Problem

Predicting the age of abalone from physical measurements.

Contents

Import the Dataset

Import the dataset and assign the column names for each fields and view the dataset

dataset=read.csv(file="abalone(1).data")
colnames(dataset)=c("Sex","Length","Diameter","Height","Whole weight","Shucked weight"
                    ,"Viscera weight","Shell weight","Rings")
head(dataset)
##   Sex Length Diameter Height Whole weight Shucked weight Viscera weight
## 1   M  0.350    0.265  0.090       0.2255         0.0995         0.0485
## 2   F  0.530    0.420  0.135       0.6770         0.2565         0.1415
## 3   M  0.440    0.365  0.125       0.5160         0.2155         0.1140
## 4   I  0.330    0.255  0.080       0.2050         0.0895         0.0395
## 5   I  0.425    0.300  0.095       0.3515         0.1410         0.0775
## 6   F  0.530    0.415  0.150       0.7775         0.2370         0.1415
##   Shell weight Rings
## 1        0.070     7
## 2        0.210     9
## 3        0.155    10
## 4        0.055     7
## 5        0.120     8
## 6        0.330    20

There is no missing values in the data set Lets see the Structure and Summary of the given Dataset

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
str(dataset)
## 'data.frame':    4176 obs. of  9 variables:
##  $ Sex           : Factor w/ 3 levels "F","I","M": 3 1 3 2 2 1 1 3 1 1 ...
##  $ Length        : num  0.35 0.53 0.44 0.33 0.425 0.53 0.545 0.475 0.55 0.525 ...
##  $ Diameter      : num  0.265 0.42 0.365 0.255 0.3 0.415 0.425 0.37 0.44 0.38 ...
##  $ Height        : num  0.09 0.135 0.125 0.08 0.095 0.15 0.125 0.125 0.15 0.14 ...
##  $ Whole weight  : num  0.226 0.677 0.516 0.205 0.351 ...
##  $ Shucked weight: num  0.0995 0.2565 0.2155 0.0895 0.141 ...
##  $ Viscera weight: num  0.0485 0.1415 0.114 0.0395 0.0775 ...
##  $ Shell weight  : num  0.07 0.21 0.155 0.055 0.12 0.33 0.26 0.165 0.32 0.21 ...
##  $ Rings         : int  7 9 10 7 8 20 16 9 19 14 ...
summary(dataset)
##  Sex          Length         Diameter          Height      
##  F:1307   Min.   :0.075   Min.   :0.0550   Min.   :0.0000  
##  I:1342   1st Qu.:0.450   1st Qu.:0.3500   1st Qu.:0.1150  
##  M:1527   Median :0.545   Median :0.4250   Median :0.1400  
##           Mean   :0.524   Mean   :0.4079   Mean   :0.1395  
##           3rd Qu.:0.615   3rd Qu.:0.4800   3rd Qu.:0.1650  
##           Max.   :0.815   Max.   :0.6500   Max.   :1.1300  
##   Whole weight    Shucked weight   Viscera weight     Shell weight   
##  Min.   :0.0020   Min.   :0.0010   Min.   :0.00050   Min.   :0.0015  
##  1st Qu.:0.4415   1st Qu.:0.1860   1st Qu.:0.09337   1st Qu.:0.1300  
##  Median :0.7997   Median :0.3360   Median :0.17100   Median :0.2340  
##  Mean   :0.8288   Mean   :0.3594   Mean   :0.18061   Mean   :0.2389  
##  3rd Qu.:1.1533   3rd Qu.:0.5020   3rd Qu.:0.25300   3rd Qu.:0.3290  
##  Max.   :2.8255   Max.   :1.4880   Max.   :0.76000   Max.   :1.0050  
##      Rings       
##  Min.   : 1.000  
##  1st Qu.: 8.000  
##  Median : 9.000  
##  Mean   : 9.932  
##  3rd Qu.:11.000  
##  Max.   :29.000
quantile(dataset$Rings)
##   0%  25%  50%  75% 100% 
##    1    8    9   11   29

Exploratory Data Analysis

Target Attributes

Target attribute is Rings

FREQUENCY BASED ON RINGS

library(ggplot2)
dataset %>% ggplot(aes(x=Rings))+geom_histogram(fill="lightblue",color="Darkblue",binwidth = 2,alpha=0.5)

dataset %>% ggplot(aes(x=Rings))+geom_bar(fill="steelblue",alpha=0.6)

boxplot(dataset$Rings,col = "steelblue",horizontal = TRUE,border="black",xlab=("Rings"))

Thus the most frequent values of the attribute Rings are highly concentrated around the median of the distribution value of 9.

Sex Attribute

table(dataset$Sex)
## 
##    F    I    M 
## 1307 1342 1527
ggplot(dataset) + aes(Rings, fill = Sex) +  geom_density(alpha=0.6)

ggplot(dataset,aes(x=Rings,y=Sex,fill=Sex))+geom_col()+facet_grid(~Sex)

From the above plots we know that the female abalone has longer lifespan than others but the count of male abalone is maximum than others.

Weight Attribute Whole weight

summary(dataset$`Whole weight`)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0020  0.4415  0.7997  0.8288  1.1533  2.8255
vect1<-round(dataset$`Whole weight`,0)    
ggplot(dataset,aes(y=`Whole weight`,x=2,fill="Orange"))+geom_boxplot()  

ggplot(dataset,aes(y=factor(vect1),x=Rings,fill=factor(vect1)))+geom_col()+facet_grid(~factor(vect1))+ylab("Whole weight")

Shell weight

boxplot(dataset$`Shell weight`,col = "darkgreen",border="black",ylab="Shell weight")

ggplot(dataset,aes(x=`Shell weight`,fill="Orange"))+geom_bar(binwidth = 0.02)
## Warning: `geom_bar()` no longer has a `binwidth` parameter. Please use
## `geom_histogram()` instead.

From the above plots we know that the weight of abalone (1.5 to 2.4)gm has longer lifespan than others but the weight of abalone (0.5 to 1.4)gm has maximum count than others.

Corelation Between The Data

library(corrplot)
## corrplot 0.84 loaded
library(corrgram)
## Registered S3 method overwritten by 'seriation':
##   method         from 
##   reorder.hclust gclus
corrgram(dataset,order=T,lower.panel=panel.shade,
         upper.panel=panel.pie, text.panel=panel.txt,
         main="Abalone data")

Spliting the Dataset

clean_dataset<-dataset %>% mutate(age=case_when(Rings %in% 1:5~"young",Rings %in% 6:13~"adult",Rings %in% 14:30~"old"))
clean_dataset<-clean_dataset %>% select(c(2,3,5,8,10)) %>% na.omit()
head(clean_dataset)
##   Length Diameter Whole weight Shell weight   age
## 1  0.350    0.265       0.2255        0.070 adult
## 2  0.530    0.420       0.6770        0.210 adult
## 3  0.440    0.365       0.5160        0.155 adult
## 4  0.330    0.255       0.2050        0.055 adult
## 5  0.425    0.300       0.3515        0.120 adult
## 6  0.530    0.415       0.7775        0.330   old
library(caTools)
set.seed(123)
sample=sample.split(clean_dataset,SplitRatio = 0.8)
traindata<-subset(clean_dataset,sample==T)
head(traindata)
##   Length Diameter Whole weight Shell weight   age
## 1  0.350    0.265       0.2255        0.070 adult
## 2  0.530    0.420       0.6770        0.210 adult
## 3  0.440    0.365       0.5160        0.155 adult
## 4  0.330    0.255       0.2050        0.055 adult
## 6  0.530    0.415       0.7775        0.330   old
## 7  0.545    0.425       0.7680        0.260   old
testdata<-subset(clean_dataset,sample==F)

Building the Model

library(rpart)
model <-rpart(formula=age~.,data=traindata,method="class")
summary(model)
## Call:
## rpart(formula = age ~ ., data = traindata, method = "class")
##   n= 3341 
## 
##           CP nsplit rel error    xerror       xstd
## 1 0.12343470      0 1.0000000 1.0000000 0.03859530
## 2 0.01118068      1 0.8765653 0.8855098 0.03673415
## 3 0.01073345      7 0.8067979 0.8729875 0.03651832
## 4 0.01000000      9 0.7853309 0.8729875 0.03651832
## 
## Variable importance
## Shell weight     Diameter Whole weight       Length 
##           27           25           24           24 
## 
## Node number 1: 3341 observations,    complexity param=0.1234347
##   predicted class=adult  expected loss=0.1673152  P(node) =1
##     class counts:  2782   403   156
##    probabilities: 0.833 0.121 0.047 
##   left son=2 (3160 obs) right son=3 (181 obs)
##   Primary splits:
##       Diameter     < 0.2225  to the right, improve=134.5335, (0 missing)
##       Length       < 0.2875  to the right, improve=131.4100, (0 missing)
##       Shell weight < 0.03525 to the right, improve=131.1960, (0 missing)
##       Whole weight < 0.12375 to the right, improve=129.8779, (0 missing)
##   Surrogate splits:
##       Shell weight < 0.03625 to the right, agree=0.994, adj=0.895, (0 split)
##       Length       < 0.2975  to the right, agree=0.993, adj=0.878, (0 split)
##       Whole weight < 0.1265  to the right, agree=0.993, adj=0.878, (0 split)
## 
## Node number 2: 3160 observations,    complexity param=0.01118068
##   predicted class=adult  expected loss=0.1373418  P(node) =0.9458246
##     class counts:  2726   403    31
##    probabilities: 0.863 0.128 0.010 
##   left son=4 (2538 obs) right son=5 (622 obs)
##   Primary splits:
##       Shell weight < 0.35775 to the left,  improve=45.62611, (0 missing)
##       Whole weight < 0.75875 to the left,  improve=26.06479, (0 missing)
##       Diameter     < 0.3775  to the left,  improve=21.87421, (0 missing)
##       Length       < 0.4775  to the left,  improve=19.01801, (0 missing)
##   Surrogate splits:
##       Whole weight < 1.341   to the left,  agree=0.930, adj=0.646, (0 split)
##       Diameter     < 0.5025  to the left,  agree=0.914, adj=0.563, (0 split)
##       Length       < 0.6325  to the left,  agree=0.913, adj=0.556, (0 split)
## 
## Node number 3: 181 observations
##   predicted class=young  expected loss=0.3093923  P(node) =0.0541754
##     class counts:    56     0   125
##    probabilities: 0.309 0.000 0.691 
## 
## Node number 4: 2538 observations
##   predicted class=adult  expected loss=0.0965327  P(node) =0.7596528
##     class counts:  2293   214    31
##    probabilities: 0.903 0.084 0.012 
## 
## Node number 5: 622 observations,    complexity param=0.01118068
##   predicted class=adult  expected loss=0.3038585  P(node) =0.1861718
##     class counts:   433   189     0
##    probabilities: 0.696 0.304 0.000 
##   left son=10 (387 obs) right son=11 (235 obs)
##   Primary splits:
##       Length       < 0.6475  to the right, improve=14.53104, (0 missing)
##       Shell weight < 0.68775 to the left,  improve=13.18727, (0 missing)
##       Diameter     < 0.4875  to the right, improve=12.85866, (0 missing)
##       Whole weight < 1.10375 to the right, improve=11.71015, (0 missing)
##   Surrogate splits:
##       Diameter     < 0.5125  to the right, agree=0.852, adj=0.609, (0 split)
##       Whole weight < 1.38375 to the right, agree=0.797, adj=0.464, (0 split)
##       Shell weight < 0.3905  to the right, agree=0.717, adj=0.251, (0 split)
## 
## Node number 10: 387 observations,    complexity param=0.01118068
##   predicted class=adult  expected loss=0.2196382  P(node) =0.1158336
##     class counts:   302    85     0
##    probabilities: 0.780 0.220 0.000 
##   left son=20 (338 obs) right son=21 (49 obs)
##   Primary splits:
##       Shell weight < 0.579   to the left,  improve=15.5442400, (0 missing)
##       Diameter     < 0.5275  to the left,  improve= 1.9524010, (0 missing)
##       Whole weight < 1.67575 to the left,  improve= 1.3805140, (0 missing)
##       Length       < 0.6675  to the right, improve= 0.5388445, (0 missing)
##   Surrogate splits:
##       Diameter     < 0.5875  to the left,  agree=0.902, adj=0.224, (0 split)
##       Whole weight < 2.23725 to the left,  agree=0.899, adj=0.204, (0 split)
##       Length       < 0.7425  to the left,  agree=0.884, adj=0.082, (0 split)
## 
## Node number 11: 235 observations,    complexity param=0.01118068
##   predicted class=adult  expected loss=0.4425532  P(node) =0.07033822
##     class counts:   131   104     0
##    probabilities: 0.557 0.443 0.000 
##   left son=22 (161 obs) right son=23 (74 obs)
##   Primary splits:
##       Shell weight < 0.418   to the left,  improve=5.920902, (0 missing)
##       Whole weight < 1.10375 to the right, improve=5.394776, (0 missing)
##       Length       < 0.5925  to the right, improve=3.646195, (0 missing)
##       Diameter     < 0.4675  to the right, improve=3.646195, (0 missing)
##   Surrogate splits:
##       Whole weight < 1.43125 to the left,  agree=0.740, adj=0.176, (0 split)
##       Diameter     < 0.5225  to the left,  agree=0.698, adj=0.041, (0 split)
## 
## Node number 20: 338 observations
##   predicted class=adult  expected loss=0.1656805  P(node) =0.1011673
##     class counts:   282    56     0
##    probabilities: 0.834 0.166 0.000 
## 
## Node number 21: 49 observations
##   predicted class=old    expected loss=0.4081633  P(node) =0.01466627
##     class counts:    20    29     0
##    probabilities: 0.408 0.592 0.000 
## 
## Node number 22: 161 observations,    complexity param=0.01118068
##   predicted class=adult  expected loss=0.3664596  P(node) =0.04818916
##     class counts:   102    59     0
##    probabilities: 0.634 0.366 0.000 
##   left son=44 (86 obs) right son=45 (75 obs)
##   Primary splits:
##       Whole weight < 1.24275 to the right, improve=9.1193140, (0 missing)
##       Length       < 0.5925  to the right, improve=8.2848600, (0 missing)
##       Diameter     < 0.4675  to the right, improve=7.5577640, (0 missing)
##       Shell weight < 0.41025 to the right, improve=0.7317899, (0 missing)
##   Surrogate splits:
##       Length       < 0.6225  to the right, agree=0.770, adj=0.507, (0 split)
##       Diameter     < 0.4775  to the right, agree=0.714, adj=0.387, (0 split)
##       Shell weight < 0.36025 to the right, agree=0.621, adj=0.187, (0 split)
## 
## Node number 23: 74 observations,    complexity param=0.01073345
##   predicted class=old    expected loss=0.3918919  P(node) =0.02214906
##     class counts:    29    45     0
##    probabilities: 0.392 0.608 0.000 
##   left son=46 (16 obs) right son=47 (58 obs)
##   Primary splits:
##       Length       < 0.6425  to the right, improve=3.5676840, (0 missing)
##       Diameter     < 0.4925  to the right, improve=2.7804740, (0 missing)
##       Shell weight < 0.54    to the left,  improve=1.9702700, (0 missing)
##       Whole weight < 1.4285  to the right, improve=0.4676095, (0 missing)
## 
## Node number 44: 86 observations
##   predicted class=adult  expected loss=0.2093023  P(node) =0.0257408
##     class counts:    68    18     0
##    probabilities: 0.791 0.209 0.000 
## 
## Node number 45: 75 observations,    complexity param=0.01118068
##   predicted class=old    expected loss=0.4533333  P(node) =0.02244837
##     class counts:    34    41     0
##    probabilities: 0.453 0.547 0.000 
##   left son=90 (53 obs) right son=91 (22 obs)
##   Primary splits:
##       Diameter     < 0.4625  to the right, improve=4.5901430, (0 missing)
##       Length       < 0.5925  to the right, improve=4.2482960, (0 missing)
##       Whole weight < 1.10375 to the right, improve=2.6625110, (0 missing)
##       Shell weight < 0.36425 to the left,  improve=0.8030326, (0 missing)
##   Surrogate splits:
##       Length       < 0.5825  to the right, agree=0.867, adj=0.545, (0 split)
##       Whole weight < 0.993   to the right, agree=0.827, adj=0.409, (0 split)
##       Shell weight < 0.4025  to the left,  agree=0.720, adj=0.045, (0 split)
## 
## Node number 46: 16 observations
##   predicted class=adult  expected loss=0.3125  P(node) =0.004788985
##     class counts:    11     5     0
##    probabilities: 0.688 0.312 0.000 
## 
## Node number 47: 58 observations
##   predicted class=old    expected loss=0.3103448  P(node) =0.01736007
##     class counts:    18    40     0
##    probabilities: 0.310 0.690 0.000 
## 
## Node number 90: 53 observations,    complexity param=0.01073345
##   predicted class=adult  expected loss=0.4339623  P(node) =0.01586351
##     class counts:    30    23     0
##    probabilities: 0.566 0.434 0.000 
##   left son=180 (41 obs) right son=181 (12 obs)
##   Primary splits:
##       Whole weight < 1.2105  to the left,  improve=3.0987110, (0 missing)
##       Diameter     < 0.5075  to the left,  improve=2.8886680, (0 missing)
##       Length       < 0.6275  to the left,  improve=1.1338900, (0 missing)
##       Shell weight < 0.36425 to the left,  improve=0.3285855, (0 missing)
##   Surrogate splits:
##       Diameter < 0.5025  to the left,  agree=0.811, adj=0.167, (0 split)
##       Length   < 0.6375  to the left,  agree=0.792, adj=0.083, (0 split)
## 
## Node number 91: 22 observations
##   predicted class=old    expected loss=0.1818182  P(node) =0.006584855
##     class counts:     4    18     0
##    probabilities: 0.182 0.818 0.000 
## 
## Node number 180: 41 observations
##   predicted class=adult  expected loss=0.3414634  P(node) =0.01227177
##     class counts:    27    14     0
##    probabilities: 0.659 0.341 0.000 
## 
## Node number 181: 12 observations
##   predicted class=old    expected loss=0.25  P(node) =0.003591739
##     class counts:     3     9     0
##    probabilities: 0.250 0.750 0.000
library(rpart.plot)
rpart.plot(model)

predicted_model<-predict(object=model,newdata=testdata,type="class")
confusion.matrix<-table(testdata$age,predicted_model)
confusion.matrix
##        predicted_model
##         adult old young
##   adult   681  20    15
##   old      72  14     0
##   young    10   0    23

Accuracy of Model

accuracy<-sum(diag(confusion.matrix))/sum(confusion.matrix)
accuracy
## [1] 0.8598802

Conclusion

*By observing the correlation between the target attribute Rings and the indepent variables, we conclude that it is possible to build a model to predict the target value in function of the independent attributes.

*The weight of the Abalones varies proportional to their sizes

*There’s no significant differences in size, weight and numbers of rigns between male/female abalones

*The Infant Abalones groups presents lower mean values of size, weight and number of rings