Data 622 - Homework 1

library(kableExtra)
library(naivebayes)
library(dplyr)
library(class) 
library(ggplot2)

Question 1

You have been hired by a local electronics retailer and the above dataset has been given to you. Manager Bayes Jr. wants to create a spreadsheet to predict if a customer is likely prospect. To that end:

Dataset

data <- read.csv("question1.csv", header = TRUE)
data %>% kable() %>% kable_styling() %>% scroll_box(width = "800px")

age.group	networth	status	credit_rating	class.prospect
youth	high	employed	fair	no
youth	high	employed	excellent	no
middle	high	employed	fair	yes
senior	medium	employed	fair	yes
senior	low	unemployed	fair	yes
senior	low	unemployed	excellent	no
middle	low	unemployed	excellent	yes
youth	medium	employed	fair	no
youth	low	unemployed	fair	yes
senior	medium	unemployed	fair	yes
youth	medium	unemployed	excellent	yes
middle	medium	employed	excellent	yes
middle	high	unemployed	fair	yes
senior	medium	employed	excellent	no

Priors

1)Compute prior probabilities for the Prospect

Prior Priorities P(prospect=yes)
Prior Priorities P(prospect=no)

(priorCount<-table(data$class.prospect))

## 
##  no yes 
##   5   9

numberOfNo<-priorCount[1]
numberOfYes<-priorCount[2]
(numberOfSamples<-nrow(data))

## [1] 14

(Pyes<-numberOfYes/numberOfSamples)

##       yes 
## 0.6428571

(Pno<-numberOfNo/numberOfSamples)

##        no 
## 0.3571429

Conditional probabilities

2. Compute the conditional probabilities. Compute the conditional probabilities for each predictor variable: age_group, networth, status, credit_rating.

age_group

data %>% select(age.group,class.prospect) %>% kable() %>% kable_styling() %>% scroll_box(width = "800px")

age.group	class.prospect
youth	no
youth	no
middle	yes
senior	yes
senior	yes
senior	no
middle	yes
youth	no
youth	yes
senior	yes
youth	yes
middle	yes
middle	yes
senior	no

P(age-group=youth|prospect=yes)

(numberOfYouthWithYes<-length(which((data$class.prospect=='yes') & (data$age.group=='youth'))))

## [1] 2

(PyouthGivenYes<-numberOfYouthWithYes/numberOfYes)

##       yes 
## 0.2222222

P(age-group=middle|prospect=yes)

(numberOfMiddleWithYes<-length(which((data$class.prospect=='yes') & (data$age.group=='middle'))))

## [1] 4

(PmiddleGivenYes<-numberOfMiddleWithYes/numberOfYes)

##       yes 
## 0.4444444

P(age-group=senior|prospect=yes)

(numberOfSeniorWithYes<-length(which((data$class.prospect=='yes') & (data$age.group=='senior'))))

## [1] 3

(PseniorGivenYes<-numberOfSeniorWithYes/numberOfYes)

##       yes 
## 0.3333333

We will add the probabilities to double check our calculations.

PyouthGivenYes+PmiddleGivenYes+PseniorGivenYes

## yes 
##   1

P(age-group=youth|prospect=no)

(numberOfYouthWithNo<-length(which((data$class.prospect=='no') & (data$age.group=='youth'))))

## [1] 3

(PyouthGivenNo<-numberOfYouthWithNo/numberOfNo)

##  no 
## 0.6

P(age-group=middle|prospect=no)

(numberOfMiddleWithNo<-length(which((data$class.prospect=='no') & (data$age.group=='middle'))))

## [1] 0

(PmiddleGivenNo<-numberOfMiddleWithNo/numberOfNo)

## no 
##  0

P(age-group=senior|prospect=no)

(numberOfSeniorWithNo<-length(which((data$class.prospect=='no') & (data$age.group=='senior'))))

## [1] 2

(PseniorGivenNo<-numberOfSeniorWithNo/numberOfNo)

##  no 
## 0.4

PyouthGivenNo+PmiddleGivenNo+PseniorGivenNo

## no 
##  1

networth

data %>% select(networth,class.prospect) %>% kable() %>% kable_styling() %>% scroll_box(width = "800px")

networth	class.prospect
high	no
high	no
high	yes
medium	yes
low	yes
low	no
low	yes
medium	no
low	yes
medium	yes
medium	yes
medium	yes
high	yes
medium	no

P(networth=high|prospect=yes)

(numberOfHighWithYes<-length(which((data$class.prospect=='yes') & (data$networth=='high'))))

## [1] 2

(PhighGivenYes<-numberOfHighWithYes/numberOfYes)

##       yes 
## 0.2222222

P(networth=low|prospect=yes)

(numberOfLowWithYes<-length(which((data$class.prospect=='yes') & (data$networth=='low'))))

## [1] 3

(PlowGivenYes<-numberOfLowWithYes/numberOfYes)

##       yes 
## 0.3333333

P(networth=medium|prospect=yes)

(numberOfMediumWithYes<-length(which((data$class.prospect=='yes') & (data$networth=='medium'))))

## [1] 4

(PmediumGivenYes<-numberOfMediumWithYes/numberOfYes)

##       yes 
## 0.4444444

PhighGivenYes+PlowGivenYes+PmediumGivenYes

## yes 
##   1

P(networth=high|prospect=no)

(numberOfHighWithNo<-length(which((data$class.prospect=='no') & (data$networth=='high'))))

## [1] 2

(PhighGivenNo<-numberOfHighWithNo/numberOfNo)

##  no 
## 0.4

P(networth=low|prospect=no)

(numberOfLowWithNo<-length(which((data$class.prospect=='no') & (data$networth=='low'))))

## [1] 1

(PlowGivenNo<-numberOfLowWithNo/numberOfNo)

##  no 
## 0.2

P(networth=medium|prospect=no)

(numberOfMediumWithNo<-length(which((data$class.prospect=='no') & (data$networth=='medium'))))

## [1] 2

(PmediumGivenNo<-numberOfMediumWithNo/numberOfNo)

##  no 
## 0.4

PhighGivenNo+PlowGivenNo+PmediumGivenNo

## no 
##  1

status

data %>% select(status,class.prospect) %>% kable() %>% kable_styling() %>% scroll_box(width = "800px")

status	class.prospect
employed	no
employed	no
employed	yes
employed	yes
unemployed	yes
unemployed	no
unemployed	yes
employed	no
unemployed	yes
unemployed	yes
unemployed	yes
employed	yes
unemployed	yes
employed	no

P(status=employed|prospect=yes)

(numberOfEmployedWithYes<-length(which((data$class.prospect=='yes') & (data$status=='employed'))))

## [1] 3

(PemployedGivenYes<-numberOfEmployedWithYes/numberOfYes)

##       yes 
## 0.3333333

P(status=unemployed|prospect=yes)

(numberOfUnemployedWithYes<-length(which((data$class.prospect=='yes') & (data$status=='unemployed'))))

## [1] 6

(PunemployedGivenYes<-numberOfUnemployedWithYes/numberOfYes)

##       yes 
## 0.6666667

PemployedGivenYes+PunemployedGivenYes

## yes 
##   1

P(status=employed|prospect=no)

(numberOfEmployedWithNo<-length(which((data$class.prospect=='no') & (data$status=='employed'))))

## [1] 4

(PemployedGivenNo<-numberOfEmployedWithNo/numberOfNo)

##  no 
## 0.8

P(status=unemployed|prospect=no)

(numberOfUnemployedWithNo<-length(which((data$class.prospect=='no') & (data$status=='unemployed'))))

## [1] 1

(PunemployedGivenNo<-numberOfUnemployedWithNo/numberOfNo)

##  no 
## 0.2

PemployedGivenNo+PunemployedGivenNo

## no 
##  1

credit_rating

data %>% select(credit_rating,class.prospect) %>% kable() %>% kable_styling() %>% scroll_box(width = "800px")

credit_rating	class.prospect
fair	no
excellent	no
fair	yes
fair	yes
fair	yes
excellent	no
excellent	yes
fair	no
fair	yes
fair	yes
excellent	yes
excellent	yes
fair	yes
excellent	no

P(credit=fair|prospect=yes)

(numberOfFairWithYes<-length(which((data$class.prospect=='yes') & (data$credit=='fair'))))

## [1] 6

(PfairGivenYes<-numberOfFairWithYes/numberOfYes)

##       yes 
## 0.6666667

P(credit=excellent|prospect=yes)

(numberOfExcellentdWithYes<-length(which((data$class.prospect=='yes') & (data$credit=='excellent'))))

## [1] 3

(PexcellentGivenYes<-numberOfExcellentdWithYes/numberOfYes)

##       yes 
## 0.3333333

PfairGivenYes+PexcellentGivenYes

## yes 
##   1

P(credit=fair|prospect=no)

(numberOfFairWithNo<-length(which((data$class.prospect=='no') & (data$credit=='fair'))))

## [1] 2

(PfairGivenNo<-numberOfFairWithNo/numberOfNo)

##  no 
## 0.4

P(credit=excellent|prospect=no)

(numberOfExcellentWithNo<-length(which((data$class.prospect=='no') & (data$credit=='excellent'))))

## [1] 3

(PexcellentGivenNo<-numberOfExcellentWithNo/numberOfNo)

##  no 
## 0.6

PfairGivenNo+PexcellentGivenNo

## no 
##  1

Posteriors

3. Assuming the assumptions of Naive Bayes are met compute the posterior probability.

The posterior probabilities answer the questions the manager has, to know if a given costumer is a likely porspect.

For example, given a costumer:
- Age group: youth
- Net worth: high
- Status: employed
- Credit rating: fair
What is the probability this is a prospect client? We canculate the propability of yes being a prospect given all the conditions, and no not being a prospects given the same conditions. The highest of the two gives us the answer. To calculate both of these probabilities, we should be dividing by the multiplication of the feature marginals. We have not calculated this, but we really don’t need to since both are devided by the same multiplication.

P(prospect=yes|age-group=youth,networth=hgh,status=employed,credit=fair)

This is a posterior probability

(PposteriorYes <- (PyouthGivenYes * PhighGivenYes * PemployedGivenYes * PfairGivenYes) * Pyes )  

##         yes 
## 0.007054674

(PposteriorNo <- (PyouthGivenNo * PhighGivenNo * PemployedGivenNo * PfairGivenNo) * Pno )  

##         no 
## 0.02742857

This costumer does not seem to be a good prospect according to our classifier.

The resusts are not probabilities. To calculate actual probabilities we need to devide both by the marginal probability of each feature. We first calculate these marginal.

(priorCount<-table(data$age.group))

## 
## middle senior  youth 
##      4      5      5

numberOfMiddle<-priorCount[1]
numberOfSenior<-priorCount[2]
numberOfYouth<-priorCount[3]

(Pyouth<-numberOfYouth/numberOfSamples)

##     youth 
## 0.3571429

(Pmiddle<-numberOfMiddle/numberOfSamples)

##    middle 
## 0.2857143

(Psenior<-numberOfSenior/numberOfSamples)

##    senior 
## 0.3571429

Pyouth+Pmiddle+Psenior

## youth 
##     1

(priorCount<-table(data$networth))

## 
##   high    low medium 
##      4      4      6

numberOfHigh<-priorCount[1]
numberOfLow<-priorCount[2]
numberOfMedium<-priorCount[3]

(Plow<-numberOfLow/numberOfSamples)

##       low 
## 0.2857143

(Pmedium<-numberOfMedium/numberOfSamples)

##    medium 
## 0.4285714

(Phigh<-numberOfHigh/numberOfSamples)

##      high 
## 0.2857143

Phigh+Plow+Pmedium

## high 
##    1

(priorCount<-table(data$status))

## 
##   employed unemployed 
##          7          7

numberOfEmployed<-priorCount[1]
numberOfUnemployed<-priorCount[2]

(Pemployed<-numberOfEmployed/numberOfSamples)

## employed 
##      0.5

(Punemployed<-numberOfUnemployed/numberOfSamples)

## unemployed 
##        0.5

Pemployed+Punemployed

## employed 
##        1

(priorCount<-table(data$credit_rating))

## 
## excellent      fair 
##         6         8

numberOfExcellent<-priorCount[1]
numberOfFair<-priorCount[2]

(Pfair<-numberOfFair/numberOfSamples)

##      fair 
## 0.5714286

(Pexcellent<-numberOfExcellent/numberOfSamples)

## excellent 
## 0.4285714

Pfair+Pexcellent

## fair 
##    1

Going back to our case:
- Age group: youth
- Net worth: high
- Status: employed
- Credit rating: fair

PposteriorYes<- (PyouthGivenYes * PhighGivenYes * PemployedGivenYes * PfairGivenYes) * Pyes 
(PposteriorYes<-PposteriorYes / (Pyouth * Phigh * Pemployed * Pfair))

##       yes 
## 0.2419753

PposteriorNo<- (PyouthGivenNo * PhighGivenNo * PemployedGivenNo * PfairGivenNo) * Pno 
(PposteriorNo<-PposteriorNo / (Pyouth * Phigh * Pemployed * Pfair))

##     no 
## 0.9408

We can try another case:

• Age group: youth
  
• Net worth: high
  
• Status: unemployed
  
• Credit rating: excellent

PposteriorYes<- (PyouthGivenYes * PhighGivenYes * PunemployedGivenYes * PexcellentGivenYes) * Pyes 
(PposteriorYes<-PposteriorYes / (Pyouth * Phigh * Punemployed * Pexcellent))

##       yes 
## 0.3226337

PposteriorNo<- (PyouthGivenNo * PhighGivenNo * PunemployedGivenNo * PexcellentGivenNo) * Pno 
(PposteriorNo<-PposteriorNo / (Pyouth * Phigh * Punemployed * Pexcellent))

##     no 
## 0.4704

We can also use the naivebayses library to calculate the classification.

test<-data[1,!(names(data) %in% c('class.prospect'))]
test[1,1]<-'youth'
test[1,2]<-'high'
test[1,3]<-'employed'
test[1,4]<-'excellent'
test

##   age.group networth   status credit_rating
## 1     youth     high employed     excellent

model<-naive_bayes(class.prospect~.,data=data,laplace = 0)

## Warning: naive_bayes(): Feature age.group - zero probabilities are present.
## Consider Laplace smoothing.

predict(model,test,type = 'prob')

##            no        yes
## [1,] 0.921036 0.07896399

As we can see we obtain silar classification results.

We can try third and final case:

• Age group: senior
  
• Net worth: low
  
• Status: unemployed
  
• Credit rating: excellent

PposteriorYes<- (PseniorGivenYes * PlowGivenYes * PunemployedGivenYes * PexcellentGivenYes) * Pyes 
(PposteriorYes<-PposteriorYes / (Psenior * Plow * Punemployed * Pexcellent))

##       yes 
## 0.7259259

PposteriorNo<- (PseniorGivenNo * PlowGivenNo * PunemployedGivenNo * PexcellentGivenNo) * Pno 
(PposteriorNo<-PposteriorNo / (Psenior * Plow * Punemployed * Pexcellent))

##     no 
## 0.1568

We can also use the naivebayses library to calculate the classification.

test<-data[1,!(names(data) %in% c('class.prospect'))]
test[1,1]<-'senior'
test[1,2]<-'low'
test[1,3]<-'unemployed'
test[1,4]<-'excellent'
test

##   age.group networth     status credit_rating
## 1    senior      low unemployed     excellent

model<-naive_bayes(class.prospect~.,data=data,laplace = 0)

## Warning: naive_bayes(): Feature age.group - zero probabilities are present.
## Consider Laplace smoothing.

predict(model,test,type = 'prob')

##             no       yes
## [1,] 0.1776316 0.8223684

Again we get a similar classification with the manual process and the library.

Question 2

You just recently joined a datascience team.

There are two datasets junk1.txt and junk2.csv They have two options 1. They can go back to the client and ask for more data to remedy problems with the data. 2. They can accept the data and undertake a major analytics exercise.

The team is relying on your dsc skills to determine how they should proceed.

Can you explore the data and recommend actions for each file enumerating the reasons.

Data load

junk1 <- read.csv("junk1.txt", sep = ' ',  header = TRUE)
junk1 %>% kable() %>% kable_styling() %>% scroll_box(width = "800px", height = "400px")

a	b	class
1.6204214	3.0036241	1
1.4340220	0.7852487	1
2.4766615	0.9367761	1
0.5283093	0.1196222	1
1.0054081	0.7872866	1
1.1032636	0.7330594	1
1.1789710	3.1022974	1
2.1099008	2.6152836	1
1.1460600	1.1797560	1
1.8310132	2.8142432	1
1.4047787	-0.0996363	1
0.1199486	0.5057891	1
0.6765030	1.3647484	1
1.1181504	-1.5489430	1
1.5704227	1.0558466	1
-0.8697279	3.0944632	1
0.4828084	1.1411314	1
0.4858466	-0.7100753	1
1.2997491	0.9445179	1
-0.3767567	-0.7262630	1
2.2148328	1.0954370	1
0.5599372	0.8047502	1
0.6725790	-1.2861484	1
1.3958583	0.7617706	1
1.8575015	0.4979771	1
-0.7657255	-1.0628475	1
-2.2985403	-1.5229682	1
-1.2245988	0.0039812	1
-0.4224027	-2.2020321	1
-0.3986345	-1.4344173	1
-0.1541545	1.2075572	1
-2.2278869	0.0441864	1
-1.3294799	-0.2382930	1
0.6964771	-0.5327920	1
-1.4964152	0.2131591	1
-1.4176253	-3.0500140	1
-1.6936362	-2.0528397	1
-0.9910132	0.8037407	1
0.0074113	-2.2418797	1
0.0244566	-1.2752123	1
-1.3692513	-0.2129825	1
-2.0327734	-0.6313832	1
-0.4648920	-1.8299871	1
-0.1866641	-1.8733288	1
-0.1235247	-1.4478383	1
1.0870333	-0.3643405	1
-1.1430852	-1.1070141	1
-0.6252176	0.0521050	1
-0.7535247	0.3371487	1
-1.5570333	-0.1268570	1
-0.9446757	1.6630737	2
-2.1754510	2.7743599	2
-1.5808068	1.0526114	2
-1.2987153	-0.4161319	2
-0.8420963	2.2892391	2
-1.8135451	-0.6236857	2
-1.0054094	2.3836180	2
-0.5810079	0.5414749	2
-1.1346434	1.2679017	2
-0.6731265	0.1716737	2
-1.2500186	2.1546548	2
-2.2548399	1.6154887	2
-2.1216527	1.3045452	2
0.8089390	-0.2678904	2
-0.8436088	1.6674678	2
0.1264992	0.7935832	2
-0.6910051	0.3472630	2
-0.3557378	1.5140557	2
0.2099927	1.4443751	2
-0.7024238	1.4116462	2
-1.2794889	1.3118886	2
-0.5944345	0.4311028	2
-0.6088464	0.4578163	2
-0.4477992	0.4690932	2
-1.8236985	2.4728836	2
0.4034355	-2.4056383	2
0.9881920	-0.9081219	2
0.5679804	-3.1717369	2
0.9243354	-1.0664954	2
-0.2793336	-0.2123748	2
0.4229422	-1.0445746	2
0.4747675	-0.8544943	2
1.8137459	-1.4255818	2
1.3863266	-1.0547404	2
-0.8093364	-0.9158605	2
0.8217856	-0.0494760	2
-0.5381374	-1.0172655	2
1.5008916	-1.4382739	2
1.5727083	-2.0152071	2
2.9208389	-2.7731913	2
0.0527032	-0.6144914	2
1.1566916	-2.1728755	2
1.3866433	-0.1587467	2
0.9578530	-0.5550774	2
-0.1024852	-1.7465024	2
0.0702465	-0.4001083	2
3.0060368	-0.5292340	2
1.8822550	-1.3784355	2
-0.1048475	-0.4203739	2
1.9732535	-1.0063869	2

junk2 <- read.csv("junk2.csv", header = TRUE)
junk2 %>% kable() %>% kable_styling() %>% scroll_box(width = "800px", height = "400px")

a	b	class
3.1886481	0.9291774	0
0.8224527	0.0476031	0
0.8147247	0.0291093	0
-1.5065362	3.1323136	0
0.4426887	2.8494282	0
0.8564405	-0.6614385	0
2.0915017	1.9789250	0
0.3770563	1.3877767	0
0.0925396	1.6587941	0
-0.5937133	-0.0310689	0
1.3026445	-0.0784188	0
2.6343924	-0.2736602	0
0.3781534	1.3426658	0
1.4671611	0.9332228	0
2.4192658	1.1945902	0
1.1102652	0.6267688	0
2.8696292	0.3677869	0
-0.0302508	-0.5252946	0
-0.3416344	2.0121204	0
1.5543983	-0.1927756	0
0.9379292	0.9722719	0
1.0966016	3.3511605	0
2.5629506	2.5909881	0
1.8282320	1.1441314	0
1.5400644	2.0620302	0
0.4050557	1.7974087	0
-0.9008409	0.2979948	0
1.1935082	1.1890270	0
0.4181997	0.8862482	0
-0.5452108	-0.2668863	0
1.4788123	0.8316610	0
1.2293416	2.1604669	0
0.8620735	1.4517620	0
3.4107390	-0.4896563	0
-0.9227946	2.7936837	0
2.6629424	-0.0364324	0
3.1213590	-1.1127498	0
0.8116194	3.5499987	0
-1.1221131	1.1649957	0
1.2765970	1.7798761	0
0.3744676	2.0995758	0
1.5460990	2.7453149	0
1.1556990	1.7621170	0
0.2961337	1.0582543	0
0.9621085	2.4698332	0
1.7051636	1.8349871	0
-0.7241028	2.5790697	0
1.2213792	0.8619945	0
1.4755514	1.5364704	0
4.3854715	1.1720348	0
-0.0103123	1.3106665	0
-0.8047218	0.5465758	0
-0.6203790	1.0205504	0
1.9111819	0.5923949	0
1.2612364	1.6178809	0
1.5805944	1.1513547	0
-0.0413213	2.1794796	0
2.1600628	3.2044725	0
3.1473536	0.7377654	0
0.3535885	1.4766146	0
0.0690691	0.3740302	0
1.7853491	1.3880545	0
0.5339464	-0.1790515	0
0.6718992	0.5800105	0
1.9153283	-0.2405698	0
2.6893674	1.1685852	0
2.6730891	3.0314342	0
1.7994683	1.9068147	0
2.3667197	0.8558302	0
0.1359159	0.1169239	0
-0.4327418	1.9929729	0
0.5587084	1.3446275	0
0.4199242	0.1963534	0
-0.9714248	0.7849007	0
2.5645640	-0.4931215	0
0.1908021	0.8434980	0
1.6966843	2.3159396	0
-0.1721230	0.9175183	0
0.4262759	0.4164779	0
1.1649945	1.0950994	0
1.2520046	0.8061823	0
1.1446041	0.9956207	0
0.9771395	0.8544062	0
0.4293051	1.5797532	0
0.4521032	-1.3241064	0
1.7384460	2.3302336	0
0.1258763	0.4248651	0
1.9523669	0.1402230	0
-0.0444428	0.8406334	0
-0.1434549	-0.5812785	0
1.2877842	-0.6123256	0
0.1219014	2.1705694	0
-0.0660868	-0.0586697	0
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1.2181100	-0.7277401	1
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0.7750401	-1.6909097	1
0.6346517	-1.1207373	1
1.6743924	-1.0967452	1
0.8170661	-1.1519663	1
1.1704709	-0.7894293	1
1.1229183	-1.6151524	1
1.1740853	-0.7793917	1
1.6860644	-1.2725559	1
1.1286603	0.1325642	1
0.7401007	-1.2639153	1
0.4384881	-1.3332027	1
1.7864283	-1.1245578	1
1.1275054	-1.5930429	1
1.1358207	-1.2963480	1
1.9362524	-0.4187385	1
0.2002097	-0.9297540	1
1.1005666	-1.4425982	1
1.1756285	-1.0213184	1
1.1094213	-0.7260741	1
1.5639458	-1.7684502	1
0.8729218	-0.4125119	1
0.9309803	-0.4474825	1
1.7281289	-1.5531501	1
0.5750994	-0.1882485	1
0.8947459	-0.9389095	1
1.4009133	-1.3375860	1
0.1857906	-1.0797908	1
1.6766901	-1.0123859	1
1.3641385	-1.7221252	1
2.2836270	-0.4534597	1
1.2488651	-0.8688289	1
1.6344316	-0.8502213	1
1.9557950	-1.2213124	1
0.7758352	-1.0620913	1
1.5468068	-0.9049870	1
1.0151144	-0.8139607	1
0.6353856	-1.2692271	1
0.8469604	-0.6703314	1
0.6079482	-0.6409569	1

Missing data

We look for any missing data and notice there isn’t any.

sapply(junk1, function(x) round(sum(is.na(x))/nrow(junk1)*100,1))

##     a     b class 
##     0     0     0

sapply(junk2, function(x) round(sum(is.na(x))/nrow(junk2)*100,1))

##     a     b class 
##     0     0     0

Descriptive statistics

We look at a summary of the data undestand some of the descriptive statistics of the dataset.

summary(junk1)

##        a                  b                class    
##  Min.   :-2.29854   Min.   :-3.17174   Min.   :1.0  
##  1st Qu.:-0.85014   1st Qu.:-1.04712   1st Qu.:1.0  
##  Median :-0.04754   Median :-0.07456   Median :1.5  
##  Mean   : 0.04758   Mean   : 0.01324   Mean   :1.5  
##  3rd Qu.: 1.09109   3rd Qu.: 1.05342   3rd Qu.:2.0  
##  Max.   : 3.00604   Max.   : 3.10230   Max.   :2.0

Data seems to be properly distributed, with no indication of outliers. We can plot a histogram to have a more graphical view.

hist(junk1$a)

hist(junk1$b)

Bor variables look well distributed around their means, showing good normality. This is a good feayure for parametric modeling where an underlaying data distribution is assumed.

summary(junk2)

##        a                  b                class       
##  Min.   :-4.16505   Min.   :-3.90472   Min.   :0.0000  
##  1st Qu.:-1.01447   1st Qu.:-0.89754   1st Qu.:0.0000  
##  Median : 0.08754   Median :-0.08358   Median :0.0000  
##  Mean   :-0.05126   Mean   : 0.05624   Mean   :0.0625  
##  3rd Qu.: 0.89842   3rd Qu.: 1.00354   3rd Qu.:0.0000  
##  Max.   : 4.62647   Max.   : 4.31052   Max.   :1.0000

hist(junk2$a)

hist(junk2$b)

Same as with the first dataset, data looks well distributed. The distributions here looks a like more skewed, but it isn’t extreme. If it is necessary to use a parametric modeling, a different distribution from normal could be considered to better handle the skew. But no major issues are expected in modeling.

Balance

We look at the class vaeibale to see if the dataset are balanced.

dim(junk1)

## [1] 100   3

table(junk1$class)

## 
##  1  2 
## 50 50

Junk1 is very well balanced with half of the 100 entries in each class. Junk2 on the other hand shows an imbalance.

dim(junk2)

## [1] 4000    3

table(junk2$class)

## 
##    0    1 
## 3750  250

table(junk2$class)[1]/nrow(junk2)

##      0 
## 0.9375

table(junk2$class)[2]/nrow(junk2)

##      1 
## 0.0625

Only ~6 percent of the data is assigned to class 1. This imbalance will make it hard to use the data with many of the classification algorithm. A recommendation would be to bootstrap the data to increase the number of class 1 entries. Although imbalance will still be present, the class will be better represented. To ameliorate imbalance, techniques such as SMOTE should also be considered.

Scattered plots

Scattered plot will help us understand the relationship between the variables and their own nature. We start by plotting variables on their own.

ggplot(junk1,aes(y=a,x=seq_along(a),color=as.factor(class))) + geom_point()

Here we see how the data is modal against the index, and we see a segregation against the class. These could be due to the nature of how the data was gathered, seems the 50 first samples were collected for one class, then the other 50.

ggplot(junk1,aes(y=b,x=seq_along(b),color=as.factor(class))) + geom_point()

The second variable shows very similar characteristics. Here the sampling seems to come from a sinusoidal wave over the index.

Finbaly we plot both together.

ggplot(junk1,aes(x=a,y=b,color=as.factor(class))) + geom_point()

Plotting both variables together it is not apparent how the split them in two classes, but the data stills shows valuable for analysis.

We do the same for the second file.

ggplot(junk2,aes(y=a,x=seq_along(a),color=as.factor(class))) + geom_point()

ggplot(junk2,aes(y=b,x=seq_along(b),color=as.factor(class))) + geom_point()

Similar results as with the first file, although not as modal.

ggplot(junk2,aes(x=a,y=b,color=as.factor(class))) + geom_point()

Plotting both variables looks a bit more interesting this time. We can see good separation between classes. We can almost suggest using a classifier such as an SVM to “circle in” one of the classes.

Conclusion

After looking at the data, there is not indication of requiring more data gathering or discarding any of the provided data. Recommendation is to continue with the analysis with the data on hand. No issues with the same as expected, other than some extra steps to balance one of the datasets.

Question 3

Load supplied data and prepare dataset, runa and edit supplied code (kNN.R) for this dataset and run same with different values of K. Plot accuracy for these different values. Provide summary of results.

Dataset preparation

The kNN.R R script requires a dataset, labelcol and K (number of nearest neighbors to be considered). The dataset MUST Be numeric, except the labelcol. The labelcol must be the last column in the data.frame. All the other columns must be before the labelcol.

Please find icu.csv

data <- read.csv("icu.csv", header = TRUE)
data %>% kable() %>% kable_styling() %>% scroll_box(width = "800px", height = "400px")

ID	STA	AGE	SEX	RACE	SER	CAN	CRN	INF	CPR	SYS	HRA	PRE	TYP	FRA	PO2	PH	PCO	BIC	CRE	LOC
8	0	27	1	1	0	0	0	1	0	142	88	0	1	0	0	0	0	0	0	0
12	0	59	0	1	0	0	0	0	0	112	80	1	1	0	0	0	0	0	0	0
14	0	77	0	1	1	0	0	0	0	100	70	0	0	0	0	0	0	0	0	0
28	0	54	0	1	0	0	0	1	0	142	103	0	1	1	0	0	0	0	0	0
32	0	87	1	1	1	0	0	1	0	110	154	1	1	0	0	0	0	0	0	0
38	0	69	0	1	0	0	0	1	0	110	132	0	1	0	1	0	0	1	0	0
40	0	63	0	1	1	0	0	0	0	104	66	0	0	0	0	0	0	0	0	0
41	0	30	1	1	0	0	0	0	0	144	110	0	1	0	0	0	0	0	0	0
42	0	35	0	2	0	0	0	0	0	108	60	0	1	0	0	0	0	0	0	0
50	0	70	1	1	1	1	0	0	0	138	103	0	0	0	0	0	0	0	0	0
51	0	55	1	1	1	0	0	1	0	188	86	1	0	0	0	0	0	0	0	0
53	0	48	0	2	1	1	0	0	0	162	100	0	0	0	0	0	0	0	0	0
58	0	66	1	1	1	0	0	0	0	160	80	1	0	0	0	0	0	0	0	0
61	0	61	1	1	0	0	1	0	0	174	99	0	1	0	0	1	0	1	1	0
73	0	66	0	1	0	0	0	0	0	206	90	0	1	0	0	0	0	0	1	0
75	0	52	0	1	1	0	0	1	0	150	71	1	0	0	0	0	0	0	0	0
82	0	55	0	1	1	0	0	1	0	140	116	0	0	0	0	0	0	0	0	0
84	0	59	0	1	0	0	0	1	0	48	39	0	1	0	1	0	1	1	0	2
92	0	63	0	1	0	0	0	0	0	132	128	1	1	0	0	0	0	0	0	0
96	0	72	0	1	1	0	0	0	0	120	80	1	0	0	0	0	0	0	0	0
98	0	60	0	1	0	0	0	1	1	114	110	0	1	0	0	0	0	0	0	0
100	0	78	0	1	1	0	0	0	0	180	75	0	0	0	0	0	0	0	0	0
102	0	16	1	1	0	0	0	0	0	104	111	0	1	0	0	0	0	0	0	0
111	0	62	0	1	1	0	1	0	0	200	120	0	0	0	0	0	0	0	0	0
112	0	61	0	1	0	0	0	1	0	110	120	0	1	0	0	0	0	0	0	0
136	0	35	0	1	0	0	0	0	0	150	98	0	1	0	0	0	0	0	0	0
137	0	74	1	1	1	0	0	0	0	170	92	0	0	0	0	0	1	0	0	0
143	0	68	0	1	1	0	0	0	0	158	96	0	0	0	0	0	0	0	0	0
153	0	69	1	1	1	0	0	0	0	132	60	0	1	0	0	0	0	0	0	0
170	0	51	0	1	0	0	0	0	0	110	99	0	1	0	0	0	0	0	0	0
173	0	55	0	1	1	0	0	0	0	128	92	0	0	0	0	0	0	0	0	0
180	0	64	1	3	1	0	0	1	0	158	90	1	1	0	0	0	0	0	0	0
184	0	88	1	1	1	0	0	1	0	140	88	1	1	0	0	0	0	0	0	0
186	0	23	1	1	1	0	0	0	0	112	64	0	1	1	0	0	0	0	0	0
187	0	73	1	1	1	1	0	0	0	134	60	0	0	0	0	0	1	0	0	0
190	0	53	0	3	1	0	0	0	0	110	70	1	0	0	0	0	0	0	0	0
191	0	74	0	1	1	0	0	0	0	174	86	0	0	0	0	0	0	0	0	0
207	0	68	0	1	1	0	0	0	0	142	89	0	0	0	0	0	0	0	0	0
211	0	66	1	1	0	0	0	1	0	170	95	1	1	0	0	0	0	0	0	0
214	0	60	0	1	1	1	0	1	0	110	92	0	0	0	0	0	0	0	0	0
219	0	64	0	1	1	0	0	1	0	160	120	0	0	0	0	0	0	0	0	0
225	0	66	0	2	1	1	0	1	0	150	120	0	0	0	0	0	1	0	0	0
237	0	19	1	1	1	0	0	1	0	142	106	0	1	1	0	0	0	0	0	0
247	0	18	1	1	0	0	0	0	0	146	112	0	1	0	0	0	0	0	0	0
249	0	63	0	1	1	0	0	1	0	162	84	1	1	0	0	0	0	0	0	0
260	0	45	0	1	0	0	0	0	0	126	110	0	1	0	0	0	0	0	0	0
266	0	64	0	1	0	0	0	0	0	162	114	0	1	0	0	0	0	0	0	0
271	0	68	1	1	0	0	0	1	0	200	170	1	1	0	0	0	0	0	0	0
276	0	64	1	1	0	0	0	1	0	126	122	0	1	0	1	0	1	0	0	0
277	0	82	0	1	1	0	0	0	0	135	70	0	0	0	0	0	0	0	0	0
278	0	73	0	1	1	0	0	0	0	170	88	0	0	0	0	0	0	0	0	0
282	0	70	0	1	0	0	0	0	0	86	153	1	1	0	0	0	1	0	0	0
292	0	61	0	1	1	0	0	1	0	68	124	0	1	0	0	0	0	0	0	0
295	0	64	0	1	1	1	0	1	0	116	88	0	0	0	0	0	0	0	0	0
297	0	47	0	1	1	1	0	1	0	120	83	0	0	0	0	0	0	0	0	0
298	0	69	0	1	1	0	0	0	0	170	100	0	0	0	0	0	0	0	0	0
308	0	67	1	1	0	0	0	1	0	190	125	0	1	0	0	0	0	0	0	0
310	0	18	0	1	1	1	0	0	0	156	99	0	0	0	0	0	0	0	0	0
319	0	77	0	1	1	0	0	1	0	158	107	0	0	0	0	0	0	0	0	0
327	0	32	0	2	1	0	0	0	0	120	84	0	1	0	0	0	0	0	0	0
333	0	19	1	1	1	0	0	1	0	104	121	1	0	0	0	0	0	0	0	0
335	0	72	1	1	1	0	0	0	0	130	86	0	1	0	0	0	0	0	0	0
343	0	49	0	1	0	0	0	1	0	112	112	0	1	0	0	0	0	0	0	0
357	0	68	1	1	1	0	0	0	0	154	74	0	0	0	0	0	0	0	0	0
362	0	82	0	1	1	0	1	1	0	130	131	0	1	0	0	0	0	0	0	0
365	0	32	1	3	0	0	0	1	1	110	118	0	1	0	0	0	0	0	0	0
369	0	78	1	1	1	0	0	1	0	126	96	0	1	0	0	0	0	0	0	0
370	0	57	0	1	0	0	0	1	0	128	104	0	1	0	0	0	1	0	0	0
371	0	46	1	1	1	1	0	0	0	132	90	0	1	0	0	0	0	0	0	0
376	0	23	0	1	0	0	0	1	0	144	88	0	1	0	0	0	0	0	0	0
378	0	55	0	1	0	0	0	0	0	132	112	0	1	0	0	0	0	0	0	0
379	0	18	0	1	1	0	0	0	0	112	76	0	1	1	0	0	0	0	0	0
381	0	20	0	1	1	0	0	0	0	164	108	0	1	0	0	0	0	0	0	0
382	0	75	1	1	1	0	0	0	0	100	48	0	0	0	0	0	0	0	0	0
398	0	79	0	1	1	0	0	1	0	112	67	0	0	0	0	0	0	0	0	0
401	0	40	0	1	1	0	0	0	0	140	65	0	1	1	0	0	0	0	0	0
409	0	76	0	1	1	0	0	1	0	110	70	0	1	0	0	0	0	0	0	0
413	0	66	1	1	1	0	0	1	0	139	92	0	0	0	0	0	0	0	0	0
416	0	76	0	1	0	0	0	1	0	190	100	0	1	0	0	0	0	0	0	0
438	0	80	1	1	1	0	0	0	0	162	44	0	1	0	0	0	0	0	0	0
439	0	23	1	1	0	0	0	1	0	120	88	0	1	0	0	0	0	0	0	0
440	0	48	0	2	1	0	0	1	0	92	162	1	1	0	0	0	0	0	0	0
455	0	67	0	2	1	0	0	0	0	90	92	1	0	0	0	0	0	0	0	0
462	0	69	1	1	1	0	0	0	0	150	85	0	1	0	0	0	0	0	0	0
495	0	65	0	3	1	0	0	0	0	208	124	0	0	0	0	0	0	0	0	0
498	0	72	0	1	1	0	0	0	0	126	88	0	0	0	0	0	0	0	0	0
502	0	55	0	1	0	0	0	0	0	190	136	0	1	0	1	1	1	0	0	0
505	0	40	0	1	0	0	0	0	0	130	65	0	1	0	0	0	0	0	0	0
508	0	55	1	1	0	0	0	1	0	110	86	0	1	0	0	0	0	0	0	0
517	0	34	0	1	1	0	0	0	0	110	80	0	1	1	0	0	0	0	0	0
522	0	47	1	1	1	0	0	0	0	132	68	0	1	0	0	0	0	0	0	0
525	0	41	1	1	0	0	0	1	0	118	145	0	1	0	0	1	0	1	0	0
526	0	84	1	1	0	0	1	1	0	100	103	0	1	0	0	0	0	1	1	0
546	0	88	1	1	1	0	0	0	0	110	46	1	0	0	0	0	0	0	0	0
548	0	77	1	1	1	1	0	0	0	212	87	0	0	0	0	0	1	0	0	0
550	0	80	0	1	0	0	0	0	0	122	126	0	1	0	1	0	0	1	0	0
552	0	16	0	1	1	0	0	0	0	100	140	0	1	1	0	0	0	0	0	0
560	0	70	0	1	1	0	0	0	0	160	60	0	0	0	0	0	0	0	0	0
563	0	83	1	1	1	0	0	1	0	138	91	0	1	0	0	0	0	0	0	0
573	0	23	0	2	0	0	0	0	0	130	52	0	1	0	0	0	0	0	0	0
575	0	67	1	1	0	0	0	0	1	120	120	0	1	0	0	1	1	0	0	0
584	0	18	0	1	1	1	0	0	0	130	140	0	0	0	0	0	0	0	0	0
597	0	77	1	1	0	0	0	1	0	136	138	0	0	0	1	1	1	0	0	0
598	0	48	1	1	0	0	0	0	1	128	96	0	1	0	0	0	0	0	0	0
601	0	24	1	2	0	0	0	0	0	140	86	0	1	0	0	0	0	0	0	0
605	0	71	1	1	0	0	0	1	0	124	106	0	1	0	0	0	0	0	0	0
607	0	72	0	1	1	0	0	0	0	134	60	0	1	0	0	0	0	0	0	0
619	0	77	1	1	1	0	1	0	0	170	115	1	0	0	0	0	0	0	0	0
620	0	60	0	1	1	0	0	1	0	124	135	0	1	0	0	0	0	0	0	0
639	0	46	0	1	1	1	0	0	0	110	128	0	0	0	0	0	0	0	0	0
644	0	65	1	1	0	0	0	0	0	100	105	0	1	0	0	0	0	0	0	0
645	0	36	0	1	0	0	0	0	0	224	125	0	1	0	0	0	0	0	0	0
648	0	68	0	1	1	0	0	0	0	112	64	0	0	0	0	0	0	0	0	0
655	0	58	0	1	0	0	0	0	0	154	98	0	1	0	0	0	0	0	0	0
659	0	76	1	1	0	0	0	1	0	92	112	0	1	0	0	0	0	0	0	0
669	0	41	1	2	0	0	0	0	0	110	144	0	1	0	0	0	0	1	1	0
670	0	20	0	3	0	0	0	0	0	120	68	0	1	0	0	0	0	0	0	0
674	0	91	0	1	0	0	1	1	0	152	125	0	1	0	0	0	0	0	0	0
675	0	75	0	1	1	0	0	0	0	140	90	0	1	0	0	0	0	0	0	0
676	0	25	1	1	0	0	0	0	0	131	135	0	1	0	0	0	0	1	0	0
709	0	70	0	1	0	0	0	1	0	78	143	0	1	0	1	0	0	0	0	0
713	0	47	0	1	1	0	0	0	0	156	112	0	1	0	0	0	0	0	0	0
727	0	75	0	3	1	0	0	0	0	144	120	0	1	0	0	0	0	0	1	0
728	0	40	0	2	0	0	0	1	0	160	150	1	1	1	0	0	0	0	0	0
732	0	71	0	1	0	0	0	1	0	148	192	0	1	0	1	1	1	0	0	0
746	0	70	1	1	0	0	0	1	0	90	140	0	1	0	1	0	0	1	0	0
749	0	58	0	1	1	0	0	0	0	148	95	1	1	0	0	0	0	0	0	0
754	0	54	0	1	1	0	0	0	0	136	80	0	0	0	0	0	0	0	0	0
761	0	77	0	1	1	0	0	0	0	128	59	0	0	0	0	0	0	0	0	0
763	0	55	0	1	1	1	0	1	0	138	140	0	0	0	0	0	0	0	0	0
764	0	21	0	1	1	0	0	0	0	120	62	0	1	0	0	0	0	0	0	0
765	0	53	0	2	0	0	1	0	1	170	115	0	1	0	0	0	0	0	0	0
766	0	31	1	1	0	1	1	1	1	146	100	0	1	0	0	1	1	0	0	0
772	0	71	0	1	1	1	0	0	0	204	52	0	0	0	0	0	0	0	0	0
776	0	49	0	2	0	0	0	0	0	150	100	0	1	0	0	0	0	0	0	0
784	0	60	1	2	0	0	0	1	0	116	92	1	1	0	0	0	0	0	0	0
794	0	50	0	1	0	0	0	1	0	156	99	0	1	0	1	0	1	0	0	0
796	0	45	1	1	1	0	0	0	0	132	109	0	1	1	0	0	0	0	0	0
809	0	21	0	1	1	0	0	0	0	110	90	0	1	0	0	0	0	0	0	0
814	0	73	1	1	1	0	0	0	0	130	83	0	1	0	0	0	0	0	0	0
816	0	28	0	1	1	0	0	1	0	122	80	1	0	1	0	0	0	0	0	0
829	0	17	0	1	1	0	0	0	0	140	78	0	1	1	0	0	0	0	0	0
837	0	17	1	3	0	0	0	0	0	130	140	0	1	0	0	0	0	0	0	0
846	0	21	1	1	1	0	0	0	0	142	79	0	1	0	0	0	0	0	0	0
847	0	68	1	1	1	1	0	0	0	91	79	0	0	0	0	0	0	0	0	0
863	0	17	0	3	1	0	0	0	0	136	78	0	1	0	0	0	0	0	0	0
867	0	60	0	1	0	0	0	1	0	108	120	0	1	0	0	0	0	0	0	0
875	0	69	0	1	1	0	0	0	0	169	73	0	1	0	0	0	0	0	0	0
877	0	88	1	1	0	0	1	0	0	190	88	0	1	0	0	0	0	0	0	0
880	0	20	0	1	1	0	0	0	0	120	80	0	1	0	0	0	0	0	0	0
881	0	89	1	1	1	0	0	0	0	190	114	0	1	0	0	0	1	0	0	2
889	0	62	1	1	0	0	0	0	0	110	78	0	1	0	0	0	0	0	0	0
893	0	46	0	1	0	0	1	1	0	142	89	0	1	0	0	1	0	1	0	0
906	0	19	0	1	1	0	0	1	0	100	137	0	1	0	0	0	0	0	0	0
912	0	71	0	1	0	0	0	1	0	124	124	0	1	0	1	1	1	0	0	0
915	0	67	0	1	1	0	0	0	0	152	78	0	0	0	0	0	0	0	0	0
923	0	20	0	1	1	0	0	0	0	104	83	0	1	0	0	0	0	0	0	0
924	0	73	1	2	0	0	1	0	0	162	100	0	1	0	0	0	0	0	0	0
925	0	59	0	1	0	0	0	0	0	100	88	0	1	0	0	0	0	0	0	0
929	0	42	0	1	1	0	0	0	0	122	84	0	1	1	0	0	0	0	0	0
4	1	87	1	1	1	0	0	1	0	80	96	0	1	1	1	1	1	0	0	0
27	1	76	1	1	1	0	0	1	0	128	90	1	1	0	0	0	0	0	0	0
47	1	78	0	1	0	0	0	1	0	130	132	0	1	0	0	0	0	1	0	0
52	1	63	0	1	0	0	1	1	0	112	106	1	1	0	1	0	0	0	0	0
127	1	19	0	1	1	0	0	0	0	140	76	0	1	0	0	0	0	0	0	0
145	1	67	1	1	0	0	0	1	0	62	145	0	1	0	0	0	0	0	1	0
154	1	53	1	1	0	0	0	1	0	148	128	0	1	0	0	1	1	0	0	0
165	1	92	0	1	0	0	0	1	0	124	80	0	1	0	0	0	0	1	0	0
195	1	57	0	1	0	0	0	1	1	110	124	0	1	0	0	0	0	0	0	2
202	1	75	1	1	1	1	0	0	0	130	136	0	0	0	0	0	0	0	0	0
204	1	91	0	1	0	0	0	1	0	64	125	0	1	0	0	0	1	0	0	0
208	1	70	0	1	1	0	0	0	0	168	122	0	0	0	1	0	0	0	0	1
222	1	88	0	1	0	0	0	1	1	141	140	0	1	0	0	0	0	0	0	0
238	1	41	0	1	1	0	0	1	0	140	58	0	1	0	0	0	0	0	0	2
241	1	61	0	1	0	0	0	0	0	140	81	0	1	0	0	0	0	0	0	0
273	1	80	0	1	1	0	0	0	0	100	85	0	1	0	0	0	0	0	0	0
285	1	40	0	1	0	0	0	1	0	86	80	1	1	0	0	0	0	0	0	0
299	1	75	0	1	0	0	0	1	0	90	100	0	1	0	0	0	0	0	0	1
331	1	63	1	1	1	0	1	1	1	36	86	0	1	1	0	0	0	0	1	2
346	1	75	1	1	0	1	0	0	0	190	94	0	1	0	0	0	0	0	0	0
380	1	20	0	1	1	0	0	0	0	148	72	0	1	1	0	0	0	0	0	0
384	1	71	0	1	0	0	0	0	0	142	95	0	1	0	0	0	0	0	0	0
412	1	51	1	1	1	0	0	1	0	134	100	1	1	0	0	0	0	0	0	1
427	1	65	0	1	0	0	0	0	0	66	94	0	1	0	0	0	0	0	0	2
442	1	69	1	3	0	0	1	0	0	170	60	1	1	0	1	0	0	0	0	0
461	1	55	0	1	1	0	1	1	0	122	100	1	1	0	0	0	0	0	0	0
468	1	50	1	1	1	1	0	0	0	120	96	0	1	0	0	0	0	0	0	0
490	1	78	0	1	0	0	0	1	0	110	81	0	1	0	0	0	0	0	0	0
518	1	71	1	1	0	0	0	0	1	70	112	0	1	0	0	0	0	0	0	2
611	1	85	1	1	1	0	0	0	0	136	96	0	1	0	0	0	0	0	0	0
613	1	75	0	1	0	0	1	1	0	130	119	0	1	0	0	1	0	1	1	0
666	1	65	1	1	0	0	0	1	1	104	150	0	1	0	0	0	1	0	0	2
671	1	49	0	1	0	0	0	1	1	140	108	0	1	0	0	0	0	1	0	0
706	1	75	1	1	0	0	1	1	1	150	66	0	1	0	0	0	0	0	1	2
740	1	72	1	1	0	0	0	0	0	90	160	0	1	0	0	0	0	0	0	0
751	1	69	0	1	0	0	1	0	0	80	81	0	1	0	0	0	0	0	0	2
752	1	64	0	1	0	1	0	1	0	80	118	0	1	0	1	0	0	0	1	0
789	1	60	0	1	0	0	0	1	0	56	114	1	1	0	0	1	0	1	0	0
871	1	60	0	3	1	0	1	1	0	130	55	0	1	0	0	0	0	0	0	1
921	1	50	1	2	0	0	0	0	0	256	64	0	1	0	0	0	0	0	0	1

Please note that the dataset does not have a predictor variable called COMA. Add a variable COMA in the dataset, here is how you can derive COMA from LOC variable:

If LOC is 2 set COMA to 1 otherwise set COMA to 0

data$COMA<-ifelse(data$LOC==2,1,0)
data %>% kable() %>% kable_styling() %>% scroll_box(width = "800px", height = "400px")

ID	STA	AGE	SEX	RACE	SER	CAN	CRN	INF	CPR	SYS	HRA	PRE	TYP	FRA	PO2	PH	PCO	BIC	CRE	LOC	COMA
8	0	27	1	1	0	0	0	1	0	142	88	0	1	0	0	0	0	0	0	0	0
12	0	59	0	1	0	0	0	0	0	112	80	1	1	0	0	0	0	0	0	0	0
14	0	77	0	1	1	0	0	0	0	100	70	0	0	0	0	0	0	0	0	0	0
28	0	54	0	1	0	0	0	1	0	142	103	0	1	1	0	0	0	0	0	0	0
32	0	87	1	1	1	0	0	1	0	110	154	1	1	0	0	0	0	0	0	0	0
38	0	69	0	1	0	0	0	1	0	110	132	0	1	0	1	0	0	1	0	0	0
40	0	63	0	1	1	0	0	0	0	104	66	0	0	0	0	0	0	0	0	0	0
41	0	30	1	1	0	0	0	0	0	144	110	0	1	0	0	0	0	0	0	0	0
42	0	35	0	2	0	0	0	0	0	108	60	0	1	0	0	0	0	0	0	0	0
50	0	70	1	1	1	1	0	0	0	138	103	0	0	0	0	0	0	0	0	0	0
51	0	55	1	1	1	0	0	1	0	188	86	1	0	0	0	0	0	0	0	0	0
53	0	48	0	2	1	1	0	0	0	162	100	0	0	0	0	0	0	0	0	0	0
58	0	66	1	1	1	0	0	0	0	160	80	1	0	0	0	0	0	0	0	0	0
61	0	61	1	1	0	0	1	0	0	174	99	0	1	0	0	1	0	1	1	0	0
73	0	66	0	1	0	0	0	0	0	206	90	0	1	0	0	0	0	0	1	0	0
75	0	52	0	1	1	0	0	1	0	150	71	1	0	0	0	0	0	0	0	0	0
82	0	55	0	1	1	0	0	1	0	140	116	0	0	0	0	0	0	0	0	0	0
84	0	59	0	1	0	0	0	1	0	48	39	0	1	0	1	0	1	1	0	2	1
92	0	63	0	1	0	0	0	0	0	132	128	1	1	0	0	0	0	0	0	0	0
96	0	72	0	1	1	0	0	0	0	120	80	1	0	0	0	0	0	0	0	0	0
98	0	60	0	1	0	0	0	1	1	114	110	0	1	0	0	0	0	0	0	0	0
100	0	78	0	1	1	0	0	0	0	180	75	0	0	0	0	0	0	0	0	0	0
102	0	16	1	1	0	0	0	0	0	104	111	0	1	0	0	0	0	0	0	0	0
111	0	62	0	1	1	0	1	0	0	200	120	0	0	0	0	0	0	0	0	0	0
112	0	61	0	1	0	0	0	1	0	110	120	0	1	0	0	0	0	0	0	0	0
136	0	35	0	1	0	0	0	0	0	150	98	0	1	0	0	0	0	0	0	0	0
137	0	74	1	1	1	0	0	0	0	170	92	0	0	0	0	0	1	0	0	0	0
143	0	68	0	1	1	0	0	0	0	158	96	0	0	0	0	0	0	0	0	0	0
153	0	69	1	1	1	0	0	0	0	132	60	0	1	0	0	0	0	0	0	0	0
170	0	51	0	1	0	0	0	0	0	110	99	0	1	0	0	0	0	0	0	0	0
173	0	55	0	1	1	0	0	0	0	128	92	0	0	0	0	0	0	0	0	0	0
180	0	64	1	3	1	0	0	1	0	158	90	1	1	0	0	0	0	0	0	0	0
184	0	88	1	1	1	0	0	1	0	140	88	1	1	0	0	0	0	0	0	0	0
186	0	23	1	1	1	0	0	0	0	112	64	0	1	1	0	0	0	0	0	0	0
187	0	73	1	1	1	1	0	0	0	134	60	0	0	0	0	0	1	0	0	0	0
190	0	53	0	3	1	0	0	0	0	110	70	1	0	0	0	0	0	0	0	0	0
191	0	74	0	1	1	0	0	0	0	174	86	0	0	0	0	0	0	0	0	0	0
207	0	68	0	1	1	0	0	0	0	142	89	0	0	0	0	0	0	0	0	0	0
211	0	66	1	1	0	0	0	1	0	170	95	1	1	0	0	0	0	0	0	0	0
214	0	60	0	1	1	1	0	1	0	110	92	0	0	0	0	0	0	0	0	0	0
219	0	64	0	1	1	0	0	1	0	160	120	0	0	0	0	0	0	0	0	0	0
225	0	66	0	2	1	1	0	1	0	150	120	0	0	0	0	0	1	0	0	0	0
237	0	19	1	1	1	0	0	1	0	142	106	0	1	1	0	0	0	0	0	0	0
247	0	18	1	1	0	0	0	0	0	146	112	0	1	0	0	0	0	0	0	0	0
249	0	63	0	1	1	0	0	1	0	162	84	1	1	0	0	0	0	0	0	0	0
260	0	45	0	1	0	0	0	0	0	126	110	0	1	0	0	0	0	0	0	0	0
266	0	64	0	1	0	0	0	0	0	162	114	0	1	0	0	0	0	0	0	0	0
271	0	68	1	1	0	0	0	1	0	200	170	1	1	0	0	0	0	0	0	0	0
276	0	64	1	1	0	0	0	1	0	126	122	0	1	0	1	0	1	0	0	0	0
277	0	82	0	1	1	0	0	0	0	135	70	0	0	0	0	0	0	0	0	0	0
278	0	73	0	1	1	0	0	0	0	170	88	0	0	0	0	0	0	0	0	0	0
282	0	70	0	1	0	0	0	0	0	86	153	1	1	0	0	0	1	0	0	0	0
292	0	61	0	1	1	0	0	1	0	68	124	0	1	0	0	0	0	0	0	0	0
295	0	64	0	1	1	1	0	1	0	116	88	0	0	0	0	0	0	0	0	0	0
297	0	47	0	1	1	1	0	1	0	120	83	0	0	0	0	0	0	0	0	0	0
298	0	69	0	1	1	0	0	0	0	170	100	0	0	0	0	0	0	0	0	0	0
308	0	67	1	1	0	0	0	1	0	190	125	0	1	0	0	0	0	0	0	0	0
310	0	18	0	1	1	1	0	0	0	156	99	0	0	0	0	0	0	0	0	0	0
319	0	77	0	1	1	0	0	1	0	158	107	0	0	0	0	0	0	0	0	0	0
327	0	32	0	2	1	0	0	0	0	120	84	0	1	0	0	0	0	0	0	0	0
333	0	19	1	1	1	0	0	1	0	104	121	1	0	0	0	0	0	0	0	0	0
335	0	72	1	1	1	0	0	0	0	130	86	0	1	0	0	0	0	0	0	0	0
343	0	49	0	1	0	0	0	1	0	112	112	0	1	0	0	0	0	0	0	0	0
357	0	68	1	1	1	0	0	0	0	154	74	0	0	0	0	0	0	0	0	0	0
362	0	82	0	1	1	0	1	1	0	130	131	0	1	0	0	0	0	0	0	0	0
365	0	32	1	3	0	0	0	1	1	110	118	0	1	0	0	0	0	0	0	0	0
369	0	78	1	1	1	0	0	1	0	126	96	0	1	0	0	0	0	0	0	0	0
370	0	57	0	1	0	0	0	1	0	128	104	0	1	0	0	0	1	0	0	0	0
371	0	46	1	1	1	1	0	0	0	132	90	0	1	0	0	0	0	0	0	0	0
376	0	23	0	1	0	0	0	1	0	144	88	0	1	0	0	0	0	0	0	0	0
378	0	55	0	1	0	0	0	0	0	132	112	0	1	0	0	0	0	0	0	0	0
379	0	18	0	1	1	0	0	0	0	112	76	0	1	1	0	0	0	0	0	0	0
381	0	20	0	1	1	0	0	0	0	164	108	0	1	0	0	0	0	0	0	0	0
382	0	75	1	1	1	0	0	0	0	100	48	0	0	0	0	0	0	0	0	0	0
398	0	79	0	1	1	0	0	1	0	112	67	0	0	0	0	0	0	0	0	0	0
401	0	40	0	1	1	0	0	0	0	140	65	0	1	1	0	0	0	0	0	0	0
409	0	76	0	1	1	0	0	1	0	110	70	0	1	0	0	0	0	0	0	0	0
413	0	66	1	1	1	0	0	1	0	139	92	0	0	0	0	0	0	0	0	0	0
416	0	76	0	1	0	0	0	1	0	190	100	0	1	0	0	0	0	0	0	0	0
438	0	80	1	1	1	0	0	0	0	162	44	0	1	0	0	0	0	0	0	0	0
439	0	23	1	1	0	0	0	1	0	120	88	0	1	0	0	0	0	0	0	0	0
440	0	48	0	2	1	0	0	1	0	92	162	1	1	0	0	0	0	0	0	0	0
455	0	67	0	2	1	0	0	0	0	90	92	1	0	0	0	0	0	0	0	0	0
462	0	69	1	1	1	0	0	0	0	150	85	0	1	0	0	0	0	0	0	0	0
495	0	65	0	3	1	0	0	0	0	208	124	0	0	0	0	0	0	0	0	0	0
498	0	72	0	1	1	0	0	0	0	126	88	0	0	0	0	0	0	0	0	0	0
502	0	55	0	1	0	0	0	0	0	190	136	0	1	0	1	1	1	0	0	0	0
505	0	40	0	1	0	0	0	0	0	130	65	0	1	0	0	0	0	0	0	0	0
508	0	55	1	1	0	0	0	1	0	110	86	0	1	0	0	0	0	0	0	0	0
517	0	34	0	1	1	0	0	0	0	110	80	0	1	1	0	0	0	0	0	0	0
522	0	47	1	1	1	0	0	0	0	132	68	0	1	0	0	0	0	0	0	0	0
525	0	41	1	1	0	0	0	1	0	118	145	0	1	0	0	1	0	1	0	0	0
526	0	84	1	1	0	0	1	1	0	100	103	0	1	0	0	0	0	1	1	0	0
546	0	88	1	1	1	0	0	0	0	110	46	1	0	0	0	0	0	0	0	0	0
548	0	77	1	1	1	1	0	0	0	212	87	0	0	0	0	0	1	0	0	0	0
550	0	80	0	1	0	0	0	0	0	122	126	0	1	0	1	0	0	1	0	0	0
552	0	16	0	1	1	0	0	0	0	100	140	0	1	1	0	0	0	0	0	0	0
560	0	70	0	1	1	0	0	0	0	160	60	0	0	0	0	0	0	0	0	0	0
563	0	83	1	1	1	0	0	1	0	138	91	0	1	0	0	0	0	0	0	0	0
573	0	23	0	2	0	0	0	0	0	130	52	0	1	0	0	0	0	0	0	0	0
575	0	67	1	1	0	0	0	0	1	120	120	0	1	0	0	1	1	0	0	0	0
584	0	18	0	1	1	1	0	0	0	130	140	0	0	0	0	0	0	0	0	0	0
597	0	77	1	1	0	0	0	1	0	136	138	0	0	0	1	1	1	0	0	0	0
598	0	48	1	1	0	0	0	0	1	128	96	0	1	0	0	0	0	0	0	0	0
601	0	24	1	2	0	0	0	0	0	140	86	0	1	0	0	0	0	0	0	0	0
605	0	71	1	1	0	0	0	1	0	124	106	0	1	0	0	0	0	0	0	0	0
607	0	72	0	1	1	0	0	0	0	134	60	0	1	0	0	0	0	0	0	0	0
619	0	77	1	1	1	0	1	0	0	170	115	1	0	0	0	0	0	0	0	0	0
620	0	60	0	1	1	0	0	1	0	124	135	0	1	0	0	0	0	0	0	0	0
639	0	46	0	1	1	1	0	0	0	110	128	0	0	0	0	0	0	0	0	0	0
644	0	65	1	1	0	0	0	0	0	100	105	0	1	0	0	0	0	0	0	0	0
645	0	36	0	1	0	0	0	0	0	224	125	0	1	0	0	0	0	0	0	0	0
648	0	68	0	1	1	0	0	0	0	112	64	0	0	0	0	0	0	0	0	0	0
655	0	58	0	1	0	0	0	0	0	154	98	0	1	0	0	0	0	0	0	0	0
659	0	76	1	1	0	0	0	1	0	92	112	0	1	0	0	0	0	0	0	0	0
669	0	41	1	2	0	0	0	0	0	110	144	0	1	0	0	0	0	1	1	0	0
670	0	20	0	3	0	0	0	0	0	120	68	0	1	0	0	0	0	0	0	0	0
674	0	91	0	1	0	0	1	1	0	152	125	0	1	0	0	0	0	0	0	0	0
675	0	75	0	1	1	0	0	0	0	140	90	0	1	0	0	0	0	0	0	0	0
676	0	25	1	1	0	0	0	0	0	131	135	0	1	0	0	0	0	1	0	0	0
709	0	70	0	1	0	0	0	1	0	78	143	0	1	0	1	0	0	0	0	0	0
713	0	47	0	1	1	0	0	0	0	156	112	0	1	0	0	0	0	0	0	0	0
727	0	75	0	3	1	0	0	0	0	144	120	0	1	0	0	0	0	0	1	0	0
728	0	40	0	2	0	0	0	1	0	160	150	1	1	1	0	0	0	0	0	0	0
732	0	71	0	1	0	0	0	1	0	148	192	0	1	0	1	1	1	0	0	0	0
746	0	70	1	1	0	0	0	1	0	90	140	0	1	0	1	0	0	1	0	0	0
749	0	58	0	1	1	0	0	0	0	148	95	1	1	0	0	0	0	0	0	0	0
754	0	54	0	1	1	0	0	0	0	136	80	0	0	0	0	0	0	0	0	0	0
761	0	77	0	1	1	0	0	0	0	128	59	0	0	0	0	0	0	0	0	0	0
763	0	55	0	1	1	1	0	1	0	138	140	0	0	0	0	0	0	0	0	0	0
764	0	21	0	1	1	0	0	0	0	120	62	0	1	0	0	0	0	0	0	0	0
765	0	53	0	2	0	0	1	0	1	170	115	0	1	0	0	0	0	0	0	0	0
766	0	31	1	1	0	1	1	1	1	146	100	0	1	0	0	1	1	0	0	0	0
772	0	71	0	1	1	1	0	0	0	204	52	0	0	0	0	0	0	0	0	0	0
776	0	49	0	2	0	0	0	0	0	150	100	0	1	0	0	0	0	0	0	0	0
784	0	60	1	2	0	0	0	1	0	116	92	1	1	0	0	0	0	0	0	0	0
794	0	50	0	1	0	0	0	1	0	156	99	0	1	0	1	0	1	0	0	0	0
796	0	45	1	1	1	0	0	0	0	132	109	0	1	1	0	0	0	0	0	0	0
809	0	21	0	1	1	0	0	0	0	110	90	0	1	0	0	0	0	0	0	0	0
814	0	73	1	1	1	0	0	0	0	130	83	0	1	0	0	0	0	0	0	0	0
816	0	28	0	1	1	0	0	1	0	122	80	1	0	1	0	0	0	0	0	0	0
829	0	17	0	1	1	0	0	0	0	140	78	0	1	1	0	0	0	0	0	0	0
837	0	17	1	3	0	0	0	0	0	130	140	0	1	0	0	0	0	0	0	0	0
846	0	21	1	1	1	0	0	0	0	142	79	0	1	0	0	0	0	0	0	0	0
847	0	68	1	1	1	1	0	0	0	91	79	0	0	0	0	0	0	0	0	0	0
863	0	17	0	3	1	0	0	0	0	136	78	0	1	0	0	0	0	0	0	0	0
867	0	60	0	1	0	0	0	1	0	108	120	0	1	0	0	0	0	0	0	0	0
875	0	69	0	1	1	0	0	0	0	169	73	0	1	0	0	0	0	0	0	0	0
877	0	88	1	1	0	0	1	0	0	190	88	0	1	0	0	0	0	0	0	0	0
880	0	20	0	1	1	0	0	0	0	120	80	0	1	0	0	0	0	0	0	0	0
881	0	89	1	1	1	0	0	0	0	190	114	0	1	0	0	0	1	0	0	2	1
889	0	62	1	1	0	0	0	0	0	110	78	0	1	0	0	0	0	0	0	0	0
893	0	46	0	1	0	0	1	1	0	142	89	0	1	0	0	1	0	1	0	0	0
906	0	19	0	1	1	0	0	1	0	100	137	0	1	0	0	0	0	0	0	0	0
912	0	71	0	1	0	0	0	1	0	124	124	0	1	0	1	1	1	0	0	0	0
915	0	67	0	1	1	0	0	0	0	152	78	0	0	0	0	0	0	0	0	0	0
923	0	20	0	1	1	0	0	0	0	104	83	0	1	0	0	0	0	0	0	0	0
924	0	73	1	2	0	0	1	0	0	162	100	0	1	0	0	0	0	0	0	0	0
925	0	59	0	1	0	0	0	0	0	100	88	0	1	0	0	0	0	0	0	0	0
929	0	42	0	1	1	0	0	0	0	122	84	0	1	1	0	0	0	0	0	0	0
4	1	87	1	1	1	0	0	1	0	80	96	0	1	1	1	1	1	0	0	0	0
27	1	76	1	1	1	0	0	1	0	128	90	1	1	0	0	0	0	0	0	0	0
47	1	78	0	1	0	0	0	1	0	130	132	0	1	0	0	0	0	1	0	0	0
52	1	63	0	1	0	0	1	1	0	112	106	1	1	0	1	0	0	0	0	0	0
127	1	19	0	1	1	0	0	0	0	140	76	0	1	0	0	0	0	0	0	0	0
145	1	67	1	1	0	0	0	1	0	62	145	0	1	0	0	0	0	0	1	0	0
154	1	53	1	1	0	0	0	1	0	148	128	0	1	0	0	1	1	0	0	0	0
165	1	92	0	1	0	0	0	1	0	124	80	0	1	0	0	0	0	1	0	0	0
195	1	57	0	1	0	0	0	1	1	110	124	0	1	0	0	0	0	0	0	2	1
202	1	75	1	1	1	1	0	0	0	130	136	0	0	0	0	0	0	0	0	0	0
204	1	91	0	1	0	0	0	1	0	64	125	0	1	0	0	0	1	0	0	0	0
208	1	70	0	1	1	0	0	0	0	168	122	0	0	0	1	0	0	0	0	1	0
222	1	88	0	1	0	0	0	1	1	141	140	0	1	0	0	0	0	0	0	0	0
238	1	41	0	1	1	0	0	1	0	140	58	0	1	0	0	0	0	0	0	2	1
241	1	61	0	1	0	0	0	0	0	140	81	0	1	0	0	0	0	0	0	0	0
273	1	80	0	1	1	0	0	0	0	100	85	0	1	0	0	0	0	0	0	0	0
285	1	40	0	1	0	0	0	1	0	86	80	1	1	0	0	0	0	0	0	0	0
299	1	75	0	1	0	0	0	1	0	90	100	0	1	0	0	0	0	0	0	1	0
331	1	63	1	1	1	0	1	1	1	36	86	0	1	1	0	0	0	0	1	2	1
346	1	75	1	1	0	1	0	0	0	190	94	0	1	0	0	0	0	0	0	0	0
380	1	20	0	1	1	0	0	0	0	148	72	0	1	1	0	0	0	0	0	0	0
384	1	71	0	1	0	0	0	0	0	142	95	0	1	0	0	0	0	0	0	0	0
412	1	51	1	1	1	0	0	1	0	134	100	1	1	0	0	0	0	0	0	1	0
427	1	65	0	1	0	0	0	0	0	66	94	0	1	0	0	0	0	0	0	2	1
442	1	69	1	3	0	0	1	0	0	170	60	1	1	0	1	0	0	0	0	0	0
461	1	55	0	1	1	0	1	1	0	122	100	1	1	0	0	0	0	0	0	0	0
468	1	50	1	1	1	1	0	0	0	120	96	0	1	0	0	0	0	0	0	0	0
490	1	78	0	1	0	0	0	1	0	110	81	0	1	0	0	0	0	0	0	0	0
518	1	71	1	1	0	0	0	0	1	70	112	0	1	0	0	0	0	0	0	2	1
611	1	85	1	1	1	0	0	0	0	136	96	0	1	0	0	0	0	0	0	0	0
613	1	75	0	1	0	0	1	1	0	130	119	0	1	0	0	1	0	1	1	0	0
666	1	65	1	1	0	0	0	1	1	104	150	0	1	0	0	0	1	0	0	2	1
671	1	49	0	1	0	0	0	1	1	140	108	0	1	0	0	0	0	1	0	0	0
706	1	75	1	1	0	0	1	1	1	150	66	0	1	0	0	0	0	0	1	2	1
740	1	72	1	1	0	0	0	0	0	90	160	0	1	0	0	0	0	0	0	0	0
751	1	69	0	1	0	0	1	0	0	80	81	0	1	0	0	0	0	0	0	2	1
752	1	64	0	1	0	1	0	1	0	80	118	0	1	0	1	0	0	0	1	0	0
789	1	60	0	1	0	0	0	1	0	56	114	1	1	0	0	1	0	1	0	0	0
871	1	60	0	3	1	0	1	1	0	130	55	0	1	0	0	0	0	0	0	1	0
921	1	50	1	2	0	0	0	0	0	256	64	0	1	0	0	0	0	0	0	1	0

The formula to fit is “STA ~ TYP + COMA + AGE + INF”

Read the icu.csv subset it with these 5 features in the formula and STA is the labelcol.

data<-subset(data, select = c(STA,TYP,COMA,AGE,INF) )
data <- data %>% select(-STA,STA)
data %>% kable() %>% kable_styling() %>% scroll_box(width = "800px", height = "400px")

TYP	COMA	AGE	INF	STA
1	0	27	1	0
1	0	59	0	0
0	0	77	0	0
1	0	54	1	0
1	0	87	1	0
1	0	69	1	0
0	0	63	0	0
1	0	30	0	0
1	0	35	0	0
0	0	70	0	0
0	0	55	1	0
0	0	48	0	0
0	0	66	0	0
1	0	61	0	0
1	0	66	0	0
0	0	52	1	0
0	0	55	1	0
1	1	59	1	0
1	0	63	0	0
0	0	72	0	0
1	0	60	1	0
0	0	78	0	0
1	0	16	0	0
0	0	62	0	0
1	0	61	1	0
1	0	35	0	0
0	0	74	0	0
0	0	68	0	0
1	0	69	0	0
1	0	51	0	0
0	0	55	0	0
1	0	64	1	0
1	0	88	1	0
1	0	23	0	0
0	0	73	0	0
0	0	53	0	0
0	0	74	0	0
0	0	68	0	0
1	0	66	1	0
0	0	60	1	0
0	0	64	1	0
0	0	66	1	0
1	0	19	1	0
1	0	18	0	0
1	0	63	1	0
1	0	45	0	0
1	0	64	0	0
1	0	68	1	0
1	0	64	1	0
0	0	82	0	0
0	0	73	0	0
1	0	70	0	0
1	0	61	1	0
0	0	64	1	0
0	0	47	1	0
0	0	69	0	0
1	0	67	1	0
0	0	18	0	0
0	0	77	1	0
1	0	32	0	0
0	0	19	1	0
1	0	72	0	0
1	0	49	1	0
0	0	68	0	0
1	0	82	1	0
1	0	32	1	0
1	0	78	1	0
1	0	57	1	0
1	0	46	0	0
1	0	23	1	0
1	0	55	0	0
1	0	18	0	0
1	0	20	0	0
0	0	75	0	0
0	0	79	1	0
1	0	40	0	0
1	0	76	1	0
0	0	66	1	0
1	0	76	1	0
1	0	80	0	0
1	0	23	1	0
1	0	48	1	0
0	0	67	0	0
1	0	69	0	0
0	0	65	0	0
0	0	72	0	0
1	0	55	0	0
1	0	40	0	0
1	0	55	1	0
1	0	34	0	0
1	0	47	0	0
1	0	41	1	0
1	0	84	1	0
0	0	88	0	0
0	0	77	0	0
1	0	80	0	0
1	0	16	0	0
0	0	70	0	0
1	0	83	1	0
1	0	23	0	0
1	0	67	0	0
0	0	18	0	0
0	0	77	1	0
1	0	48	0	0
1	0	24	0	0
1	0	71	1	0
1	0	72	0	0
0	0	77	0	0
1	0	60	1	0
0	0	46	0	0
1	0	65	0	0
1	0	36	0	0
0	0	68	0	0
1	0	58	0	0
1	0	76	1	0
1	0	41	0	0
1	0	20	0	0
1	0	91	1	0
1	0	75	0	0
1	0	25	0	0
1	0	70	1	0
1	0	47	0	0
1	0	75	0	0
1	0	40	1	0
1	0	71	1	0
1	0	70	1	0
1	0	58	0	0
0	0	54	0	0
0	0	77	0	0
0	0	55	1	0
1	0	21	0	0
1	0	53	0	0
1	0	31	1	0
0	0	71	0	0
1	0	49	0	0
1	0	60	1	0
1	0	50	1	0
1	0	45	0	0
1	0	21	0	0
1	0	73	0	0
0	0	28	1	0
1	0	17	0	0
1	0	17	0	0
1	0	21	0	0
0	0	68	0	0
1	0	17	0	0
1	0	60	1	0
1	0	69	0	0
1	0	88	0	0
1	0	20	0	0
1	1	89	0	0
1	0	62	0	0
1	0	46	1	0
1	0	19	1	0
1	0	71	1	0
0	0	67	0	0
1	0	20	0	0
1	0	73	0	0
1	0	59	0	0
1	0	42	0	0
1	0	87	1	1
1	0	76	1	1
1	0	78	1	1
1	0	63	1	1
1	0	19	0	1
1	0	67	1	1
1	0	53	1	1
1	0	92	1	1
1	1	57	1	1
0	0	75	0	1
1	0	91	1	1
0	0	70	0	1
1	0	88	1	1
1	1	41	1	1
1	0	61	0	1
1	0	80	0	1
1	0	40	1	1
1	0	75	1	1
1	1	63	1	1
1	0	75	0	1
1	0	20	0	1
1	0	71	0	1
1	0	51	1	1
1	1	65	0	1
1	0	69	0	1
1	0	55	1	1
1	0	50	0	1
1	0	78	1	1
1	1	71	0	1
1	0	85	0	1
1	0	75	1	1
1	1	65	1	1
1	0	49	1	1
1	1	75	1	1
1	0	72	0	1
1	1	69	0	1
1	0	64	1	1
1	0	60	1	1
1	0	60	1	1
1	0	50	0	1

data$TYP<-as.numeric(data$TYP)
data$AGE<-as.numeric(data$AGE)
data$INF<-as.numeric(data$INF)
data$STA<-as.factor(data$STA)
str(data)

## 'data.frame':    200 obs. of  5 variables:
##  $ TYP : num  1 1 0 1 1 1 0 1 1 0 ...
##  $ COMA: num  0 0 0 0 0 0 0 0 0 0 ...
##  $ AGE : num  27 59 77 54 87 69 63 30 35 70 ...
##  $ INF : num  1 0 0 1 1 1 0 0 0 0 ...
##  $ STA : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...

We compare the structure of our dataframe with that of the datset used in the supplied kNN function.

knn.df<-iris
str(knn.df)

## 'data.frame':    150 obs. of  5 variables:
##  $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
##  $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
##  $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
##  $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
##  $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

We observe they both have the same structure.

kNN.r

run the kNN.R for K=(3,5,7,15,25,50)

euclideanDist <- function(a, b){
  d = 0
  for(i in c(1:(length(a)) ))
  {
    d = d + (a[[i]]-b[[i]])^2
  }
  d = sqrt(d)
  return(d)
}

knn_predict2 <- function(test_data, train_data, k_value, labelcol){
  pred <- c()  #empty pred vector 
  #LOOP-1
  for(i in c(1:nrow(test_data))){   #looping over each record of test data
    eu_dist =c()          #eu_dist & eu_char empty  vector
    eu_char = c()
    good = 0              #good & bad variable initialization with 0 value
    bad = 0
    
    #LOOP-2-looping over train data 
    for(j in c(1:nrow(train_data))){
 
      #adding euclidean distance b/w test data point and train data to eu_dist vector
      eu_dist <- c(eu_dist, euclideanDist(test_data[i,-c(labelcol)], train_data[j,-c(labelcol)]))
 
      #adding class variable of training data in eu_char
      eu_char <- c(eu_char, as.character(train_data[j,][[labelcol]]))
    }
    
    eu <- data.frame(eu_char, eu_dist) #eu dataframe created with eu_char & eu_dist columns
 
    eu <- eu[order(eu$eu_dist),]       #sorting eu dataframe to gettop K neighbors
    eu <- eu[1:k_value,]               #eu dataframe with top K neighbors
 
    tbl.sm.df<-table(eu$eu_char)
    cl_label<-  names(tbl.sm.df)[[as.integer(which.max(tbl.sm.df))]]
    
    pred <- c(pred, cl_label)
    }
    return(pred) #return pred vector
  }
  

accuracy <- function(test_data,labelcol,predcol){
  correct = 0
  for(i in c(1:nrow(test_data))){
    if(test_data[i,labelcol] == test_data[i,predcol]){ 
      correct = correct+1
    }
  }
  accu = (correct/nrow(test_data)) * 100  
  return(accu)
}

We load our data to run the supplied function.

#load data
#knn.df<-iris
knn.df<-data
labelcol <- 5 # for our new dataset it is the fifth col 
predictioncol<-labelcol+1
# create train/test partitions
set.seed(2)
n<-nrow(knn.df)
knn.df<- knn.df[sample(n),]
train.df <- knn.df[1:as.integer(0.7*n),]

Model results

run the kNN.R for K=(3,5,7,15,25,50) submit the result confusionMatrix, Accuracy for each K

ks<-c(3,5,7,15,25,50)
acc<-vector()
for(i in 1:length(ks)) {
  K = ks[i] # number of neighbors to determine the class
  #table(train.df[,labelcol])
  test.df <- knn.df[as.integer(0.7*n +1):n,]
  #table(test.df[,labelcol])

  predictions <- knn_predict2(test.df, train.df, K,labelcol) #calling knn_predict()

  test.df[,predictioncol] <- predictions #Adding predictions in test data as 7th column
  acc<-c(acc,accuracy(test.df,labelcol,predictioncol))
  print(paste('Accuracy for K=',K,' is ',acc[i]))
  print('Confusion Matrix')
  print(table(test.df[[predictioncol]],test.df[[labelcol]]))
}

## [1] "Accuracy for K= 3  is  78.3333333333333"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 44  9
##   1  4  3
## [1] "Accuracy for K= 5  is  80"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 47 11
##   1  1  1
## [1] "Accuracy for K= 7  is  80"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 48 12
## [1] "Accuracy for K= 15  is  80"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 48 12
## [1] "Accuracy for K= 25  is  80"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 48 12
## [1] "Accuracy for K= 50  is  80"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 48 12

Plot Accuracy vs K.

plot(ks,acc)

Results with the new dataset are not very good, in fact the high accuracy is really due to how imbalanced the dataset is. We run the same code with the Iris dataset, which is observed in the confusion matrices.

#load data
knn.df<-iris
labelcol <- 5 # for iris it is the fifth col 
predictioncol<-labelcol+1
# create train/test partitions
set.seed(2)
n<-nrow(knn.df)
knn.df<- knn.df[sample(n),]
train.df <- knn.df[1:as.integer(0.7*n),]

acc<-vector()
for(i in 1:length(ks)) {
  K = ks[i] # number of neighbors to determine the class
  #table(train.df[,labelcol])
  test.df <- knn.df[as.integer(0.7*n +1):n,]
  #table(test.df[,labelcol])

  predictions <- knn_predict2(test.df, train.df, K,labelcol) #calling knn_predict()

  test.df[,predictioncol] <- predictions #Adding predictions in test data as 7th column
  acc<-c(acc,accuracy(test.df,labelcol,predictioncol))
  print(paste('Accuracy for K=',K,' is ',acc[i]))
  print('Confusion Matrix')
  print(table(test.df[[predictioncol]],test.df[[labelcol]]))
}

## [1] "Accuracy for K= 3  is  86.6666666666667"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         13         4
##   virginica       0          2        12
## [1] "Accuracy for K= 5  is  91.1111111111111"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         14         3
##   virginica       0          1        13
## [1] "Accuracy for K= 7  is  91.1111111111111"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         15         4
##   virginica       0          0        12
## [1] "Accuracy for K= 15  is  88.8888888888889"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         14         4
##   virginica       0          1        12
## [1] "Accuracy for K= 25  is  86.6666666666667"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         14         5
##   virginica       0          1        11
## [1] "Accuracy for K= 50  is  80"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         14         8
##   virginica       0          1         8

plot(ks,acc)

We can see how the same code shows much better results in both accuracy and on the confusion matrices. We also observe how higher values of K do not necesarily reflect in beter results, same as we saw with the new dataset.

We can also compare our results from the Iris dataset to those using the Class library knn function.

#load data
knn.df<-iris
labelcol <- 5 # for iris it is the fifth col 
predictioncol<-labelcol+1
# create train/test partitions
set.seed(2)
n<-nrow(knn.df)
knn.df<- knn.df[sample(n),]
train.df <- knn.df[1:as.integer(0.7*n),]

acc<-vector()
for(i in 1:length(ks)) {
  K = ks[i] # number of neighbors to determine the class
  #table(train.df[,labelcol])
  test.df <- knn.df[as.integer(0.7*n +1):n,]
  #table(test.df[,labelcol])

  #predictions <- knn_predict2(test.df, train.df, K,labelcol) #calling knn_predict()
  predictions <-knn(train.df[,-5],test.df[,-5],train.df$Species,k=K)

  test.df[,predictioncol] <- predictions #Adding predictions in test data as 7th column
  acc<-c(acc,accuracy(test.df,labelcol,predictioncol))
  print(paste('Accuracy for K=',K,' is ',acc[i]))
  print('Confusion Matrix')
  print(table(test.df[[predictioncol]],test.df[[labelcol]]))
}

## [1] "Accuracy for K= 3  is  86.6666666666667"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         13         4
##   virginica       0          2        12
## [1] "Accuracy for K= 5  is  91.1111111111111"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         14         3
##   virginica       0          1        13
## [1] "Accuracy for K= 7  is  91.1111111111111"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         15         4
##   virginica       0          0        12
## [1] "Accuracy for K= 15  is  88.8888888888889"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         14         4
##   virginica       0          1        12
## [1] "Accuracy for K= 25  is  86.6666666666667"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         14         5
##   virginica       0          1        11
## [1] "Accuracy for K= 50  is  80"
## [1] "Confusion Matrix"
##             
##              setosa versicolor virginica
##   setosa         14          0         0
##   versicolor      0         14         8
##   virginica       0          1         8

plot(ks,acc)

We see how we get the same results, validating out by hand function.

#load data
knn.df<-data
labelcol <- 5 # for iris it is the fifth col 
predictioncol<-labelcol+1
# create train/test partitions
set.seed(2)
n<-nrow(knn.df)
knn.df<- knn.df[sample(n),]
train.df <- knn.df[1:as.integer(0.7*n),]

acc<-vector()
for(i in 1:length(ks)) {
  K = ks[i] # number of neighbors to determine the class
  #table(train.df[,labelcol])
  test.df <- knn.df[as.integer(0.7*n +1):n,]
  #table(test.df[,labelcol])

  #predictions <- knn_predict2(test.df, train.df, K,labelcol) #calling knn_predict()
  predictions <-knn(train.df,test.df,train.df$STA,k=K)

  test.df[,predictioncol] <- predictions #Adding predictions in test data as 7th column
  acc<-c(acc,accuracy(test.df,labelcol,predictioncol))
  print(paste('Accuracy for K=',K,' is ',acc[i]))
  print('Confusion Matrix')
  print(table(test.df[[predictioncol]],test.df[[labelcol]]))
}

## [1] "Accuracy for K= 3  is  83.3333333333333"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 46  8
##   1  2  4
## [1] "Accuracy for K= 5  is  81.6666666666667"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 48 11
##   1  0  1
## [1] "Accuracy for K= 7  is  80"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 48 12
##   1  0  0
## [1] "Accuracy for K= 15  is  80"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 48 12
##   1  0  0
## [1] "Accuracy for K= 25  is  80"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 48 12
##   1  0  0
## [1] "Accuracy for K= 50  is  80"
## [1] "Confusion Matrix"
##    
##      0  1
##   0 48 12
##   1  0  0

plot(ks,acc)

Again we see similar results, with the unbalanced dataset affects the results, especially visible in the confusion matrices.

Summary

In this exercise we were able to successfully run the provided kNN function to our data. Some data conditioning was required to fulfill the requirements of the function. The data provided was conditioned to have the same structure as the sample data used in the kNN function. The results though were not ideal. The newly supplied dataset is highly unbalanced, which is reflected in the results. Even though the accuracy calculation are encouraging, the confusion matrix shows this is due to the imbalance in the data itself. The knn function from the CLass library was used to confirm the findings.