] 0 0 0 0 0 0 0 0 1 0 ...
## $ BOAT : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ BRIDGE : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ BUILDING : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ BUSHES : num [1:403] 1 0 0 1 0 0 0 1 0 1 ...
## $ CABIN : num [1:403] 0 1 1 0 0 1 0 0 0 0 ...
## $ CACTUS : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ CIRCLE_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ CIRRUS : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ CLIFF : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ CLOUDS : num [1:403] 0 1 0 1 0 0 0 0 1 0 ...
## $ CONIFER : num [1:403] 0 1 1 1 0 1 0 1 0 1 ...
## $ CUMULUS : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ DECIDUOUS : num [1:403] 1 0 0 0 1 0 1 0 0 1 ...
## $ DIANE_ANDRE : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ DOCK : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ DOUBLE_OVAL_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ FARM : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ FENCE : num [1:403] 0 0 1 0 0 0 0 0 1 0 ...
## $ FIRE : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ FLORIDA_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ FLOWERS : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ FOG : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ FRAMED : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ GRASS : num [1:403] 1 0 0 0 0 0 0 0 0 0 ...
## $ GUEST : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ HALF_CIRCLE_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ HALF_OVAL_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ HILLS : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ LAKE : num [1:403] 0 0 0 1 0 1 1 1 0 1 ...
## $ LAKES : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ LIGHTHOUSE : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ MILL : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ MOON : num [1:403] 0 0 0 0 0 1 0 0 0 0 ...
## $ MOUNTAIN : num [1:403] 0 1 1 1 0 1 1 1 0 1 ...
## $ MOUNTAINS : num [1:403] 0 0 1 0 0 1 1 1 0 0 ...
## $ NIGHT : num [1:403] 0 0 0 0 0 1 0 0 0 0 ...
## $ OCEAN : num [1:403] 0 0 0 0 0 0 0 0 1 0 ...
## $ OVAL_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ PALM_TREES : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ PATH : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ PERSON : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ PORTRAIT : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ RECTANGLE_3D_FRAME: num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ RECTANGULAR_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ RIVER : num [1:403] 1 0 0 0 1 0 0 0 0 0 ...
## $ ROCKS : num [1:403] 0 0 0 0 1 0 0 0 0 0 ...
## $ SEASHELL_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ SNOW : num [1:403] 0 1 0 0 0 1 0 0 0 0 ...
## $ SNOWY_MOUNTAIN : num [1:403] 0 1 0 1 0 1 1 0 0 0 ...
## $ SPLIT_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ STEVE_ROSS : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ STRUCTURE : num [1:403] 0 0 1 0 0 1 0 0 0 0 ...
## $ SUN : num [1:403] 0 0 1 0 0 0 0 0 0 0 ...
## $ TOMB_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ TREE : num [1:403] 1 1 1 1 1 1 1 1 0 1 ...
## $ TREES : num [1:403] 1 1 1 1 1 1 1 1 0 1 ...
## $ TRIPLE_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ WATERFALL : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ WAVES : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ WINDMILL : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ WINDOW_FRAME : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## $ WINTER : num [1:403] 0 1 1 0 0 1 0 0 0 0 ...
## $ WOOD_FRAMED : num [1:403] 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "spec")=
## .. cols(
## .. EPISODE = col_character(),
## .. TITLE = col_character(),
## .. APPLE_FRAME = col_double(),
## .. AURORA_BOREALIS = col_double(),
## .. BARN = col_double(),
## .. BEACH = col_double(),
## .. BOAT = col_double(),
## .. BRIDGE = col_double(),
## .. BUILDING = col_double(),
## .. BUSHES = col_double(),
## .. CABIN = col_double(),
## .. CACTUS = col_double(),
## .. CIRCLE_FRAME = col_double(),
## .. CIRRUS = col_double(),
## .. CLIFF = col_double(),
## .. CLOUDS = col_double(),
## .. CONIFER = col_double(),
## .. CUMULUS = col_double(),
## .. DECIDUOUS = col_double(),
## .. DIANE_ANDRE = col_double(),
## .. DOCK = col_double(),
## .. DOUBLE_OVAL_FRAME = col_double(),
## .. FARM = col_double(),
## .. FENCE = col_double(),
## .. FIRE = col_double(),
## .. FLORIDA_FRAME = col_double(),
## .. FLOWERS = col_double(),
## .. FOG = col_double(),
## .. FRAMED = col_double(),
## .. GRASS = col_double(),
## .. GUEST = col_double(),
## .. HALF_CIRCLE_FRAME = col_double(),
## .. HALF_OVAL_FRAME = col_double(),
## .. HILLS = col_double(),
## .. LAKE = col_double(),
## .. LAKES = col_double(),
## .. LIGHTHOUSE = col_double(),
## .. MILL = col_double(),
## .. MOON = col_double(),
## .. MOUNTAIN = col_double(),
## .. MOUNTAINS = col_double(),
## .. NIGHT = col_double(),
## .. OCEAN = col_double(),
## .. OVAL_FRAME = col_double(),
## .. PALM_TREES = col_double(),
## .. PATH = col_double(),
## .. PERSON = col_double(),
## .. PORTRAIT = col_double(),
## .. RECTANGLE_3D_FRAME = col_double(),
## .. RECTANGULAR_FRAME = col_double(),
## .. RIVER = col_double(),
## .. ROCKS = col_double(),
## .. SEASHELL_FRAME = col_double(),
## .. SNOW = col_double(),
## .. SNOWY_MOUNTAIN = col_double(),
## .. SPLIT_FRAME = col_double(),
## .. STEVE_ROSS = col_double(),
## .. STRUCTURE = col_double(),
## .. SUN = col_double(),
## .. TOMB_FRAME = col_double(),
## .. TREE = col_double(),
## .. TREES = col_double(),
## .. TRIPLE_FRAME = col_double(),
## .. WATERFALL = col_double(),
## .. WAVES = col_double(),
## .. WINDMILL = col_double(),
## .. WINDOW_FRAME = col_double(),
## .. WINTER = col_double(),
## .. WOOD_FRAMED = col_double()
## .. )
## - attr(*, "problems")=<externalptr>bobross$EPISODE = NULL
bobross$TITLE = NULL
bobross <- as(as.matrix(bobross), "transactions")- Perform association analysis to determine rules with a support of at least 30% and confidence of at least 90%. Bob Ross included trees in a large number of his drawings. Display all of the rules that you find in your output, and using these rules, describe some of the types of landscapes in which Bob Ross tended to draw tree(s).
bob_rules <- apriori(bobross, parameter = list(sup = 0.3, conf = 0.9, target = "rules"))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.9 0.1 1 none FALSE TRUE 5 0.3 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 120
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[66 item(s), 403 transaction(s)] done [0.00s].
## sorting and recoding items ... [9 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [31 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].inspect(bob_rules)## lhs rhs support confidence coverage
## [1] {RIVER} => {TREES} 0.3002481 0.9603175 0.3126551
## [2] {RIVER} => {TREE} 0.3126551 1.0000000 0.3126551
## [3] {GRASS} => {TREE} 0.3374690 0.9577465 0.3523573
## [4] {LAKE} => {TREES} 0.3325062 0.9370629 0.3548387
## [5] {LAKE} => {TREE} 0.3523573 0.9930070 0.3548387
## [6] {MOUNTAIN} => {TREES} 0.3672457 0.9250000 0.3970223
## [7] {MOUNTAIN} => {TREE} 0.3870968 0.9750000 0.3970223
## [8] {DECIDUOUS} => {TREES} 0.5136476 0.9118943 0.5632754
## [9] {DECIDUOUS} => {TREE} 0.5632754 1.0000000 0.5632754
## [10] {CONIFER} => {TREES} 0.5161290 0.9811321 0.5260546
## [11] {CONIFER} => {TREE} 0.5260546 1.0000000 0.5260546
## [12] {TREES} => {TREE} 0.8362283 1.0000000 0.8362283
## [13] {TREE} => {TREES} 0.8362283 0.9335180 0.8957816
## [14] {RIVER, TREES} => {TREE} 0.3002481 1.0000000 0.3002481
## [15] {RIVER, TREE} => {TREES} 0.3002481 0.9603175 0.3126551
## [16] {GRASS, TREES} => {TREE} 0.3126551 1.0000000 0.3126551
## [17] {GRASS, TREE} => {TREES} 0.3126551 0.9264706 0.3374690
## [18] {LAKE, TREES} => {TREE} 0.3325062 1.0000000 0.3325062
## [19] {LAKE, TREE} => {TREES} 0.3325062 0.9436620 0.3523573
## [20] {CONIFER, MOUNTAIN} => {TREES} 0.3126551 0.9767442 0.3200993
## [21] {CONIFER, MOUNTAIN} => {TREE} 0.3200993 1.0000000 0.3200993
## [22] {MOUNTAIN, TREES} => {TREE} 0.3672457 1.0000000 0.3672457
## [23] {MOUNTAIN, TREE} => {TREES} 0.3672457 0.9487179 0.3870968
## [24] {CLOUDS, TREES} => {TREE} 0.3424318 1.0000000 0.3424318
## [25] {CLOUDS, TREE} => {TREES} 0.3424318 0.9387755 0.3647643
## [26] {DECIDUOUS, TREES} => {TREE} 0.5136476 1.0000000 0.5136476
## [27] {DECIDUOUS, TREE} => {TREES} 0.5136476 0.9118943 0.5632754
## [28] {CONIFER, TREES} => {TREE} 0.5161290 1.0000000 0.5161290
## [29] {CONIFER, TREE} => {TREES} 0.5161290 0.9811321 0.5260546
## [30] {CONIFER, MOUNTAIN, TREES} => {TREE} 0.3126551 1.0000000 0.3126551
## [31] {CONIFER, MOUNTAIN, TREE} => {TREES} 0.3126551 0.9767442 0.3200993
## lift count
## [1] 1.148392 121
## [2] 1.116343 126
## [3] 1.069174 136
## [4] 1.120583 134
## [5] 1.108537 142
## [6] 1.106157 148
## [7] 1.088435 156
## [8] 1.090485 207
## [9] 1.116343 227
## [10] 1.173283 208
## [11] 1.116343 212
## [12] 1.116343 337
## [13] 1.116343 337
## [14] 1.116343 121
## [15] 1.148392 121
## [16] 1.116343 126
## [17] 1.107916 126
## [18] 1.116343 134
## [19] 1.128474 134
## [20] 1.168035 126
## [21] 1.116343 129
## [22] 1.116343 148
## [23] 1.134520 148
## [24] 1.116343 138
## [25] 1.122631 138
## [26] 1.116343 207
## [27] 1.090485 207
## [28] 1.116343 208
## [29] 1.173283 208
## [30] 1.116343 126
## [31] 1.168035 126Part 2: Predicting a Numeric Column of Data
- Load the nhanes_train csv file into R. This data contains information about the weight, age, height, and pulse of various individuals. Use this data in completing the next question.
nhanes_train <- read_csv("C:/Users/Lynx/Documents/MSDA/MSDA 622 - Big Data/Homework 1/nhanes_train.csv")## Rows: 2871 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (4): Age, Weight, Height, Pulse
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.str(nhanes_train)## spc_tbl_ [2,871 × 4] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Age : num [1:2871] 80 48 20 18 46 63 42 43 46 50 ...
## $ Weight: num [1:2871] 97.6 120.7 46.8 100.2 112.2 ...
## $ Height: num [1:2871] 176 186 164 177 180 ...
## $ Pulse : num [1:2871] 58 56 78 84 90 66 100 100 54 74 ...
## - attr(*, "spec")=
## .. cols(
## .. Age = col_double(),
## .. Weight = col_double(),
## .. Height = col_double(),
## .. Pulse = col_double()
## .. )
## - attr(*, "problems")=<externalptr>- Develop analytical models to predict a person’s weight based on his/her age, height, and pulse (i.e., use the variable Weight as your target variable). In particular, create a regression model, a decision tree, a bagging model using 100 bootstrapped samples, a random forest with 200 trees, and a boosting model with 200 trees each having 5 splits and a shrinkage/weight of 0.03.
#Regression Model
model <- lm(Weight ~., data = nhanes_train)
summary(model)##
## Call:
## lm(formula = Weight ~ ., data = nhanes_train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.860 -13.096 -3.099 10.227 116.080
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -112.64017 6.78932 -16.591 < 2e-16 ***
## Age 0.12471 0.02045 6.097 1.22e-09 ***
## Height 1.01324 0.03522 28.768 < 2e-16 ***
## Pulse 0.24685 0.03019 8.177 4.32e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.67 on 2867 degrees of freedom
## Multiple R-squared: 0.2311, Adjusted R-squared: 0.2303
## F-statistic: 287.2 on 3 and 2867 DF, p-value: < 2.2e-16#Decision Tree
library(rpart)
library(rpart.plot)
reg_tree <- rpart(formula = Weight ~ ., data = nhanes_train)
prp(reg_tree, digits = 4, extra = 1)
#Bagging Model
library(ipred)
bag_model <- bagging(formula = Weight ~., data = nhanes_train, nbagg = 100)
bag_model##
## Bagging regression trees with 100 bootstrap replications
##
## Call: bagging.data.frame(formula = Weight ~ ., data = nhanes_train,
## nbagg = 100)#Random Forest
library(randomForest)## randomForest 4.7-1.1## Type rfNews() to see new features/changes/bug fixes.rf_model <- randomForest(Weight ~., data = nhanes_train, importance = TRUE, ntree = 200)
rf_model##
## Call:
## randomForest(formula = Weight ~ ., data = nhanes_train, importance = TRUE, ntree = 200)
## Type of random forest: regression
## Number of trees: 200
## No. of variables tried at each split: 1
##
## Mean of squared residuals: 272.8998
## % Var explained: 39.73#Boosting Model
library(gbm)## Loaded gbm 2.1.8.1bob_boost <- gbm(formula = Weight ~., data = nhanes_train, distribution = "gaussian", n.trees = 200, shrinkage = 0.03, interaction.depth = 5)
summary(bob_boost)
## var rel.inf
## Height Height 66.04329
## Pulse Pulse 17.56052
## Age Age 16.39619- Load the nhanes_test csv file into R, and use this data to calculate the mean squared error (MSE) for each of the models that you developed in the previous question. Based on your results, which model is best for predicting body weight?
nhanes_test <- read_csv("C:/Users/Lynx/Documents/MSDA/MSDA 622 - Big Data/Homework 1/nhanes_test.csv")## Rows: 2872 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (4): Age, Weight, Height, Pulse
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.#Regression MSE
model_pred <- predict(model, nhanes_test)
mean((model_pred - nhanes_test$Weight)^2)## [1] 332.8215#Decision Tree MSE
tree_pred = predict(reg_tree, nhanes_test)
mean((tree_pred - nhanes_test$Weight)^2)## [1] 334.6264#Bagging MSE
bag_pred <- predict(bag_model, newdata = nhanes_test)
mean((bag_pred - nhanes_test$Weight)^2)## [1] 326.7834#Random Forest MSE
rf_pred <- predict(rf_model, nhanes_test)
mean((rf_pred - nhanes_test$Weight)^2)## [1] 262.4927#Boosting MSE
boost_pred <- predict(bob_boost, nhanes_test, n.trees = 200)
mean((boost_pred - nhanes_test$Weight)^2)## [1] 315.4649Based on the results, the best model is the Random Forest Model with a Mean Squared Error of 261.5092.
Part 3: Clustering
- Use R to compute the mean of each variable in the nhanes_train csv file.
str(nhanes_train)## spc_tbl_ [2,871 × 4] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Age : num [1:2871] 80 48 20 18 46 63 42 43 46 50 ...
## $ Weight: num [1:2871] 97.6 120.7 46.8 100.2 112.2 ...
## $ Height: num [1:2871] 176 186 164 177 180 ...
## $ Pulse : num [1:2871] 58 56 78 84 90 66 100 100 54 74 ...
## - attr(*, "spec")=
## .. cols(
## .. Age = col_double(),
## .. Weight = col_double(),
## .. Height = col_double(),
## .. Pulse = col_double()
## .. )
## - attr(*, "problems")=<externalptr>#Mean of Age
mean(nhanes_train$Age)## [1] 45.14699#Mean of Weight
mean(nhanes_train$Weight)## [1] 82.63375#Mean of Height
mean(nhanes_train$Height)## [1] 169.5465#Mean of Pulse
mean(nhanes_train$Pulse)## [1] 72.32045Perform k-means clustering on the data in the nhanes_train csv file. Create 4 distinct clusters.
- Use R to display the mean of each variable in each cluster, and compare these means with those that you obtained in the previous question.
library(fpc)
fit <- kmeans(nhanes_train[, 1:4], 4)
fit## K-means clustering with 4 clusters of sizes 716, 487, 847, 821
##
## Cluster means:
## Age Weight Height Pulse
## 1 30.04888 63.92165 165.1246 75.13966
## 2 48.06571 117.06982 176.2801 75.34292
## 3 64.30224 73.19764 164.9505 68.76033
## 4 36.82095 88.26090 174.1502 71.74178
##
## Clustering vector:
## [1] 3 2 1 4 2 3 4 4 4 3 1 1 4 2 2 4 1 1 1 3 4 1 3 4 3 3 3 2 1 4 4 3 1 2 1 4 3
## [38] 3 4 4 4 3 3 4 4 3 1 3 4 3 3 3 1 2 1 3 2 3 3 3 4 1 1 1 3 1 2 4 4 1 3 3 4 3
## [75] 2 1 1 4 1 4 3 4 2 1 2 1 1 3 3 4 1 3 1 2 2 3 4 1 1 1 3 3 3 1 1 2 3 4 3 1 1
## [112] 1 4 2 3 1 3 4 3 1 1 3 3 3 3 4 4 2 2 4 4 4 3 2 3 1 1 2 2 3 3 3 3 3 4 2 3 4
## [149] 1 3 4 1 4 1 3 3 4 1 4 4 4 1 2 4 2 1 1 4 1 3 4 4 4 1 4 4 1 4 1 3 4 1 4 1 1
## [186] 3 2 3 4 1 3 4 2 4 3 4 3 1 1 3 4 3 4 4 2 3 2 3 3 1 4 4 2 2 4 2 3 1 1 2 4 1
## [223] 1 2 4 4 1 2 3 3 1 4 2 3 4 2 2 3 3 4 1 1 4 3 3 2 1 3 3 3 1 4 3 4 1 2 3 4 3
## [260] 4 3 2 2 3 4 3 2 2 3 1 4 1 4 2 1 4 4 2 4 3 3 3 3 3 3 2 4 1 4 1 4 2 2 1 1 1
## [297] 3 2 2 1 4 2 1 1 4 2 3 4 1 3 3 1 1 4 1 3 1 4 3 1 2 2 4 4 4 1 2 3 1 1 1 3 4
## [334] 1 3 3 3 1 1 2 3 4 4 3 4 3 1 1 4 3 2 3 2 1 2 1 2 1 2 4 3 3 1 4 4 1 3 1 3 1
## [371] 3 1 4 1 4 1 3 4 1 3 4 3 4 4 3 1 4 1 2 1 3 3 3 1 3 2 4 4 1 4 4 4 1 4 3 4 3
## [408] 3 2 1 4 4 3 4 3 2 3 3 1 3 3 3 3 4 4 1 3 2 3 4 2 1 1 1 4 1 1 2 4 1 3 1 4 4
## [445] 1 3 1 4 1 2 3 4 3 3 4 3 2 3 1 1 4 4 4 2 2 4 4 3 4 3 4 3 4 2 4 4 2 4 2 4 1
## [482] 4 3 1 1 3 2 3 4 4 4 1 4 1 3 1 4 4 3 1 3 2 2 4 2 4 4 4 1 3 3 4 3 1 3 3 4 2
## [519] 4 1 1 1 4 4 3 3 1 2 1 4 3 3 3 3 4 2 4 4 1 3 2 2 3 4 1 4 2 1 4 1 3 4 4 3 4
## [556] 2 3 1 2 3 4 4 3 3 4 4 1 3 3 3 2 1 3 2 1 4 2 1 3 4 1 1 2 4 3 1 1 3 2 2 3 1
## [593] 4 4 3 4 3 3 3 1 1 4 1 3 3 1 3 2 1 4 3 1 4 3 3 4 1 4 3 1 1 4 1 4 4 4 2 4 3
## [630] 3 3 4 3 4 2 3 3 2 2 4 3 2 3 1 1 2 4 4 3 4 1 2 3 1 3 4 4 1 4 3 4 1 1 1 1 3
## [667] 4 4 1 1 1 1 2 3 2 1 3 4 2 4 2 4 4 2 2 1 1 1 3 4 3 2 4 4 3 3 1 2 3 4 2 4 1
## [704] 2 2 2 3 3 3 3 1 1 3 3 1 1 1 1 4 3 3 3 3 4 1 1 4 3 2 3 2 2 1 4 1 3 3 4 2 4
## [741] 1 3 2 1 1 3 1 1 3 4 1 4 4 3 3 3 3 3 4 4 1 4 4 3 1 4 1 4 1 3 4 2 2 2 1 4 2
## [778] 4 3 4 1 4 3 3 4 3 4 2 1 1 2 1 1 3 4 3 3 4 3 2 1 4 3 4 3 1 4 3 3 1 1 2 4 2
## [815] 2 4 2 4 1 4 3 1 4 1 4 4 3 2 4 3 3 2 3 4 1 3 3 1 4 4 4 4 1 3 4 3 1 4 4 3 1
## [852] 2 3 4 1 4 1 4 4 1 3 2 3 1 1 3 1 3 1 3 3 2 2 4 3 4 3 3 4 1 4 3 2 3 4 4 4 4
## [889] 2 3 4 4 2 3 1 4 2 3 4 2 3 2 3 4 4 3 3 1 3 4 4 1 4 4 4 4 1 4 1 3 1 4 2 4 1
## [926] 1 2 3 3 1 1 4 3 1 2 3 4 4 3 3 3 4 4 3 4 3 4 1 2 4 1 1 3 3 3 4 2 4 3 4 1 1
## [963] 1 2 1 1 1 2 4 4 3 4 3 1 4 2 1 4 2 2 1 2 3 2 4 3 1 3 1 3 1 4 1 2 1 3 2 4 2
## [1000] 3 1 4 3 2 3 4 1 2 3 4 2 1 1 3 4 4 4 4 3 1 4 2 2 3 4 3 1 2 1 2 3 1 1 2 2 1
## [1037] 2 4 1 3 2 1 1 4 1 3 2 1 3 1 1 1 1 3 2 3 4 4 4 4 4 1 4 3 3 3 1 1 1 3 4 1 1
## [1074] 4 2 3 4 2 3 3 3 2 2 1 4 2 3 1 1 1 1 3 3 2 2 4 1 4 4 1 4 3 4 3 3 4 1 2 4 4
## [1111] 4 1 3 4 2 3 2 2 1 3 2 2 2 4 4 3 1 4 4 3 3 4 1 4 1 1 4 3 2 1 2 4 4 1 3 1 4
## [1148] 3 1 3 3 3 1 1 1 3 3 4 4 2 3 1 1 4 1 2 2 1 3 4 4 2 2 3 3 2 4 2 3 1 2 1 1 3
## [1185] 3 1 3 4 2 2 4 3 4 4 2 2 3 4 4 3 4 3 3 1 4 1 4 3 1 1 2 4 4 4 4 3 4 3 3 2 4
## [1222] 4 4 1 3 3 1 3 1 1 3 2 1 1 2 3 1 2 4 4 4 3 3 1 2 2 1 2 3 3 1 1 1 3 3 1 2 2
## [1259] 2 3 3 3 4 3 1 1 1 3 3 4 3 4 4 1 4 4 3 4 4 3 3 3 3 3 1 4 3 4 1 1 1 1 1 1 1
## [1296] 1 2 4 4 2 4 2 4 3 3 3 3 4 3 3 2 1 2 4 3 4 2 1 3 3 2 4 1 4 1 3 4 3 3 2 2 2
## [1333] 3 3 1 4 2 3 3 2 3 3 3 2 4 4 3 1 2 1 4 1 3 3 4 3 2 4 1 4 3 3 3 2 3 4 3 1 4
## [1370] 4 4 3 1 3 3 4 1 3 1 2 4 1 3 3 3 3 3 1 1 3 4 3 4 4 2 1 3 4 3 3 3 4 3 1 2 1
## [1407] 3 2 4 3 2 4 3 2 4 2 1 4 3 3 1 2 4 3 2 4 4 3 3 3 3 2 3 2 2 1 1 4 3 3 3 1 4
## [1444] 2 4 1 1 3 3 3 2 3 3 1 2 4 1 1 3 4 4 4 3 1 2 1 1 4 1 1 1 1 4 3 2 4 1 1 4 3
## [1481] 3 3 2 2 1 2 4 3 4 1 1 3 2 4 1 1 4 3 2 1 3 3 2 4 3 3 3 2 4 1 3 1 4 4 3 1 3
## [1518] 2 4 3 3 1 3 2 2 3 3 3 1 3 2 4 1 4 4 4 1 3 4 4 3 4 2 1 1 2 1 3 3 4 4 4 1 4
## [1555] 2 3 3 1 4 3 2 3 3 3 1 1 3 3 4 2 4 1 2 2 1 4 3 4 4 2 3 1 2 4 4 1 4 3 1 4 3
## [1592] 3 4 1 4 1 3 1 2 4 3 4 3 3 3 4 3 3 3 4 4 4 2 2 4 3 2 2 3 4 1 4 4 3 4 4 2 3
## [1629] 4 3 4 3 4 1 1 1 4 2 3 1 4 4 3 1 4 4 3 3 4 3 4 1 4 3 2 4 4 1 3 4 4 3 2 3 4
## [1666] 3 3 4 1 4 2 1 1 1 2 3 4 1 2 2 4 1 1 4 1 4 3 3 1 4 2 3 3 3 1 2 2 1 2 2 4 4
## [1703] 2 1 3 3 4 2 1 1 1 4 2 3 3 3 2 3 2 4 4 3 2 3 2 1 4 4 1 4 3 2 3 1 3 1 4 1 2
## [1740] 4 2 2 1 1 3 4 4 3 4 4 4 3 2 3 1 4 4 4 1 3 1 3 3 1 2 4 2 4 1 1 4 3 1 1 1 1
## [1777] 3 2 3 2 3 4 1 4 4 3 4 1 4 3 4 3 4 4 4 1 2 1 3 4 1 3 3 3 3 1 3 2 3 3 3 2 4
## [1814] 3 1 4 4 1 1 4 3 1 1 3 2 3 4 3 3 3 3 3 4 3 4 1 1 3 4 3 2 4 2 4 1 3 1 1 4 1
## [1851] 2 4 3 3 4 3 3 3 3 1 4 2 3 3 4 3 4 1 4 1 4 3 3 2 3 4 1 3 3 3 1 1 4 3 4 4 4
## [1888] 4 1 1 4 3 4 2 1 3 2 3 2 4 4 3 4 3 3 4 1 1 4 2 1 2 1 2 3 4 3 1 3 2 1 4 1 2
## [1925] 4 4 2 3 2 4 3 2 2 3 3 1 3 2 4 4 1 1 2 4 2 1 2 1 2 2 3 3 1 4 4 4 1 3 3 3 4
## [1962] 3 4 1 3 4 1 3 3 3 1 1 1 4 4 3 3 1 3 2 1 4 4 4 3 2 1 1 3 3 1 3 1 4 4 2 4 1
## [1999] 1 4 1 1 3 2 4 4 2 2 4 4 4 3 2 3 1 4 3 4 1 1 4 1 3 4 3 2 2 4 2 1 1 2 4 2 1
## [2036] 3 3 1 4 4 3 4 4 4 4 1 2 2 1 1 4 1 4 2 1 1 2 2 1 1 2 3 3 1 4 2 1 4 2 4 4 2
## [2073] 1 1 4 1 2 2 3 2 1 3 3 1 4 2 2 2 1 3 3 4 1 4 1 2 4 3 2 4 2 4 3 3 4 3 1 4 4
## [2110] 3 1 4 4 1 3 1 4 2 2 1 2 1 1 4 1 4 2 3 3 4 1 3 4 3 1 4 4 4 1 1 3 1 3 1 3 1
## [2147] 1 2 1 4 2 3 2 4 1 1 4 3 3 4 1 2 2 3 4 4 3 3 2 4 4 1 2 2 1 2 3 3 2 3 3 3 4
## [2184] 4 4 4 1 3 3 2 2 1 4 4 3 2 4 1 3 1 3 2 2 4 1 3 3 4 3 2 1 2 4 4 2 4 2 1 1 2
## [2221] 2 1 3 2 1 1 2 1 2 4 4 4 4 1 4 4 2 3 4 4 3 3 2 2 1 3 3 1 1 1 3 3 1 1 4 3 4
## [2258] 1 2 1 1 2 3 3 4 3 2 2 3 1 2 2 1 3 4 4 1 4 4 1 3 1 4 2 4 1 2 1 2 4 2 3 2 4
## [2295] 4 1 3 4 1 3 3 1 3 2 4 4 1 3 4 1 1 3 1 1 1 3 1 2 4 2 3 3 1 4 3 3 4 2 3 1 3
## [2332] 2 4 3 2 4 3 3 3 2 1 1 3 3 4 4 1 4 1 4 3 1 1 4 3 3 3 4 3 4 3 3 2 1 3 1 3 3
## [2369] 2 1 4 4 3 4 2 2 2 4 3 4 1 3 2 3 4 2 3 3 3 1 1 1 4 4 2 2 4 3 3 3 4 4 1 3 1
## [2406] 1 1 1 4 3 1 4 3 1 4 4 4 4 3 4 4 4 4 1 1 1 3 1 2 2 2 2 1 3 1 1 4 4 4 1 3 1
## [2443] 3 4 3 4 3 3 4 1 1 3 4 2 4 3 1 3 3 1 1 2 4 1 1 4 2 4 4 4 1 1 2 2 1 3 4 1 4
## [2480] 4 4 2 1 4 4 4 1 4 2 1 2 1 4 3 3 2 4 3 4 3 1 2 4 2 1 4 1 4 1 2 1 4 3 4 2 3
## [2517] 3 3 4 3 3 3 1 2 4 3 3 1 1 4 4 1 3 2 2 1 4 1 4 2 3 1 4 3 1 3 4 4 4 4 1 3 1
## [2554] 3 3 3 1 4 3 1 2 1 3 1 1 2 2 1 2 4 2 2 2 1 4 3 1 3 4 4 3 4 2 4 3 3 2 2 2 1
## [2591] 3 3 4 3 3 2 3 4 4 3 4 3 4 4 1 1 3 3 4 3 4 4 2 3 1 4 4 4 1 1 3 4 3 4 3 4 4
## [2628] 4 3 2 3 2 4 1 4 3 4 1 3 4 1 3 3 4 3 2 3 1 2 3 4 1 4 4 4 2 1 3 4 3 3 3 1 1
## [2665] 1 2 3 4 2 2 4 1 3 1 3 1 1 2 4 4 2 3 4 3 3 4 1 3 1 3 3 4 2 4 2 3 2 1 1 1 3
## [2702] 4 2 1 3 3 3 2 3 4 3 3 4 4 2 4 4 1 3 1 4 3 3 3 3 3 2 1 4 1 3 2 2 1 4 3 3 2
## [2739] 4 3 4 4 1 2 4 2 4 2 4 2 2 2 3 4 3 4 1 4 1 3 3 3 3 1 1 1 3 3 3 2 4 3 4 2 1
## [2776] 3 1 1 4 4 3 4 4 4 1 3 4 4 4 3 3 1 3 2 3 2 3 3 4 1 3 4 1 1 3 2 2 4 3 4 4 2
## [2813] 1 1 4 3 3 1 1 1 3 4 4 3 1 4 2 2 4 4 3 1 2 4 1 3 4 4 3 4 4 3 3 2 3 4 4 4 4
## [2850] 4 2 3 2 3 2 2 3 4 3 3 1 1 1 2 1 3 3 1 1 3 2
##
## Within cluster sum of squares by cluster:
## [1] 262863.8 365425.0 370405.2 317006.3
## (between_SS / total_SS = 54.2 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault" b) Determine which cluster the data in row 2000 was placed in.fit$cluster[2000]## [1] 4