ClusteranalysisAssessment3
wendy wong
Wednesday, May 27, 2015
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setwd("~/statistical thinking course/Assignment 3")
studentpor<- read.table("student-por.csv", header=TRUE,sep=";")
#Remove any missing values
na.rm=TRUE#Obtain names of the variables
names(studentpor)## [1] "school" "sex" "age" "address" "famsize"
## [6] "Pstatus" "Medu" "Fedu" "Mjob" "Fjob"
## [11] "reason" "guardian" "traveltime" "studytime" "failures"
## [16] "schoolsup" "famsup" "fatherd" "activities" "nursery"
## [21] "higher" "internet" "romantic" "famrel" "freetime"
## [26] "goout" "Dalc" "Walc" "health" "absences"
## [31] "G1" "G2" "G3"#obtain structure of the dataset
str(studentpor)## 'data.frame': 649 obs. of 33 variables:
## $ school : Factor w/ 2 levels "GP","MS": 1 1 1 1 1 1 1 1 1 1 ...
## $ sex : Factor w/ 2 levels "F","M": 1 1 1 1 1 2 2 1 2 2 ...
## $ age : int 18 17 15 15 16 16 16 17 15 15 ...
## $ address : Factor w/ 2 levels "R","U": 2 2 2 2 2 2 2 2 2 2 ...
## $ famsize : Factor w/ 2 levels "GT3","LE3": 1 1 2 1 1 2 2 1 2 1 ...
## $ Pstatus : Factor w/ 2 levels "A","T": 1 2 2 2 2 2 2 1 1 2 ...
## $ Medu : int 4 1 1 4 3 4 2 4 3 3 ...
## $ Fedu : int 4 1 1 2 3 3 2 4 2 4 ...
## $ Mjob : Factor w/ 5 levels "at_home","health",..: 1 1 1 2 3 4 3 3 4 3 ...
## $ Fjob : Factor w/ 5 levels "at_home","health",..: 5 3 3 4 3 3 3 5 3 3 ...
## $ reason : Factor w/ 4 levels "course","home",..: 1 1 3 2 2 4 2 2 2 2 ...
## $ guardian : Factor w/ 3 levels "father","mother",..: 2 1 2 2 1 2 2 2 2 2 ...
## $ traveltime: int 2 1 1 1 1 1 1 2 1 1 ...
## $ studytime : int 2 2 2 3 2 2 2 2 2 2 ...
## $ failures : int 0 0 0 0 0 0 0 0 0 0 ...
## $ schoolsup : Factor w/ 2 levels "no","yes": 2 1 2 1 1 1 1 2 1 1 ...
## $ famsup : Factor w/ 2 levels "no","yes": 1 2 1 2 2 2 1 2 2 2 ...
## $ fatherd : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
## $ activities: Factor w/ 2 levels "no","yes": 1 1 1 2 1 2 1 1 1 2 ...
## $ nursery : Factor w/ 2 levels "no","yes": 2 1 2 2 2 2 2 2 2 2 ...
## $ higher : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...
## $ internet : Factor w/ 2 levels "no","yes": 1 2 2 2 1 2 2 1 2 2 ...
## $ romantic : Factor w/ 2 levels "no","yes": 1 1 1 2 1 1 1 1 1 1 ...
## $ famrel : int 4 5 4 3 4 5 4 4 4 5 ...
## $ freetime : int 3 3 3 2 3 4 4 1 2 5 ...
## $ goout : int 4 3 2 2 2 2 4 4 2 1 ...
## $ Dalc : int 1 1 2 1 1 1 1 1 1 1 ...
## $ Walc : int 1 1 3 1 2 2 1 1 1 1 ...
## $ health : int 3 3 3 5 5 5 3 1 1 5 ...
## $ absences : int 4 2 6 0 0 6 0 2 0 0 ...
## $ G1 : int 0 9 12 14 11 12 13 10 15 12 ...
## $ G2 : int 11 11 13 14 13 12 12 13 16 12 ...
## $ G3 : int 11 11 12 14 13 13 13 13 17 13 ...head(studentpor)## school sex age address famsize Pstatus Medu Fedu Mjob Fjob
## 1 GP F 18 U GT3 A 4 4 at_home teacher
## 2 GP F 17 U GT3 T 1 1 at_home other
## 3 GP F 15 U LE3 T 1 1 at_home other
## 4 GP F 15 U GT3 T 4 2 health services
## 5 GP F 16 U GT3 T 3 3 other other
## 6 GP M 16 U LE3 T 4 3 services other
## reason guardian traveltime studytime failures schoolsup famsup
## 1 course mother 2 2 0 yes no
## 2 course father 1 2 0 no yes
## 3 other mother 1 2 0 yes no
## 4 home mother 1 3 0 no yes
## 5 home father 1 2 0 no yes
## 6 reputation mother 1 2 0 no yes
## fatherd activities nursery higher internet romantic famrel freetime
## 1 no no yes yes no no 4 3
## 2 no no no yes yes no 5 3
## 3 no no yes yes yes no 4 3
## 4 no yes yes yes yes yes 3 2
## 5 no no yes yes no no 4 3
## 6 no yes yes yes yes no 5 4
## goout Dalc Walc health absences G1 G2 G3
## 1 4 1 1 3 4 0 11 11
## 2 3 1 1 3 2 9 11 11
## 3 2 2 3 3 6 12 13 12
## 4 2 1 1 5 0 14 14 14
## 5 2 1 2 5 0 11 13 13
## 6 2 1 2 5 6 12 12 13#Data exploration
summary(studentpor)## school sex age address famsize Pstatus
## GP:423 F:383 Min. :15.00 R:197 GT3:457 A: 80
## MS:226 M:266 1st Qu.:16.00 U:452 LE3:192 T:569
## Median :17.00
## Mean :16.74
## 3rd Qu.:18.00
## Max. :22.00
## Medu Fedu Mjob Fjob
## Min. :0.000 Min. :0.000 at_home :135 at_home : 42
## 1st Qu.:2.000 1st Qu.:1.000 health : 48 health : 23
## Median :2.000 Median :2.000 other :258 other :367
## Mean :2.515 Mean :2.307 services:136 services:181
## 3rd Qu.:4.000 3rd Qu.:3.000 teacher : 72 teacher : 36
## Max. :4.000 Max. :4.000
## reason guardian traveltime studytime
## course :285 father:153 Min. :1.000 Min. :1.000
## home :149 mother:455 1st Qu.:1.000 1st Qu.:1.000
## other : 72 other : 41 Median :1.000 Median :2.000
## reputation:143 Mean :1.569 Mean :1.931
## 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :4.000 Max. :4.000
## failures schoolsup famsup fatherd activities nursery
## Min. :0.0000 no :581 no :251 no :610 no :334 no :128
## 1st Qu.:0.0000 yes: 68 yes:398 yes: 39 yes:315 yes:521
## Median :0.0000
## Mean :0.2219
## 3rd Qu.:0.0000
## Max. :3.0000
## higher internet romantic famrel freetime
## no : 69 no :151 no :410 Min. :1.000 Min. :1.00
## yes:580 yes:498 yes:239 1st Qu.:4.000 1st Qu.:3.00
## Median :4.000 Median :3.00
## Mean :3.931 Mean :3.18
## 3rd Qu.:5.000 3rd Qu.:4.00
## Max. :5.000 Max. :5.00
## goout Dalc Walc health
## Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.00 1st Qu.:2.000
## Median :3.000 Median :1.000 Median :2.00 Median :4.000
## Mean :3.185 Mean :1.502 Mean :2.28 Mean :3.536
## 3rd Qu.:4.000 3rd Qu.:2.000 3rd Qu.:3.00 3rd Qu.:5.000
## Max. :5.000 Max. :5.000 Max. :5.00 Max. :5.000
## absences G1 G2 G3
## Min. : 0.000 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.000 1st Qu.:10.0 1st Qu.:10.00 1st Qu.:10.00
## Median : 2.000 Median :11.0 Median :11.00 Median :12.00
## Mean : 3.659 Mean :11.4 Mean :11.57 Mean :11.91
## 3rd Qu.: 6.000 3rd Qu.:13.0 3rd Qu.:13.00 3rd Qu.:14.00
## Max. :32.000 Max. :19.0 Max. :19.00 Max. :19.00#load car to produce a scatterplot
library("car")## Warning: package 'car' was built under R version 3.1.3# Generate a scatterplotmatrix on the continuous variables
scatterplotMatrix(studentpor[31:33])
# The diagonal cells show th histograms of each of the variables,the first two grades and final grade
#There may be a positive relationship between G1 & G2, G1 & G3 and G2 & G3#Use the plot function to examine the two-variable relationship
plot(studentpor$G1,studentpor$G2)
plot(studentpor$G1, studentpor$G3)
plot(studentpor$G2,studentpor$G3)
#Check the distribution of the dependent variable G3 final grade
hist(studentpor$G3)
# Examine strucure of the databy examining the descriptive statistics and of the multivariate data
sapply(studentpor[31:33],var)## G1 G2 G3
## 7.536481 8.489290 10.437140sapply(studentpor[31:33],sd)## G1 G2 G3
## 2.745265 2.913639 3.230656#The output illustrates that the means, variance and the standard deviation are different# Calcuate the correlations for the mutlivariate data to calcuate the correlation coefficientfor each pair of variables
cor.test(studentpor$G1,studentpor$G2)##
## Pearson's product-moment correlation
##
## data: studentpor$G1 and studentpor$G2
## t = 43.8455, df = 647, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8442202 0.8831514
## sample estimates:
## cor
## 0.8649816cor.test(studentpor$G1,studentpor$G3)##
## Pearson's product-moment correlation
##
## data: studentpor$G1 and studentpor$G3
## t = 37.3292, df = 647, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8003265 0.8493311
## sample estimates:
## cor
## 0.8263871cor.test(studentpor$G2,studentpor$G3)##
## Pearson's product-moment correlation
##
## data: studentpor$G2 and studentpor$G3
## t = 59.104, df = 647, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.9056064 0.9297806
## sample estimates:
## cor
## 0.918548```
# Need to standardise the variables in order to compare different variables with different means and different variances.
standardisedgrades<- as.data.frame(scale(studentpor[31:33]))```
# Check that the variables are standardised and exhibit means of 0 and variances of 1 by generating descriptive statistics
sapply(standardisedgrades,mean)## G1 G2 G3
## 2.942242e-16 -3.052555e-17 -2.244161e-17sapply(standardisedgrades,sd)## G1 G2 G3
## 1 1 1sapply(standardisedgrades,var)## G1 G2 G3
## 1 1 1#Use k means clustering to identify the number of k clusters within the multivariate dataset.
wss <- (nrow(standardisedgrades)-1)*sum(sapply(standardisedgrades,var))
for(i in 2:33) wss[i] <- sum(kmeans(standardisedgrades,centers=i)$withinss)
plot(1:33,wss,type="b",xlab="Number of Clusters", ylab="Within clusters sum of squares")
# Use k-means clustering to determine the clusters in the data
studentgradefit<- kmeans(standardisedgrades,5)
studentgradefit## K-means clustering with 5 clusters of sizes 58, 112, 193, 47, 239
##
## Cluster means:
## G1 G2 G3
## 1 -1.6212640 -1.7342118 -1.9508609
## 2 0.9864502 1.0055784 0.9825706
## 3 0.2736288 0.2097856 0.2472111
## 4 1.8542057 1.8782169 1.6426250
## 5 -0.6544231 -0.5891435 -0.5096782
##
## Clustering vector:
## [1] 1 5 3 2 3 3 3 3 4 3 2 3 3 3 2 4 3 2 1 3 3 3 3 5 5 5 3 5 3 3 5 2 2 3 3
## [36] 5 2 3 3 3 5 5 2 5 5 5 3 4 3 3 3 2 5 3 3 3 2 2 2 2 4 3 3 3 3 2 3 5 5 2
## [71] 3 5 3 3 5 5 3 3 5 3 3 5 3 3 3 3 3 2 5 5 5 3 3 2 3 3 5 3 3 3 5 4 3 5 4
## [106] 5 5 2 5 2 2 5 5 4 5 2 2 2 3 2 2 3 3 3 3 5 5 5 2 3 5 5 5 3 3 2 5 3 3 2
## [141] 5 3 3 3 3 5 5 2 5 5 5 2 3 3 5 1 3 5 5 3 5 5 3 1 5 3 5 3 1 5 5 5 1 5 5
## [176] 1 5 5 1 1 5 4 3 4 5 4 5 3 2 5 3 5 5 3 5 3 4 2 2 3 5 2 3 5 3 3 5 5 3 2
## [211] 3 5 2 5 2 3 2 3 3 5 3 2 3 3 3 3 3 3 3 2 5 5 3 3 5 3 3 5 2 1 4 5 5 2 3
## [246] 3 3 3 5 3 4 5 3 5 5 1 1 5 2 5 3 3 5 1 5 2 2 2 3 2 2 3 2 5 5 5 2 5 5 1
## [281] 5 3 1 5 1 3 3 5 3 2 5 5 3 3 3 3 4 5 5 3 2 5 5 3 3 5 2 3 5 3 5 3 4 3 4
## [316] 2 2 3 5 3 3 2 5 5 5 5 3 4 3 3 3 3 4 3 2 4 2 4 4 2 2 3 2 4 4 2 3 1 4 4
## [351] 5 2 5 5 3 3 4 2 3 2 3 5 3 3 2 2 3 3 5 5 5 5 3 5 4 2 2 3 4 5 3 2 3 3 5
## [386] 5 2 2 5 5 2 3 3 2 2 3 4 3 3 2 2 2 3 2 2 5 3 5 5 2 2 2 4 5 2 5 4 4 2 5
## [421] 4 5 3 5 3 5 5 4 1 5 5 5 1 2 5 5 1 3 5 2 1 5 3 1 5 5 5 5 4 3 2 5 5 5 5
## [456] 5 2 5 3 5 5 3 2 3 5 5 5 2 3 3 3 3 2 5 5 3 5 5 1 5 5 5 5 5 1 5 5 5 5 5
## [491] 5 1 5 5 5 3 2 5 2 4 1 3 5 2 3 5 5 5 5 4 4 5 1 1 1 5 2 2 1 1 1 5 1 1 1
## [526] 2 2 5 5 5 5 5 1 2 3 5 2 3 5 5 5 5 5 5 3 5 2 5 5 4 3 3 5 3 5 3 5 5 5 3
## [561] 5 5 3 1 5 5 5 1 5 1 1 5 1 5 5 5 5 5 5 5 5 1 1 1 5 1 1 1 5 5 1 3 3 3 4
## [596] 4 4 1 5 3 3 5 3 1 5 1 4 3 5 3 1 2 5 5 3 2 2 4 2 3 2 3 5 2 5 5 1 5 5 1
## [631] 4 5 1 2 4 5 4 1 2 1 1 2 5 5 5 2 5 5 5
##
## Within cluster sum of squares by cluster:
## [1] 136.07384 31.06787 57.40460 14.28357 90.83135
## (between_SS / total_SS = 83.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault"#Use studentgradefit to obtain the means of each of the variables for each cluster
aggregate(standardisedgrades,by=list(studentgradefit$cluster),FUN=mean)## Group.1 G1 G2 G3
## 1 1 -1.6212640 -1.7342118 -1.9508609
## 2 2 0.9864502 1.0055784 0.9825706
## 3 3 0.2736288 0.2097856 0.2472111
## 4 4 1.8542057 1.8782169 1.6426250
## 5 5 -0.6544231 -0.5891435 -0.5096782#Create a new data frame which appends the clusters to the studentpor file
studentporclust1<-data.frame(studentpor, studentgradefit$cluster)
studentporclust1## school sex age address famsize Pstatus Medu Fedu Mjob Fjob
## 1 GP F 18 U GT3 A 4 4 at_home teacher
## 2 GP F 17 U GT3 T 1 1 at_home other
## 3 GP F 15 U LE3 T 1 1 at_home other
## 4 GP F 15 U GT3 T 4 2 health services
## 5 GP F 16 U GT3 T 3 3 other other
## 6 GP M 16 U LE3 T 4 3 services other
## 7 GP M 16 U LE3 T 2 2 other other
## 8 GP F 17 U GT3 A 4 4 other teacher
## 9 GP M 15 U LE3 A 3 2 services other
## 10 GP M 15 U GT3 T 3 4 other other
## 11 GP F 15 U GT3 T 4 4 teacher health
## 12 GP F 15 U GT3 T 2 1 services other
## 13 GP M 15 U LE3 T 4 4 health services
## 14 GP M 15 U GT3 T 4 3 teacher other
## 15 GP M 15 U GT3 A 2 2 other other
## 16 GP F 16 U GT3 T 4 4 health other
## 17 GP F 16 U GT3 T 4 4 services services
## 18 GP F 16 U GT3 T 3 3 other other
## 19 GP M 17 U GT3 T 3 2 services services
## 20 GP M 16 U LE3 T 4 3 health other
## 21 GP M 15 U GT3 T 4 3 teacher other
## 22 GP M 15 U GT3 T 4 4 health health
## 23 GP M 16 U LE3 T 4 2 teacher other
## 24 GP M 16 U LE3 T 2 2 other other
## 25 GP F 15 R GT3 T 2 4 services health
## 26 GP F 16 U GT3 T 2 2 services services
## 27 GP M 15 U GT3 T 2 2 other other
## 28 GP M 15 U GT3 T 4 2 health services
## 29 GP M 16 U LE3 A 3 4 services other
## 30 GP M 16 U GT3 T 4 4 teacher teacher
## 31 GP M 15 U GT3 T 4 4 health services
## 32 GP M 15 U GT3 T 4 4 services services
## 33 GP M 15 R GT3 T 4 3 teacher at_home
## 34 GP M 15 U LE3 T 3 3 other other
## 35 GP M 16 U GT3 T 3 2 other other
## 36 GP F 15 U GT3 T 2 3 other other
## 37 GP M 15 U LE3 T 4 3 teacher services
## 38 GP M 16 R GT3 A 4 4 other teacher
## 39 GP F 15 R GT3 T 3 4 services health
## 40 GP F 15 R GT3 T 2 2 at_home other
## 41 GP F 16 U LE3 T 2 2 other other
## 42 GP M 15 U LE3 T 4 4 teacher other
## 43 GP M 15 U GT3 T 4 4 services teacher
## 44 GP M 15 U GT3 T 2 2 services services
## 45 GP F 16 U LE3 T 2 2 other at_home
## 46 GP F 15 U LE3 A 4 3 other other
## 47 GP F 16 U LE3 A 3 3 other services
## 48 GP M 16 U GT3 T 4 3 health services
## 49 GP M 15 U GT3 T 4 2 teacher other
## 50 GP F 15 U GT3 T 4 4 services teacher
## 51 GP F 16 U LE3 T 2 2 services services
## 52 GP F 15 U LE3 T 4 2 health other
## 53 GP M 15 U LE3 A 4 2 health health
## 54 GP F 15 U GT3 T 4 4 services services
## 55 GP F 15 U LE3 A 3 3 other other
## 56 GP F 16 U GT3 A 2 1 other other
## 57 GP F 15 U GT3 A 4 3 services services
## 58 GP M 15 U GT3 T 4 4 teacher health
## 59 GP M 15 U LE3 T 1 2 other at_home
## 60 GP F 16 U GT3 T 4 2 services other
## 61 GP F 16 R GT3 T 4 4 health teacher
## 62 GP F 16 U GT3 T 1 1 services services
## 63 GP F 16 U LE3 T 1 2 other services
## 64 GP F 16 U GT3 T 4 3 teacher health
## 65 GP F 15 U LE3 T 4 3 services services
## 66 GP F 16 U LE3 T 4 3 teacher services
## 67 GP M 15 U GT3 A 4 4 other services
## 68 GP F 16 U GT3 T 3 1 services other
## 69 GP F 15 R LE3 T 2 2 health services
## 70 GP F 15 R LE3 T 3 1 other other
## 71 GP M 16 U GT3 T 3 1 other other
## 72 GP M 15 U GT3 T 4 2 other other
## 73 GP F 15 R GT3 T 1 1 other other
## 74 GP M 16 U GT3 T 3 1 other other
## 75 GP F 16 U GT3 T 3 3 other services
## 76 GP M 15 U GT3 T 4 3 teacher other
## 77 GP M 15 U GT3 T 4 0 teacher other
## 78 GP F 16 U GT3 T 2 2 other other
## 79 GP M 17 U GT3 T 2 1 other other
## 80 GP F 16 U GT3 T 3 4 at_home other
## 81 GP M 15 U GT3 T 2 3 other services
## 82 GP M 15 U GT3 T 2 3 other other
## 83 GP F 15 U LE3 T 3 2 services other
## 84 GP M 15 U LE3 T 2 2 services services
## 85 GP F 15 U GT3 T 1 1 other other
## 86 GP F 15 U GT3 T 4 4 services services
## 87 GP F 16 U LE3 T 2 2 at_home other
## 88 GP F 15 U GT3 T 4 2 other other
## 89 GP M 16 U GT3 T 2 2 services other
## 90 GP M 16 U LE3 A 4 4 teacher health
## 91 GP F 16 U GT3 T 3 3 other other
## 92 GP F 15 U GT3 T 4 3 services other
## 93 GP F 16 U LE3 T 3 1 other other
## 94 GP F 16 U GT3 T 4 2 teacher services
## 95 GP M 15 U LE3 T 2 2 services health
## 96 GP F 15 R GT3 T 1 1 at_home other
## 97 GP M 16 R GT3 T 4 3 services other
## 98 GP F 16 U GT3 T 2 1 other other
## 99 GP F 16 U GT3 T 4 4 other other
## 100 GP F 16 U GT3 T 4 3 other at_home
## 101 GP M 16 U GT3 T 4 4 services services
## 102 GP M 16 U GT3 T 4 4 services teacher
## 103 GP M 15 U GT3 T 4 4 services other
## 104 GP F 15 U GT3 T 3 2 services other
## 105 GP M 15 U GT3 A 3 4 services other
## 106 GP F 15 U GT3 A 3 3 other health
## 107 GP F 15 U GT3 T 2 2 other other
## 108 GP M 16 U GT3 T 3 3 services other
## 109 GP M 15 R GT3 T 4 4 other other
## 110 GP F 16 U LE3 T 4 4 health health
## 111 GP M 15 U LE3 A 4 4 teacher teacher
## 112 GP F 16 R GT3 T 3 3 services other
## 113 GP F 16 U GT3 T 2 2 at_home other
## 114 GP M 15 U LE3 T 4 2 teacher other
## 115 GP M 15 R GT3 T 2 1 health services
## 116 GP M 16 U GT3 T 4 4 teacher teacher
## 117 GP M 15 U GT3 T 4 4 other teacher
## 118 GP M 16 U GT3 T 3 3 other services
## 119 GP M 17 R GT3 T 1 3 other other
## 120 GP M 15 U GT3 T 3 4 other other
## 121 GP F 15 U GT3 T 1 2 at_home services
## 122 GP M 15 U GT3 T 2 2 services services
## 123 GP F 16 U LE3 T 2 4 other health
## 124 GP M 16 U GT3 T 4 4 health other
## 125 GP F 16 U GT3 T 2 2 other other
## 126 GP M 15 U GT3 T 3 4 services services
## 127 GP F 15 U LE3 A 3 4 other other
## 128 GP F 19 U GT3 T 0 1 at_home other
## 129 GP M 16 R GT3 T 4 4 teacher teacher
## 130 GP M 16 U GT3 T 2 3 other other
## 131 GP F 15 R GT3 T 3 4 services teacher
## 132 GP F 18 U GT3 T 2 1 services other
## 133 GP F 17 U LE3 A 2 1 other other
## 134 GP F 15 U GT3 T 1 1 at_home other
## 135 GP F 17 U LE3 T 2 2 other other
## 136 GP F 16 U GT3 A 3 4 services other
## 137 GP M 16 U GT3 T 2 1 at_home other
## 138 GP F 16 U GT3 A 2 2 other other
## 139 GP M 15 R GT3 T 3 4 at_home teacher
## 140 GP F 15 U GT3 T 4 4 services at_home
## 141 GP M 17 R GT3 T 3 4 at_home other
## 142 GP F 16 R GT3 T 1 1 at_home other
## 143 GP M 18 U LE3 T 3 1 services services
## 144 GP F 18 U GT3 A 3 2 other services
## 145 GP F 16 R GT3 T 1 1 other services
## 146 GP F 16 U GT3 A 3 3 other other
## 147 GP M 16 U LE3 T 1 1 services other
## 148 GP F 15 U GT3 T 4 4 teacher teacher
## 149 GP F 15 R GT3 T 1 1 other other
## 150 GP M 15 U GT3 T 4 3 teacher services
## 151 GP F 15 U GT3 A 3 3 services services
## 152 GP M 16 U GT3 T 4 4 services services
## 153 GP M 16 U LE3 T 2 2 services services
## 154 GP F 15 U GT3 T 4 4 teacher services
## 155 GP F 16 U LE3 T 1 1 at_home at_home
## 156 GP M 17 U GT3 T 2 1 other other
## 157 GP F 15 U GT3 T 1 1 other services
## 158 GP F 15 U LE3 A 2 1 at_home other
## 159 GP F 15 U GT3 T 3 2 health services
## 160 GP F 15 U GT3 T 1 2 at_home other
## 161 GP F 15 U GT3 T 1 2 at_home services
## 162 GP M 16 U GT3 T 4 4 teacher teacher
## 163 GP M 15 U LE3 A 2 1 services other
## 164 GP M 18 U LE3 T 1 1 other other
## 165 GP M 16 U LE3 T 2 1 at_home other
## 166 GP F 15 R GT3 T 3 3 services services
## 167 GP M 19 U GT3 T 3 2 services at_home
## 168 GP F 17 U GT3 T 4 4 other teacher
## 169 GP M 15 R GT3 T 2 3 at_home services
## 170 GP M 17 R LE3 T 1 2 other other
## 171 GP F 18 R GT3 T 1 1 at_home other
## 172 GP M 16 R GT3 T 2 2 at_home other
## 173 GP M 16 U GT3 T 3 3 other services
## 174 GP M 16 U LE3 T 1 2 health services
## 175 GP M 17 R LE3 T 2 1 at_home other
## 176 GP M 17 R GT3 T 3 2 other other
## 177 GP M 15 U LE3 T 1 2 other other
## 178 GP M 16 U GT3 T 1 3 at_home services
## 179 GP M 17 R LE3 T 1 1 other services
## 180 GP M 17 U GT3 T 3 2 services services
## 181 GP M 16 U GT3 T 2 2 other other
## 182 GP F 16 U GT3 T 4 2 health services
## 183 GP F 16 U GT3 T 2 2 other other
## 184 GP F 16 U GT3 T 4 4 health health
## 185 GP M 16 U GT3 T 3 4 other other
## 186 GP M 16 U GT3 T 1 0 other other
## 187 GP M 17 U LE3 T 4 4 teacher other
## 188 GP F 16 U GT3 T 1 3 at_home services
## 189 GP F 16 U LE3 T 3 3 other other
## 190 GP M 17 U LE3 T 4 3 teacher other
## 191 GP F 16 U GT3 T 2 2 services other
## 192 GP M 17 U GT3 T 3 3 other other
## 193 GP M 16 R GT3 T 4 2 teacher services
## 194 GP M 17 U GT3 T 4 3 other other
## 195 GP M 16 U GT3 T 4 3 teacher other
## 196 GP M 16 U GT3 T 3 3 services other
## 197 GP F 17 U GT3 T 2 4 services services
## 198 GP F 17 U LE3 T 3 3 other other
## 199 GP F 16 U GT3 T 3 2 other other
## 200 GP M 17 U GT3 T 3 3 services services
## 201 GP M 16 U GT3 T 1 2 services services
## 202 GP M 16 U LE3 T 2 1 other other
## 203 GP F 17 U GT3 A 3 3 health other
## 204 GP M 17 R GT3 T 1 2 at_home other
## 205 GP F 16 U GT3 T 2 3 services services
## 206 GP F 17 U GT3 T 1 1 at_home services
## 207 GP M 17 U GT3 T 1 2 at_home services
## 208 GP M 16 R GT3 T 3 3 services services
## 209 GP M 16 U GT3 T 2 3 other other
## 210 GP F 17 U LE3 T 2 4 services services
## 211 GP M 17 U GT3 T 4 4 services teacher
## 212 GP M 16 R LE3 T 3 3 teacher other
## 213 GP F 17 U GT3 T 4 4 services teacher
## 214 GP F 16 U LE3 T 4 4 teacher teacher
## 215 GP F 16 U GT3 T 4 3 health other
## 216 GP F 16 U GT3 T 2 3 other other
## 217 GP F 17 U GT3 T 1 1 other other
## 218 GP F 17 R GT3 T 2 2 other other
## 219 GP F 16 R GT3 T 2 2 services services
## 220 GP F 17 U GT3 T 3 4 at_home services
## 221 GP F 16 U GT3 A 3 1 services other
## 222 GP F 16 U GT3 T 4 3 teacher other
## 223 GP F 16 U GT3 T 1 1 at_home other
## 224 GP F 17 R GT3 T 4 3 teacher other
## 225 GP F 19 U GT3 T 3 3 other other
## 226 GP M 17 U LE3 T 4 4 services other
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## fatherd activities nursery higher internet romantic famrel freetime
## 1 no no yes yes no no 4 3
## 2 no no no yes yes no 5 3
## 3 no no yes yes yes no 4 3
## 4 no yes yes yes yes yes 3 2
## 5 no no yes yes no no 4 3
## 6 no yes yes yes yes no 5 4
## 7 no no yes yes yes no 4 4
## 8 no no yes yes no no 4 1
## 9 no no yes yes yes no 4 2
## 10 no yes yes yes yes no 5 5
## 11 no no yes yes yes no 3 3
## 12 no yes yes yes yes no 5 2
## 13 no yes yes yes yes no 4 3
## 14 no no yes yes yes no 5 4
## 15 no no yes yes yes yes 4 5
## 16 no no yes yes yes no 4 4
## 17 no yes yes yes yes no 3 2
## 18 no yes yes yes no no 5 3
## 19 yes yes yes yes yes no 5 5
## 20 no yes yes yes yes no 3 1
## 21 no no yes yes yes no 4 4
## 22 yes no yes yes yes no 5 4
## 23 no yes yes yes yes no 4 5
## 24 no yes yes yes yes no 5 4
## 25 no yes yes yes yes no 4 3
## 26 no no no yes yes no 1 2
## 27 no no yes yes yes no 4 2
## 28 no no yes yes yes no 2 2
## 29 yes yes yes yes yes no 5 3
## 30 yes yes yes yes yes yes 4 4
## 31 yes no no yes yes no 5 4
## 32 no yes yes yes yes no 4 3
## 33 no yes yes yes yes yes 4 5
## 34 no yes no yes yes no 5 3
## 35 no no no yes yes no 5 4
## 36 no yes yes yes no no 3 5
## 37 no yes yes yes yes no 5 4
## 38 no yes yes yes yes yes 2 4
## 39 no yes yes yes yes no 4 3
## 40 no yes yes yes no no 4 3
## 41 no yes no yes yes yes 3 3
## 42 no no no yes yes yes 5 4
## 43 no yes yes yes yes no 4 3
## 44 no no yes yes yes no 5 4
## 45 no yes yes yes yes no 4 3
## 46 yes yes yes yes yes yes 5 2
## 47 no no yes yes yes no 2 3
## 48 no yes yes yes yes no 4 2
## 49 no no yes yes no no 4 3
## 50 no yes no yes yes no 4 4
## 51 no no yes yes yes no 4 3
## 52 no no yes yes yes no 4 3
## 53 no no yes yes no no 5 5
## 54 no no yes yes yes no 3 3
## 55 no no yes yes yes no 5 3
## 56 no yes yes yes yes yes 5 3
## 57 no yes yes yes yes no 4 3
## 58 no yes yes yes no no 3 2
## 59 no yes yes yes yes no 4 3
## 60 yes no yes yes yes no 4 2
## 61 no yes yes yes no no 2 4
## 62 no yes no yes yes yes 5 5
## 63 no yes yes yes yes no 4 4
## 64 no yes yes yes yes no 3 4
## 65 no yes yes yes yes yes 4 4
## 66 no yes yes yes yes no 5 4
## 67 no yes no yes yes yes 1 3
## 68 no no yes yes yes no 4 3
## 69 no no yes yes yes no 4 1
## 70 no no no yes yes no 4 4
## 71 no no yes yes yes no 4 3
## 72 no no yes yes yes no 3 3
## 73 no no no yes yes yes 3 3
## 74 no yes yes yes no no 5 3
## 75 no yes yes yes yes no 4 3
## 76 no yes yes yes yes no 4 3
## 77 no yes yes yes yes no 3 4
## 78 no no yes yes yes yes 5 2
## 79 no yes yes no yes no 4 5
## 80 no no yes yes yes no 2 4
## 81 no yes no yes yes yes 3 2
## 82 no no no yes yes no 5 3
## 83 no no yes yes yes no 4 4
## 84 yes yes yes yes yes no 5 3
## 85 no yes no yes yes no 4 3
## 86 no no yes yes yes yes 4 4
## 87 no no yes yes no no 4 3
## 88 no yes yes yes yes no 5 3
## 89 no yes no yes yes no 4 4
## 90 no no yes yes no no 4 1
## 91 no no yes yes yes yes 4 3
## 92 no yes yes yes yes no 4 5
## 93 no no yes yes no no 3 3
## 94 no yes yes yes yes no 5 3
## 95 no yes yes yes yes no 4 3
## 96 yes yes yes yes yes no 3 1
## 97 yes yes no yes yes no 3 3
## 98 no no yes yes no yes 4 3
## 99 no yes no yes yes no 5 3
## 100 no no yes yes yes no 5 3
## 101 no yes yes yes yes no 4 5
## 102 no yes yes yes yes yes 4 4
## 103 yes yes no yes yes no 5 3
## 104 no no yes yes yes no 4 3
## 105 no yes yes yes yes no 5 4
## 106 no no yes yes no no 4 3
## 107 no no yes yes yes no 5 1
## 108 no yes yes yes yes no 5 3
## 109 no yes yes yes yes yes 1 3
## 110 no yes yes yes yes yes 5 4
## 111 no yes yes yes yes no 5 5
## 112 no yes yes yes yes no 4 1
## 113 no yes yes yes yes no 3 1
## 114 no no yes yes yes no 3 5
## 115 no yes yes yes yes yes 5 4
## 116 no yes yes yes yes no 5 4
## 117 no yes yes yes no no 4 4
## 118 no yes yes yes yes no 5 4
## 119 no yes yes yes yes no 5 2
## 120 no no yes yes yes no 3 4
## 121 no no no yes yes no 3 2
## 122 no yes yes yes yes no 5 5
## 123 no yes yes yes yes yes 4 2
## 124 no yes yes yes yes no 3 4
## 125 no no yes yes yes yes 5 4
## 126 no no yes yes yes no 5 5
## 127 no yes yes yes yes yes 5 3
## 128 no no no no no no 3 4
## 129 no yes yes yes yes no 3 5
## 130 no no no yes yes yes 3 2
## 131 no no yes yes yes yes 4 2
## 132 no yes yes no yes yes 5 4
## 133 no no yes yes yes no 3 2
## 134 no yes no yes yes yes 4 3
## 135 no no yes yes yes yes 3 4
## 136 no no yes yes yes no 3 2
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## 138 no no yes yes no no 5 3
## 139 no no yes yes no yes 5 3
## 140 no yes yes yes yes yes 4 3
## 141 no no yes yes no no 5 4
## 142 no no yes yes no no 5 1
## 143 no yes yes yes yes yes 3 3
## 144 no yes no yes yes yes 4 3
## 145 no yes yes yes no yes 3 3
## 146 no yes no yes yes yes 4 3
## 147 no no yes yes no yes 4 4
## 148 no yes yes yes yes no 4 3
## 149 no yes yes yes yes yes 5 5
## 150 no no yes yes yes no 2 2
## 151 no no no yes no yes 1 3
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## 153 no yes yes yes yes no 2 3
## 154 no yes yes yes yes no 4 2
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## 156 no no yes yes yes no 5 4
## 157 no no yes yes yes no 4 4
## 158 no yes yes no yes yes 4 4
## 159 no no yes yes yes no 3 3
## 160 no no no yes yes no 4 3
## 161 no no no yes no yes 2 3
## 162 no no yes no yes yes 3 3
## 163 no no yes yes yes no 4 5
## 164 no no yes no yes yes 2 3
## 165 no yes yes yes no yes 4 4
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## 167 no no yes no yes yes 4 5
## 168 no no yes yes no yes 4 2
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## 170 no no yes yes no no 2 2
## 171 no yes no yes no no 5 2
## 172 no no no yes no no 4 2
## 173 no no yes yes yes yes 4 5
## 174 no no no yes yes no 4 4
## 175 yes yes yes no yes yes 3 3
## 176 no no yes yes yes yes 4 4
## 177 no yes yes yes no no 4 4
## 178 no no yes no yes no 5 3
## 179 no yes yes no no yes 5 3
## 180 no yes no no no no 4 5
## 181 no no yes no yes no 4 3
## 182 no no yes yes yes yes 4 2
## 183 no no no yes yes no 5 1
## 184 no no yes yes yes yes 4 4
## 185 no yes no yes yes no 3 4
## 186 no yes yes yes yes yes 4 3
## 187 no yes yes yes yes no 4 4
## 188 no yes no yes yes yes 4 3
## 189 no yes yes yes yes no 4 4
## 190 no yes yes yes yes no 4 4
## 191 no yes no yes yes no 3 4
## 192 no yes no yes yes no 4 3
## 193 no yes yes yes yes yes 4 3
## 194 yes yes yes yes yes yes 5 2
## 195 yes yes yes yes yes no 3 4
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## 197 no yes yes yes no no 5 4
## 198 no yes yes yes yes yes 5 3
## 199 no no yes yes yes no 1 2
## 200 no yes yes yes yes yes 4 3
## 201 no yes yes yes yes yes 3 3
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## 247 5 1 3 2 0 13 13 13 3
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## 591 4 2 2 5 3 7 8 7 1
## 592 5 1 1 1 2 12 13 14 3
## 593 3 1 1 4 0 11 12 13 3
## 594 3 1 2 4 0 12 13 14 3
## 595 5 1 2 1 0 18 18 18 4
## 596 5 1 1 5 3 17 17 17 4
## 597 3 1 2 4 0 17 18 18 4
## 598 3 1 1 4 0 9 0 0 1
## 599 4 5 5 1 8 10 11 11 5
## 600 5 1 1 1 5 12 13 14 3
## 601 3 3 4 4 4 12 13 14 3
## 602 1 1 1 2 4 8 8 10 5
## 603 5 1 4 3 0 11 12 13 3
## 604 1 1 1 5 0 5 0 0 1
## 605 2 1 2 2 2 9 10 10 5
## 606 5 2 3 2 0 5 0 0 1
## 607 3 3 1 5 0 18 18 18 4
## 608 3 1 2 2 5 11 11 12 3
## 609 3 1 2 3 2 8 10 11 5
## 610 1 1 1 4 0 11 11 12 3
## 611 4 1 4 1 0 8 0 0 1
## 612 1 1 1 4 5 14 14 15 2
## 613 5 1 3 2 4 10 11 11 5
## 614 4 1 1 5 0 10 10 10 5
## 615 3 1 2 5 2 12 12 12 3
## 616 3 1 2 5 0 15 14 15 2
## 617 2 1 2 3 2 14 13 14 2
## 618 2 1 1 4 0 19 17 18 4
## 619 4 1 4 5 0 16 15 15 2
## 620 2 1 3 3 6 13 12 13 3
## 621 4 1 1 1 4 15 14 15 2
## 622 2 1 2 3 0 13 13 13 3
## 623 4 2 4 3 0 8 10 9 5
## 624 2 2 2 5 0 15 16 16 2
## 625 1 1 2 1 0 8 8 9 5
## 626 3 1 2 4 0 10 10 10 5
## 627 2 4 2 5 0 7 5 0 1
## 628 3 2 3 3 3 9 10 10 5
## 629 3 1 1 3 8 10 11 12 5
## 630 5 1 3 1 4 7 8 9 1
## 631 4 1 1 1 0 15 17 17 4
## 632 2 1 2 4 4 10 11 12 5
## 633 3 1 1 3 4 7 8 9 1
## 634 3 3 4 2 1 13 14 14 2
## 635 3 1 2 1 1 16 16 16 4
## 636 4 2 3 1 10 8 9 9 5
## 637 4 1 4 2 4 17 18 19 4
## 638 3 1 3 5 0 7 7 0 1
## 639 3 1 1 3 4 14 15 16 2
## 640 2 1 3 5 0 5 8 0 1
## 641 3 4 3 3 0 7 7 0 1
## 642 3 1 3 4 0 14 17 15 2
## 643 4 1 1 1 0 6 9 11 5
## 644 3 2 2 5 4 7 9 10 5
## 645 2 1 2 5 4 10 11 10 5
## 646 4 1 1 1 4 15 15 16 2
## 647 1 1 1 5 6 11 12 9 5
## 648 5 3 4 2 6 10 10 10 5
## 649 1 3 4 5 4 10 11 11 5#find out if the clusters that were found through k-means clustering were approximately the same as the unstandardised variables
head(studentporclust1)## school sex age address famsize Pstatus Medu Fedu Mjob Fjob
## 1 GP F 18 U GT3 A 4 4 at_home teacher
## 2 GP F 17 U GT3 T 1 1 at_home other
## 3 GP F 15 U LE3 T 1 1 at_home other
## 4 GP F 15 U GT3 T 4 2 health services
## 5 GP F 16 U GT3 T 3 3 other other
## 6 GP M 16 U LE3 T 4 3 services other
## reason guardian traveltime studytime failures schoolsup famsup
## 1 course mother 2 2 0 yes no
## 2 course father 1 2 0 no yes
## 3 other mother 1 2 0 yes no
## 4 home mother 1 3 0 no yes
## 5 home father 1 2 0 no yes
## 6 reputation mother 1 2 0 no yes
## fatherd activities nursery higher internet romantic famrel freetime
## 1 no no yes yes no no 4 3
## 2 no no no yes yes no 5 3
## 3 no no yes yes yes no 4 3
## 4 no yes yes yes yes yes 3 2
## 5 no no yes yes no no 4 3
## 6 no yes yes yes yes no 5 4
## goout Dalc Walc health absences G1 G2 G3 studentgradefit.cluster
## 1 4 1 1 3 4 0 11 11 1
## 2 3 1 1 3 2 9 11 11 5
## 3 2 2 3 3 6 12 13 12 3
## 4 2 1 1 5 0 14 14 14 2
## 5 2 1 2 5 0 11 13 13 3
## 6 2 1 2 5 6 12 12 13 3#Use a crosstabulation of(studentpor$G1)and (studentpor$G2)to check correlation
table(studentporclust1$G1,studentporclust1$studentgradefit.cluster)##
## 1 2 3 4 5
## 0 1 0 0 0 0
## 4 2 0 0 0 0
## 5 5 0 0 0 0
## 6 7 0 0 0 2
## 7 24 0 0 0 9
## 8 14 0 0 0 28
## 9 3 0 0 0 62
## 10 1 0 8 0 86
## 11 1 1 43 0 46
## 12 0 3 73 0 6
## 13 0 21 51 0 0
## 14 0 51 17 3 0
## 15 0 30 1 4 0
## 16 0 6 0 16 0
## 17 0 0 0 16 0
## 18 0 0 0 7 0
## 19 0 0 0 1 0table(studentporclust1$G2,studentporclust1$studentgradefit.cluster)##
## 1 2 3 4 5
## 0 7 0 0 0 0
## 5 3 0 0 0 0
## 6 7 0 0 0 0
## 7 15 0 0 0 1
## 8 21 0 0 0 19
## 9 3 0 0 0 69
## 10 1 0 2 0 80
## 11 1 0 36 0 66
## 12 0 0 83 0 3
## 13 0 10 69 0 1
## 14 0 51 3 0 0
## 15 0 38 0 0 0
## 16 0 11 0 14 0
## 17 0 2 0 18 0
## 18 0 0 0 14 0
## 19 0 0 0 1 0#Determine if the (studentpor$G1)and(studentpor$G2) are a signficant predictors of the clusters by performing a chi-square test:
chisq.test(studentporclust1$G1,studentporclust1$studentgradefit.cluster)## Warning in chisq.test(studentporclust1$G1,
## studentporclust1$studentgradefit.cluster): Chi-squared approximation may
## be incorrect##
## Pearson's Chi-squared test
##
## data: studentporclust1$G1 and studentporclust1$studentgradefit.cluster
## X-squared = 1577.143, df = 64, p-value < 2.2e-16chisq.test(studentporclust1$G2,studentporclust1$studentgradefit.cluster)## Warning in chisq.test(studentporclust1$G2,
## studentporclust1$studentgradefit.cluster): Chi-squared approximation may
## be incorrect##
## Pearson's Chi-squared test
##
## data: studentporclust1$G2 and studentporclust1$studentgradefit.cluster
## X-squared = 1939.732, df = 60, p-value < 2.2e-16#Plot clusters to see which datapoints fall into which cluster
library(cluster)
clusplot(studentporclust1,studentporclust1$studentgradefit.cluster,colour=TRUE, shade=FALSE,labels=2,lines=3)## Warning in plot.window(...): "colour" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "colour" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "colour" is
## not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "colour" is
## not a graphical parameter## Warning in box(...): "colour" is not a graphical parameter## Warning in title(...): "colour" is not a graphical parameter## Warning in polygon(z[[i]], density = if (shade) density[i] else 0, col =
## col.clus, : "colour" is not a graphical parameter## Warning in polygon(z[[i]], density = if (shade) density[i] else 0, col =
## col.clus, : "colour" is not a graphical parameter## Warning in polygon(z[[i]], density = if (shade) density[i] else 0, col =
## col.clus, : "colour" is not a graphical parameter## Warning in polygon(z[[i]], density = if (shade) density[i] else 0, col =
## col.clus, : "colour" is not a graphical parameter## Warning in polygon(z[[i]], density = if (shade) density[i] else 0, col =
## col.clus, : "colour" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "colour" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "colour" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "colour" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "colour" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "colour" is not a
## graphical parameter## Warning in text.default(xy, labels = labs, ...): "colour" is not a
## graphical parameter## Warning in text.default(xy, labels = labs, ...): "colour" is not a
## graphical parameter
clusplot(studentpor,studentporclust1$studentgradefit.cluster,colour=TRUE, shade=FALSE,labels=2,lines=3)## Warning in plot.window(...): "colour" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "colour" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "colour" is
## not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "colour" is
## not a graphical parameter## Warning in box(...): "colour" is not a graphical parameter## Warning in title(...): "colour" is not a graphical parameter## Warning in polygon(z[[i]], density = if (shade) density[i] else 0, col =
## col.clus, : "colour" is not a graphical parameter## Warning in polygon(z[[i]], density = if (shade) density[i] else 0, col =
## col.clus, : "colour" is not a graphical parameter## Warning in polygon(z[[i]], density = if (shade) density[i] else 0, col =
## col.clus, : "colour" is not a graphical parameter## Warning in polygon(z[[i]], density = if (shade) density[i] else 0, col =
## col.clus, : "colour" is not a graphical parameter## Warning in polygon(z[[i]], density = if (shade) density[i] else 0, col =
## col.clus, : "colour" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "colour" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "colour" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "colour" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "colour" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "colour" is not a
## graphical parameter## Warning in text.default(xy, labels = labs, ...): "colour" is not a
## graphical parameter## Warning in text.default(xy, labels = labs, ...): "colour" is not a
## graphical parameter
# An alternative clustering analysis technique is hierarchical clustering
d<- dist(standardisedgrades,method="euclidean")
studentgradefit<- hclust(d)
studentgradefit##
## Call:
## hclust(d = d)
##
## Cluster method : complete
## Distance : euclidean
## Number of objects: 649#Graph the fit
plot(studentgradefit)
groups<- cutree(studentgradefit, k=5)
groups<- cutree(studentgradefit, k=2:5)
rect.hclust(studentgradefit,k=2, border="green")
rect.hclust(studentgradefit,k=3, border="blue")
rect.hclust(studentgradefit,k=5, border="red")
summary(studentgradefit)## Length Class Mode
## merge 1296 -none- numeric
## height 648 -none- numeric
## order 649 -none- numeric
## labels 0 -none- NULL
## method 1 -none- character
## call 2 -none- call
## dist.method 1 -none- character```
# Fit a varying intercept model to obtain the AIC by first generating a generalised linear model(fixed effects model) to check the significance of each of the fixed effects (G1 and G2)
studentpor<- read.table("student-por.csv", header=TRUE,sep=";")
model1<- glm(formula=G3~G1+G2,data=studentpor)
model1##
## Call: glm(formula = G3 ~ G1 + G2, data = studentpor)
##
## Coefficients:
## (Intercept) G1 G2
## -0.1713 0.1489 0.8971
##
## Degrees of Freedom: 648 Total (i.e. Null); 646 Residual
## Null Deviance: 6763
## Residual Deviance: 1030 AIC: 2149summary(model1)##
## Call:
## glm(formula = G3 ~ G1 + G2, data = studentpor)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -9.5408 -0.4380 -0.0942 0.6296 5.7109
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.17128 0.21510 -0.796 0.426
## G1 0.14890 0.03600 4.136 4e-05 ***
## G2 0.89714 0.03392 26.448 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 1.593853)
##
## Null deviance: 6763.3 on 648 degrees of freedom
## Residual deviance: 1029.6 on 646 degrees of freedom
## AIC: 2149.3
##
## Number of Fisher Scoring iterations: 2# Generate linear mixed effects model to fita varying intercept model with lmer
library(lme4)## Loading required package: Matrix
## Loading required package: Rcppstudentpor<- read.table("student-por.csv", header=TRUE,sep=";")
model2<- lmer(formula=G3~G1+G2+(1|school),data=studentpor)
summary(model2)## Linear mixed model fit by REML ['lmerMod']
## Formula: G3 ~ G1 + G2 + (1 | school)
## Data: studentpor
##
## REML criterion at convergence: 2155.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.6242 -0.3732 -0.0730 0.5106 4.4800
##
## Random effects:
## Groups Name Variance Std.Dev.
## school (Intercept) 0.01724 0.1313
## Residual 1.58667 1.2596
## Number of obs: 649, groups: school, 2
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -0.10084 0.23744 -0.425
## G1 0.14234 0.03612 3.940
## G2 0.89541 0.03386 26.445
##
## Correlation of Fixed Effects:
## (Intr) G1
## G1 -0.315
## G2 -0.163 -0.857coef(model2)## $school
## (Intercept) G1 G2
## GP -0.0206979 0.1423439 0.895405
## MS -0.1809790 0.1423439 0.895405
##
## attr(,"class")
## [1] "coef.mer"#Interpret the effect of schools on
table(studentpor$G1,studentpor$G2)##
## 0 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
## 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## 4 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
## 5 2 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0
## 6 0 0 1 2 4 1 0 1 0 0 0 0 0 0 0 0
## 7 2 1 3 6 10 8 2 1 0 0 0 0 0 0 0 0
## 8 1 1 2 5 10 13 8 1 0 1 0 0 0 0 0 0
## 9 1 0 0 3 9 17 24 9 2 0 0 0 0 0 0 0
## 10 0 0 0 0 5 21 25 37 4 3 0 0 0 0 0 0
## 11 0 0 0 0 0 11 18 28 27 6 0 1 0 0 0 0
## 12 0 0 0 0 0 1 5 20 26 27 0 2 1 0 0 0
## 13 0 0 0 0 0 0 1 4 22 21 21 2 0 1 0 0
## 14 0 0 0 0 0 0 0 1 4 20 21 17 4 4 0 0
## 15 0 0 0 0 0 0 0 0 1 2 10 12 8 2 0 0
## 16 0 0 0 0 0 0 0 0 0 0 2 4 10 5 1 0
## 17 0 0 0 0 0 0 0 0 0 0 0 0 2 6 8 0
## 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 1
## 19 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0```
anova(model2)## Analysis of Variance Table
## Df Sum Sq Mean Sq F value
## G1 1 4212.2 4212.2 2654.72
## G2 1 1109.6 1109.6 699.32You can also embed plots, for example:
Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.