Predicting the Sex and Age of Abalone using Classification and Regression
Tay Shi Hui
12/22/2021
Dataset details
There are seven predictor variables included in the dataset. The first three constitute the shell measurements:
- Length - longest shell measurement (mm)
- Diameter - measured perpendicular to length (mm)
- Height - with meat in shell (mm)
The other four variables are related to the weight of abalone:
- Whole.weight - whole abalone weight (g)
- Shucked.weight - weight of meat only (g)
- Viscera.weight - gut weight, after bleeding (g)
- Shell.weight - weight after being dried (g)
The response variable, that is the dependent variable in this analysis is:
- Rings - number of rings in the shell (+1.5 gives the age in years)
Import dataset
Import the csv file from Google drive.
id <- "18dk-yeiB7jFTRv1KR3bTzgiya3dwnKCc" # sharable google drive link
df<-read.csv(sprintf("https://docs.google.com/uc?id=%s&export=download", id))Data Cleaning/Preprocessing
Load the required libraries.
defaultW <- getOption("warn")
options(warn = -1)
library(plyr)
library(dplyr)
library(tidyr)
library(tidyverse)
library(ggplot2)
library(corrplot)
library(caret)
options(warn = defaultW)Inspect the dataset.
class(df)## [1] "data.frame"typeof(df)## [1] "list"dim(df)## [1] 4187 9ncol(df)## [1] 9nrow((df))## [1] 4187colnames(df)## [1] "Sex" "Length" "Diameter" "Height"
## [5] "Whole.weight" "Shucked.weight" "Viscera.weight" "Shell.weight"
## [9] "Rings"str(df)## 'data.frame': 4187 obs. of 9 variables:
## $ Sex : chr "M" "M" "F" "M" ...
## $ Length : num 0.455 0.35 0.53 0.44 0.33 0.425 0.53 0.545 0.475 0.55 ...
## $ Diameter : num 0.365 0.265 0.42 0.365 0.255 0.3 0.415 0.425 0.37 0.44 ...
## $ Height : num 0.095 0.09 0.135 0.125 0.08 0.095 0.15 0.125 0.125 0.15 ...
## $ Whole.weight : num 0.514 0.226 0.677 0.516 0.205 ...
## $ Shucked.weight: num 0.2245 0.0995 0.2565 0.2155 0.0895 ...
## $ Viscera.weight: num 0.101 0.0485 0.1415 0.114 0.0395 ...
## $ Shell.weight : num 0.15 0.07 0.21 0.155 0.055 0.12 0.33 0.26 0.165 0.32 ...
## $ Rings : int 15 7 9 10 7 8 20 16 9 19 ...glimpse(df)## Rows: 4,187
## Columns: 9
## $ Sex <chr> "M", "M", "F", "M", "I", "I", "F", "F", "M", "F", "F", ~
## $ Length <dbl> 0.455, 0.350, 0.530, 0.440, 0.330, 0.425, 0.530, 0.545,~
## $ Diameter <dbl> 0.365, 0.265, 0.420, 0.365, 0.255, 0.300, 0.415, 0.425,~
## $ Height <dbl> 0.095, 0.090, 0.135, 0.125, 0.080, 0.095, 0.150, 0.125,~
## $ Whole.weight <dbl> 0.5140, 0.2255, 0.6770, 0.5160, 0.2050, 0.3515, 0.7775,~
## $ Shucked.weight <dbl> 0.2245, 0.0995, 0.2565, 0.2155, 0.0895, 0.1410, 0.2370,~
## $ Viscera.weight <dbl> 0.1010, 0.0485, 0.1415, 0.1140, 0.0395, 0.0775, 0.1415,~
## $ Shell.weight <dbl> 0.150, 0.070, 0.210, 0.155, 0.055, 0.120, 0.330, 0.260,~
## $ Rings <int> 15, 7, 9, 10, 7, 8, 20, 16, 9, 19, 14, 10, 11, 10, 10, ~summary(df)## Sex Length Diameter Height
## Length:4187 Min. :0.075 Min. :0.0550 Min. :0.0000
## Class :character 1st Qu.:0.450 1st Qu.:0.3500 1st Qu.:0.1150
## Mode :character Median :0.545 Median :0.4250 Median :0.1400
## Mean :0.524 Mean :0.4078 Mean :0.1395
## 3rd Qu.:0.615 3rd Qu.:0.4800 3rd Qu.:0.1650
## Max. :0.815 Max. :0.6500 Max. :1.1300
## NA's :1 NA's :1 NA's :1
## Whole.weight Shucked.weight Viscera.weight Shell.weight
## Min. :0.0020 Min. :0.0010 Min. :0.0005 Min. :0.0015
## 1st Qu.:0.4421 1st Qu.:0.1862 1st Qu.:0.0935 1st Qu.:0.1300
## Median :0.7995 Median :0.3355 Median :0.1710 Median :0.2335
## Mean :0.8286 Mean :0.3593 Mean :0.1805 Mean :0.2388
## 3rd Qu.:1.1530 3rd Qu.:0.5020 3rd Qu.:0.2527 3rd Qu.:0.3289
## Max. :2.8255 Max. :1.4880 Max. :0.7600 Max. :1.0050
## NA's :1 NA's :1
## Rings
## Min. : 1.000
## 1st Qu.: 8.000
## Median : 9.000
## Mean : 9.932
## 3rd Qu.:11.000
## Max. :29.000
## head(df, 5)## Sex Length Diameter Height Whole.weight Shucked.weight Viscera.weight
## 1 M 0.455 0.365 0.095 0.5140 0.2245 0.1010
## 2 M 0.350 0.265 0.090 0.2255 0.0995 0.0485
## 3 F 0.530 0.420 0.135 0.6770 0.2565 0.1415
## 4 M 0.440 0.365 0.125 0.5160 0.2155 0.1140
## 5 I 0.330 0.255 0.080 0.2050 0.0895 0.0395
## Shell.weight Rings
## 1 0.150 15
## 2 0.070 7
## 3 0.210 9
## 4 0.155 10
## 5 0.055 7tail(df, 5)## Sex Length Diameter Height Whole.weight Shucked.weight Viscera.weight
## 4183 F 0.565 0.450 0.165 0.8870 0.3700 0.2390
## 4184 M 0.590 0.440 0.135 0.9660 0.4390 0.2145
## 4185 M 0.600 0.475 0.205 1.1760 0.5255 0.2875
## 4186 F 0.625 0.485 0.150 1.0945 0.5310 0.2610
## 4187 M 0.710 0.555 0.195 1.9485 0.9455 0.3765
## Shell.weight Rings
## 4183 0.2490 11
## 4184 0.2605 10
## 4185 0.3080 9
## 4186 0.2960 10
## 4187 0.4950 12Check for duplicate rows and remove them; then check the number of duplicate rows again.
df[duplicated(df),]## Sex Length Diameter Height Whole.weight Shucked.weight Viscera.weight
## 4025 M 0.660 0.485 0.155 1.2275 0.6100 0.2740
## 4105 M 0.635 0.500 0.180 1.2915 0.5940 0.2695
## 4123 F 0.570 0.450 0.150 0.9645 0.5310 0.1890
## 4135 I 0.540 0.415 0.135 0.7090 0.3195 0.1740
## 4168 M 0.475 0.360 0.140 0.5135 0.2410 0.1045
## Shell.weight Rings
## 4025 0.300 8
## 4105 0.370 9
## 4123 0.209 9
## 4135 0.185 9
## 4168 0.155 8df<-df[!duplicated(df),]
sum(duplicated(df))## [1] 0Check for rows containing NA or missing values.
df[!complete.cases(df),]## Sex Length Diameter Height Whole.weight Shucked.weight Viscera.weight
## 3893 F 0.500 0.40 0.150 0.8085 0.2730 0.1120
## 3923 M 0.375 0.28 NA 0.2225 0.0875 0.0430
## 3951 F 0.530 NA 0.165 0.7720 0.2855 0.1975
## 3980 I NA 0.35 0.135 0.4940 0.1925 0.0945
## 4001 I 0.315 0.23 0.000 NA 0.0575 0.0285
## Shell.weight Rings
## 3893 NA 13
## 3923 0.0800 10
## 3951 0.2300 12
## 3980 0.1405 7
## 4001 0.3640 6which(is.na(df), arr.ind=TRUE)## row col
## 3980 3980 2
## 3951 3951 3
## 3923 3923 4
## 4001 4001 5
## 3893 3893 8The 2nd, 3rd, 4th, 5th and 8th columns (all with “numeric” type data) contain missing values; therefore, we impute them by mean.
df[2][is.na(df[2])] <- mean(df[,2], na.rm = TRUE)
df[3][is.na(df[3])] <- mean(df[,3], na.rm = TRUE)
df[4][is.na(df[4])] <- mean(df[,4], na.rm = TRUE)
df[5][is.na(df[5])] <- mean(df[,5], na.rm = TRUE)
df[8][is.na(df[8])] <- mean(df[,8], na.rm = TRUE)Check if there is any remaining missing values.
sum(!complete.cases(df))## [1] 0The minimum value of ’Height” column is 0.0; we inspect and get the total number of rows with “Height” = 0.
df[df$Height==0,]## Sex Length Diameter Height Whole.weight Shucked.weight Viscera.weight
## 1258 I 0.430 0.34 0 0.4280000 0.2065 0.0860
## 4001 I 0.315 0.23 0 0.8284987 0.0575 0.0285
## 4002 I 0.315 0.23 0 0.1340000 0.0575 0.0285
## Shell.weight Rings
## 1258 0.1150 8
## 4001 0.3640 6
## 4002 0.3505 6nrow(df[df$Height==0,])## [1] 3The next cleaning steps are:
- Remove leading and trailing white space in columns with ‘character’ type data
- Add a column containing the weight difference (before and after the abalone was processed)
- Remove the three rows with “Height” = 0
- Since the whole weight of each abalone must be greater than the total of its sub parts (shucked, viscera and shell), subset the data where “Weight.dff” >0
- Remove the “Weight.diff” column
df<- df %>%
mutate_if(is.character, str_trim) %>%
mutate(Weight.diff=Whole.weight-(Viscera.weight + Shucked.weight + Shell.weight)) %>%
subset(Height>0) %>%
subset(Weight.diff>0) %>%
select(-Weight.diff)Rename the columns.
names(df)<-c("Sex", "Length", "Diameter", "Height", "Whole", "Shucked", "Viscera", "Shell", "Rings") Convert “Sex” column into ‘factor’ type.
df$Sex <- ordered(df$Sex,
levels = c("I", "M", "F"),
labels = c("Infant", "Male", "Female"))Create two way contingency table.
table('Sex'=df$Sex,'Rings'=df$Rings)## Rings
## Sex 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## Infant 1 10 42 87 200 252 255 163 91 62 21 24 14 8 6 7 5
## Male 0 2 6 11 22 76 170 269 289 218 115 88 56 51 30 25 18
## Female 0 0 0 4 16 41 118 230 241 198 125 88 56 41 30 26 19
## Rings
## Sex 19 20 21 22 23 24 25 26 27 29
## Infant 2 2 1 0 0 0 0 0 0 0
## Male 14 12 6 3 3 1 0 1 1 0
## Female 15 12 7 3 6 1 1 0 1 1Show the preprocessed dataset.
head(df,10)## Sex Length Diameter Height Whole Shucked Viscera Shell Rings
## 1 Male 0.455 0.365 0.095 0.5140 0.2245 0.1010 0.150 15
## 2 Male 0.350 0.265 0.090 0.2255 0.0995 0.0485 0.070 7
## 3 Female 0.530 0.420 0.135 0.6770 0.2565 0.1415 0.210 9
## 4 Male 0.440 0.365 0.125 0.5160 0.2155 0.1140 0.155 10
## 5 Infant 0.330 0.255 0.080 0.2050 0.0895 0.0395 0.055 7
## 6 Infant 0.425 0.300 0.095 0.3515 0.1410 0.0775 0.120 8
## 7 Female 0.530 0.415 0.150 0.7775 0.2370 0.1415 0.330 20
## 8 Female 0.545 0.425 0.125 0.7680 0.2940 0.1495 0.260 16
## 9 Male 0.475 0.370 0.125 0.5095 0.2165 0.1125 0.165 9
## 10 Female 0.550 0.440 0.150 0.8945 0.3145 0.1510 0.320 19Exploratory Data Analysis
Visualize the distribution of “Sex”.
ggplot(data=df,aes(x=Sex,fill=Sex))+geom_bar()
Create boxplots and violin plots of “Sex” versus “Whole”.
qplot(Sex, Whole, data = df, geom = "boxplot", fill = Sex)
qplot(Sex, Whole, data = df, geom = "violin", fill = Sex)
Create a scatterplot of “Whole” versus “Shucked”, “Whole” versus “Viscera” and “Whole” versus “Shell” to examine how they relate to each other.
qplot(Whole, Shucked, data = df, color = Sex)
qplot(Whole, Viscera, data = df, color = Sex)
qplot(Whole, Shell, data = df, color = Sex)
It appears that “Whole” versus “Shucked” has the strongest positive correlation.
Create a correlation matrix.
corr<-cor(df[c(-1,-10)], method = "pearson", use = "complete.obs")
round(corr, 2)## Length Diameter Height Whole Shucked Viscera Shell Rings
## Length 1.00 0.99 0.82 0.93 0.90 0.90 0.90 0.54
## Diameter 0.99 1.00 0.83 0.93 0.90 0.90 0.91 0.56
## Height 0.82 0.83 1.00 0.81 0.77 0.79 0.81 0.54
## Whole 0.93 0.93 0.81 1.00 0.97 0.97 0.96 0.53
## Shucked 0.90 0.90 0.77 0.97 1.00 0.93 0.88 0.41
## Viscera 0.90 0.90 0.79 0.97 0.93 1.00 0.91 0.49
## Shell 0.90 0.91 0.81 0.96 0.88 0.91 1.00 0.62
## Rings 0.54 0.56 0.54 0.53 0.41 0.49 0.62 1.00corrplot(corr, type = 'lower', order = 'hclust', tl.col = 'black',
tl.srt = 45, tl.cex=0.8, addCoef.col = 'black', number.cex=0.8, col = COL2('RdYlBu'), cl.pos='n')
The correlation matrix shows that “Shell” and “Shucked” have the strongest and lowest correlation with “Rings”,respectively.
To examine the relationship between some of the predictor variables and the dependent variable, we plot “Shell” versus “Rings” and “Shucked” versus “Rings”.
ggplot(data=df,aes(x=Shell,y=Rings,color=Sex))+geom_point()+geom_smooth(method="lm")## `geom_smooth()` using formula 'y ~ x'
ggplot(data=df,aes(x=Shucked,y=Rings,color=Sex))+geom_point()+geom_smooth(method="lm")## `geom_smooth()` using formula 'y ~ x'
The relationship between “Shell” & “Rings” and “Shucked” & “Rings” appears similar for males and females but steeper for infants.
Draw histograms to show the distribution of each variable.
par(mfrow=c(3,3))
Length<-df$Length; hist(Length, col="blue")
Diameter<-df$Diameter; hist(Diameter, col="blue")
Height<-df$Height; hist(Height, col="blue")
Whole<-df$Whole; hist(Whole, col="blue")
Shucked<-df$Shucked; hist(Shucked, col="blue")
Viscera<-df$Viscera; hist(Viscera, col="blue")
Shell<-df$Shell; hist(Shell, col="blue")
Rings<-df$Rings; hist(Rings, col="blue")
Classifying the abalones into Adult and Infant
Transform Female and Male to Adults
levels(df$Sex) <- c(levels(df$Sex), "Adult")
df2 = df
df2$Sex[df2$Sex=="Male"] <- "Adult"
df2$Sex[df2$Sex=="Female"] <- "Adult"
df2$Sex <- ordered(df2$Sex,
levels = c("Infant", "Adult"),
labels = c("Infant", "Adult"))
head(df,5)## Sex Length Diameter Height Whole Shucked Viscera Shell Rings
## 1 Male 0.455 0.365 0.095 0.5140 0.2245 0.1010 0.150 15
## 2 Male 0.350 0.265 0.090 0.2255 0.0995 0.0485 0.070 7
## 3 Female 0.530 0.420 0.135 0.6770 0.2565 0.1415 0.210 9
## 4 Male 0.440 0.365 0.125 0.5160 0.2155 0.1140 0.155 10
## 5 Infant 0.330 0.255 0.080 0.2050 0.0895 0.0395 0.055 7Split the dataset to training and testing data.
trainIndex <- createDataPartition(df2$Sex, p = 0.8, list = F)
trainingset <- df2[trainIndex,]
testingset <- df2[-trainIndex,]Models building
fitControl <- trainControl(## 10-fold CV
method = "repeatedcv",
number = 10,
## repeated ten times
repeats = 10)
set.seed(888)
svm <- train(Sex ~ ., data = trainingset,
method = "svmPoly",
preProcess=c("scale","center"),
trControl=fitControl,
tuneGrid = data.frame(degree=1,scale=1,C=1))
options(warn=-1)
nb <- train(Sex~., trainingset, trControl=fitControl, method="nb")
options(warn=1)
knn <- train(Sex~., data = trainingset,
method = "knn",
preProcess = c("center", "scale"),
tuneLength = 10,
trControl = fitControl)
svm_pred<-predict(svm, newdata = testingset)
options(warn=-1)
nb_pred<-predict(nb, newdata = testingset)
options(warn=1)
knn_pred<-predict(knn, newdata = testingset)Models’ Performance Evaluation
# Support Vector Machines (SVM)
svm_cm<-confusionMatrix(svm_pred,testingset$Sex)
svm_cm## Confusion Matrix and Statistics
##
## Reference
## Prediction Infant Adult
## Infant 172 68
## Adult 78 485
##
## Accuracy : 0.8182
## 95% CI : (0.7897, 0.8443)
## No Information Rate : 0.6887
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.5713
##
## Mcnemar's Test P-Value : 0.4564
##
## Sensitivity : 0.6880
## Specificity : 0.8770
## Pos Pred Value : 0.7167
## Neg Pred Value : 0.8615
## Prevalence : 0.3113
## Detection Rate : 0.2142
## Detection Prevalence : 0.2989
## Balanced Accuracy : 0.7825
##
## 'Positive' Class : Infant
## # Naive Bayes (NB)
nb_cm<-confusionMatrix(nb_pred,testingset$Sex)
nb_cm## Confusion Matrix and Statistics
##
## Reference
## Prediction Infant Adult
## Infant 189 115
## Adult 61 438
##
## Accuracy : 0.7808
## 95% CI : (0.7506, 0.809)
## No Information Rate : 0.6887
## P-Value [Acc > NIR] : 3.742e-09
##
## Kappa : 0.5174
##
## Mcnemar's Test P-Value : 6.469e-05
##
## Sensitivity : 0.7560
## Specificity : 0.7920
## Pos Pred Value : 0.6217
## Neg Pred Value : 0.8778
## Prevalence : 0.3113
## Detection Rate : 0.2354
## Detection Prevalence : 0.3786
## Balanced Accuracy : 0.7740
##
## 'Positive' Class : Infant
## # K-Nearest Neighbors (KNN)
knn_cm<-confusionMatrix(knn_pred,testingset$Sex)
knn_cm## Confusion Matrix and Statistics
##
## Reference
## Prediction Infant Adult
## Infant 168 54
## Adult 82 499
##
## Accuracy : 0.8306
## 95% CI : (0.8029, 0.8559)
## No Information Rate : 0.6887
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.5925
##
## Mcnemar's Test P-Value : 0.0206
##
## Sensitivity : 0.6720
## Specificity : 0.9024
## Pos Pred Value : 0.7568
## Neg Pred Value : 0.8589
## Prevalence : 0.3113
## Detection Rate : 0.2092
## Detection Prevalence : 0.2765
## Balanced Accuracy : 0.7872
##
## 'Positive' Class : Infant
## Predicting the number of rings using regression.
Split the dataset to training and testing data.
reg_trainIndex <- createDataPartition(df$Rings, p=0.8, list = FALSE)
reg_trainingset <- df[reg_trainIndex,]
reg_testingset <- df[-reg_trainIndex,]Model building
# Linear Regression
reg <- lm(Rings ~. , data=trainingset)
summary(reg)##
## Call:
## lm(formula = Rings ~ ., data = trainingset)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.3170 -1.2770 -0.2897 0.8974 13.3415
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.635437 0.316501 11.486 < 2e-16 ***
## Sex.L 0.604648 0.071566 8.449 < 2e-16 ***
## Length 0.007127 2.065793 0.003 0.997247
## Diameter 10.664756 2.510270 4.248 2.21e-05 ***
## Height 8.664939 1.605086 5.398 7.21e-08 ***
## Whole 12.467377 0.973853 12.802 < 2e-16 ***
## Shucked -23.965396 1.068335 -22.432 < 2e-16 ***
## Viscera -12.898012 1.573127 -8.199 3.47e-16 ***
## Shell 4.775017 1.442872 3.309 0.000945 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.156 on 3208 degrees of freedom
## Multiple R-squared: 0.5442, Adjusted R-squared: 0.5431
## F-statistic: 478.8 on 8 and 3208 DF, p-value: < 2.2e-16## if a P-value(Pr(>|t|)) is 0.05 or below we can say that there’s a low chance it is not significant for the analysis
options(warn=-1) #turn off warnings
reg_pred <- predict(reg, testingset)
options(warn=1)
modelEval <- cbind(testingset$Rings, reg_pred)
colnames(modelEval) <- c('Actual', 'Predicted')
modelEval <- as.data.frame(modelEval)
modelEval## Actual Predicted
## 1 15 9.223590
## 8 16 11.524882
## 9 9 9.595922
## 18 10 9.174553
## 22 10 7.677932
## 25 10 10.376858
## 29 15 11.510046
## 36 8 8.297595
## 38 8 8.786167
## 49 6 6.513450
## 53 10 9.090057
## 54 10 9.209412
## 57 8 9.166942
## 60 7 9.947487
## 68 13 16.427000
## 83 16 11.488588
## 95 15 14.119465
## 96 14 14.981136
## 102 15 11.359502
## 103 15 13.012310
## 108 10 10.836992
## 121 9 9.538523
## 122 7 7.449538
## 131 17 13.070207
## 132 9 9.521951
## 145 10 9.980281
## 151 15 11.109395
## 162 13 11.175338
## 171 14 14.953033
## 197 11 10.070273
## 199 15 10.340038
## 209 13 13.049208
## 212 7 7.709851
## 217 8 9.703264
## 218 7 8.080191
## 223 9 10.318032
## 224 11 9.988706
## 226 9 10.061920
## 231 13 11.570083
## 234 7 6.223383
## 240 5 4.839978
## 251 7 7.189738
## 268 8 8.275496
## 270 13 9.861073
## 275 13 16.178374
## 310 10 10.121075
## 316 8 8.821566
## 317 14 11.769909
## 321 5 6.013337
## 323 11 8.743105
## 326 7 7.426143
## 328 12 9.842427
## 340 15 11.466808
## 341 14 9.274773
## 345 8 11.226421
## 346 13 9.596221
## 347 9 11.860927
## 348 6 6.799371
## 350 14 10.196933
## 353 12 9.879464
## 356 20 17.264503
## 360 16 12.779972
## 361 18 12.616327
## 362 12 11.812180
## 363 20 12.560862
## 365 12 11.538214
## 370 17 15.425835
## 371 16 12.433903
## 374 14 13.750677
## 375 13 14.692797
## 379 15 13.019429
## 384 12 9.984901
## 388 10 9.449450
## 391 10 7.606902
## 403 7 9.093718
## 407 8 9.096289
## 410 8 10.022200
## 419 16 13.629637
## 430 18 13.991177
## 431 18 12.449394
## 432 20 11.877977
## 433 18 13.013946
## 434 22 12.725380
## 446 9 12.334568
## 450 18 10.892053
## 457 15 12.864869
## 465 6 6.062526
## 469 17 18.233594
## 476 17 12.437380
## 477 9 9.762137
## 480 16 14.000299
## 482 17 10.941299
## 483 15 10.492685
## 493 11 12.392300
## 498 19 11.579579
## 501 12 11.244180
## 511 10 12.243305
## 512 10 9.192998
## 515 5 6.847652
## 526 4 5.761960
## 531 20 10.470477
## 532 13 9.347411
## 533 12 9.020661
## 534 9 8.683416
## 536 11 9.217283
## 542 11 9.656488
## 553 12 10.235528
## 555 9 7.698248
## 567 12 8.595462
## 571 16 8.236584
## 573 20 13.445499
## 577 10 9.492314
## 579 11 9.653105
## 592 9 8.234497
## 596 13 12.105627
## 599 12 12.855557
## 610 12 8.289421
## 621 10 7.856903
## 626 12 11.236420
## 634 9 9.360286
## 636 8 8.339780
## 637 7 7.812151
## 638 6 7.645785
## 643 19 12.385791
## 645 9 9.079824
## 648 9 12.967746
## 659 18 12.508734
## 661 18 14.423212
## 663 10 9.332746
## 666 10 8.650209
## 671 14 11.129101
## 676 22 13.782648
## 679 23 12.532192
## 681 7 7.484644
## 685 10 10.520467
## 689 11 10.507332
## 698 5 7.039745
## 706 10 9.643745
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## 3789 8 11.087961
## 3792 11 11.945851
## 3795 10 11.384639
## 3803 6 6.546248
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## 3811 8 9.076140
## 3826 11 12.635452
## 3828 11 18.276410
## 3834 11 10.309915
## 3840 8 8.879594
## 3848 9 9.173670
## 3858 16 15.780711
## 3860 9 10.980630
## 3866 19 12.177083
## 3872 12 9.129708
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## 3889 12 9.275766
## 3898 14 15.485531
## 3902 15 9.177116
## 3904 4 4.672602
## 3906 16 13.508525
## 3907 6 8.167598
## 3912 13 10.064449
## 3913 10 7.541120
## 3914 15 9.407773
## 3917 11 9.391731
## 3924 10 8.379368
## 3937 5 5.934926
## 3947 20 13.784769
## 3948 6 5.747332
## 3961 10 9.805682
## 3964 11 12.502724
## 3969 6 6.273202
## 3976 8 8.042724
## 3986 8 10.459417
## 3993 8 11.130625
## 3999 4 5.138119
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## 4018 8 9.506157
## 4021 10 7.350731
## 4027 11 11.140564
## 4034 6 6.828775
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## 4039 8 7.572003
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## 4046 11 9.353512
## 4047 12 10.276833
## 4058 10 11.156631
## 4061 10 11.612528
## 4062 9 11.098543
## 4068 10 11.214523
## 4089 9 8.898034
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## 4110 11 12.970208
## 4128 4 6.173584
## 4131 8 8.855758
## 4132 8 8.820237
## 4137 10 9.154696
## 4139 10 9.909075
## 4152 13 11.708512
## 4158 11 13.327851
## 4161 6 6.376446
## 4169 8 8.258059
## 4175 7 7.277003
## 4183 11 10.593591Model’s Performance Evaluation
mse <- mean((modelEval$Actual - modelEval$Predicted)^2)
rmse <- sqrt(mse)
mse; rmse## [1] 5.518349## [1] 2.349117