# Essay on Project Statistics

Submitted By CristinaYang
Words: 962
Pages: 4

Laboratory Report

Example B: The Scottish Referendum
There was great interest from the public in knowing the results of the Scottish Independence Referendum. The Financial Times reported the voting patterns dividing them by Council area, together with a diversity of characteristics of each Council region. The information stored in the file ‘scottish-referendum.dat’ is: the name of each Council, the percentages of people who voted and those who voted no, the size of the population, the percentage of people who are unemployed, the percentage who identify themselves as Scottish only, the percentage who are 16 years of age and the percentages of those who are over 50 and 65 years of age. We will explore the relationship between them.

We start by studying the relationship between the percentage of people who voted ‘no’ and the unemployment rate of the Council areas. Firstly we identify the proportion of people who voted ‘no' across the whole country by using the following syntax in the R program: d<-read.table("scottish-referendum.dat") d\$Vote <- d\$Turnout*d\$Population sum(d\$Voted.no*d\$Vote)/sum(d\$Vote) The next step is to obtain Figure 1 by compile the code : plot(d\$Unemployment.rate, d\$Voted.no, main="'No' Voters and the Unemployment rate",xlab="Unemployment rate(%)",ylab="'No' voters(%)")

Figure1: Plot of 'No' Voters and the Unemployment rate
In Figure 1 it can be observed a moderate negative linear relationship between the percentage of people who voted no and the unemployment rate; as one variable increases in its values, the other variable decreases in its values. In our case as the unemployment rate increases the percentage of people who voted no, decreases.
In addition, we add labels to the points and scale their sizes so that the area of each point shows the number of people who voted in that particular Council region. The enhancements can be seen in Figure 2.
Figure2: Plot of 'No' Voters and the Unemployment rate (with filled points that indicate through their size the number of people who voted in that particular Council region)

The syntax used in R was: d\$Scale<-sqrt(d\$Vote/mean(d\$Vote)) plot(d\$Unemployment.rate,d\$Voted.no,pch=16,cex=d\$Scale, main="'No' Voters and the Unemployment rate",xlab="Unemployment rate(%)",ylab="'No' voters(%)") text(d\$Unemployment.rate,d\$Voted.no,d\$Scottish.Council,cex=0.5,pos=1)
In Figure 2 it can be seen that Council regions as Orkney Islands, Shetland Islands or Aberdeen with a small unemployment rate (<1%) have voted ‘No’ in a large percentage (>60%) and regions such as Glasgow, West Dunbartonshire or North Ayrshire which have high unemployment rates(>4%) have voted ‘No’ in a smaller proportion (<50%).

Figure 3: ‘No’ Voters against Scottish identity only
The syntax used in R was: d\$Scale<-sqrt(d\$Vote/mean(d\$Vote)) plot(d\$Scottish.identity.only, d\$Voted.no,main="'No' Voters against Scottish identity only",xlab="Scottish identity only(%)",ylab="'No' voters(%)", pch=16, cex=d\$Scale) text(d\$Scottish.identity.only, d\$Voted.no, d\$Scottish.Council, cex=0.5, pos=1)
In Figure 3, it can be seen a moderate negative linear relationship between the percentage of people who are Scottish identity only and the percentage of people who voted ‘No’. This means that as the percentage of people who are Scottish identity only increases, the percentage of ‘No’ voters decreases.

Figure 4: ‘No’ Voters against Aged Over 50
The syntax used in R was: plot(d\$Aged.over.50, d\$Voted.no,main="'No' Voters against Aged over 50",xlab="Aged over 50(%)",ylab="'No' voters(%)", pch=16, cex=d\$Scale) text(d\$Aged.over.50, d\$Voted.no, d\$Scottish.Council, cex=0.5, pos=1)
In Figure 4, it can be seen a weak positive linear relationship between the percentage of people aged over 50 and the percentage of people who voted ‘No’. This means…