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ENVS450 – Assignment 3 200923027
Page 1
England’s North-South Divide: exploring the impact of socio-demographic
variables on the rate of home-ownership by geographic location
Introduction
The “north-south divide” is a widely debated
social phenomena in the UK, and is often used
to describe the cultural, social, political and
economic differences between the two halves
of the country, with the south generally
determined to be “out-performing” the north.
This has been officially recognised by the
current Conservative government with the
instatement of the Northern Powerhouse
project, which aims to re-balance economic
disparity between the north and south.
However, house prices between the north and
south differ enormously, with the average
house price in the south far-exceeding the
wages of all but the most senior employees,
making the prospect of mortgages completely
unrealistic for most the workforce.
Several factors were identified which would
realistically impact home ownership across the
whole of the UK. These were taken from a list
of census variables and include: rate of
professional employment, rate of households
without a car, rate of residents aged 65 plus,
rate of illness and location within the UK. Given
the nature of the census dataset, each variable
has 348 instances, existing once for each
district in England and Wales. These variables
were then used to determine whether there is in
fact a clear north-south divide in home
ownership in the UK.
Literature Review
Home-ownership in the United Kingdom is
somewhat hegemonic; there is a widely held
cultural expectation and desire to own a home.
This is despite the average house price
increasing by some 35% in the last 10 years to
over £216,000 (The Land Registry, 2017).
Because of this, home ownership has
decreased in the last 30 years as younger
people are “priced out” of the housing market
(Osborne, 2016). The Office for National
Statistics states that in 1991 36% of 16-24 year
olds owned their own home, falling to 9% in
2014. The 35-44 age group has also seen a
drastic fall from 1991 to 2014, from 78%
ownership to 59%. By contrast, home
ownership amongst older age groups has
increased. However, Osborne (2016) found that
overall, the proportion of ownership has fallen
across every part of the UK since the early
2000s and as of publication, England was
seeing the lowest levels of home ownership in
30 years.
Throughout 2016 there were multiple news
articles published highlighting the deepening
north-south divide in the UK as defined by
house prices (Fraser, 2016; Milligan, 2016;
Shaw, 2016; Lynch, 2015). Research
conducted by ‘e-moov’, an online estate agent,
defined the north-south divide based on a “clear
boundary” which snaked across the Midlands
from Bristol to Norfolk. Along this boundary, the
difference in average house prices is as much
as £160,000 between neighbouring counties (e-
moov, 2016). This disparity has led to the claim
that “house prices may permanently diverge
from earnings” causing increasingly
unaffordable houses (Gregoriou, et al., 2014).
However, given the complexity of the national
social demographic, and the additional
complexity of factors affecting home ownership
ENVS450 – Assignment 3 200923027
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rates across the country, the research best
describes the factors as “heterogenic” as they
vary from one part of the country to another
depending on a web of other variables
(Montagnoli & Nagayasu, 2013).
Methodology
A census subset used was taken from the 2011
census – a survey of England and Wales which
determined a resident population of 56.1 million
people (Office for National Statistics, 2011).
The dataset is not raw data, but rather a rate of
variable occurrence within the population of
each of the 348 districts in England and Wales.
An Ordinary Least Squares Regression
analysis was used in alignment with the
standard demographic approach to analyse
only variables that were statistically significant
to the model. The explanatory variables chosen
at the start of the study are as follows:
 Rate of professional employment
$Professionals
 Rate of households which do not own a
car $No_Cars
 Rate of residents Aged 65 or more
$Age_65plus
 Rate of Illness $illness
 Location within England and Wales
$NorthMidlandsSouth
The statistical significance of these variables
was not known when they were selected, so
some may be subject to dismissal during the
statistical analysis. These variables were
selected based on sparse literature surrounding
factors concerning home ownership
$Owner_occupied (Montagnoli & Nagayasu,
2013), as well as using empirical reasoning.
All the explanatory variables are continuous,
except for $NorthMidlandsSouth which is
categoric. This variable was created by
grouping districts based on their region in the
UK. The categories are: North, Midlands,
South; with Midlands encompassing the area
along the north-south boundary described by
‘e-moov’ which lacks some clarity. It is hoped
that by the end of the analysis, the Midlands
category will identify more with either North or
South, rather than existing as its own unique
region, as this would suggest that there is
indeed a “north-south divide” when it comes to
house prices.
Results
Before the main regression analysis can begin,
it is important to gain some understanding of the
relationship between the outcome variable
$Owner_occupied and the continuous
explanatory variables. Each of the 4 continuous
explanatory variables was plotted against
$Owner_occupied, with a second graph
plotted to assess Skewness. Figure 1 shows
the graphs.
From Figure 1, it is evident that all variables
except $Age_65plus are not normally
distributed. Pearson’s correlation requires
normal distribution, so Spearman’s Rank
correlation coefficient must be used instead to
establish the correlation between the variables.
The rs results from the Spearman’s Rank
calculations are included on each graph. The
results from Figure 1 are perhaps not
surprising, apart from that of
$Professionals, which shows weak
correlation between the explanatory and
outcome variables. However, this is not yet
cause for concern as this analysis does not
ENVS450 – Assignment 3 200923027
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consider spatial distribution of the districts
within each region at this stage.
Figure 1 – the relationship of each explanatory
variable in relation to the outcome variable, and
their Skewness
Next, a Multivariate Linear Regression Model
was fitted to establish the variance between the
variables. The following code was run in R:
> lm(Owner_occupied ~ No_Cars + Pr
ofessionals + illness + Age_65plus
+ NorthMidlandsSouth, data=census)
This model was developed by creating 5
progressively more complex models, each one
incorporating an additional variable from the 5
explanatory variables. Table 1 shows how each
model fared in increasing the model’s statistical
significance using Akaike’s Information
Criterion (AIC). For AIC, the smaller the value,
the more significant the model is.
Table 1 – multiple regression model output of
AIC results for each progressive model
Model Additional Variable AIC
1 $NorthMidlandsSouth 2582.018
2 $Age_65plus 2381.025
3 $No_Cars 1894.315
4 $Professionals 1889.316
5 $illness 1871.359
Table 1 shows the AIC reducing with each
additional variable, but the reduction in AIC gets
smaller and smaller, particularly between
models 3 and 4 where there is only a 5 point
reduction in AIC. However, the reduction still
contributes to the understanding and outcome
of the model, even if it does increase the
complexity by 20%. Therefore, model 5 will
become the model used for this study.
From this model, the coefficients can be
examined to write the fitted model in readable
terms:
> coefficients(model)
The output of the above code is displayed in
Table 2, the data from which was used to write
the fitted model:
% Home Owners = 67.37 – 0.82 + 0.37 +
0.64 + 0.13 – 1.17 + 1.94
The R2
of the model can also be obtained:
> summary(model)$r.squared
[1] 0.8767051
The R2
value of 0.87 suggests that the model
has a good fit. However, such a high R2
value
ENVS450 – Assignment 3 200923027
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does not necessarily mean that the fit is good.
The residuals must be considered to check how
the data is distributed about the horizon.
> plot(resid(model))
This outputs the graph in Figure 2, which shows
that the residuals are fairly evenly distributed
throughout the plot, suggesting that there is in
fact a good fit within this model, and that the R2
value of 0.87 can be respected.
Table 2 – coefficients of the fitted linear
regression model of all predictor variables
Variable Coefficient
(Intercept) 67.37
$No_Cars -0.82
$Professionals 0.37
$illness 0.64
$Age_65plus 0.13
$NorthMidlandsSouth[S] -1.17
$NorthMidlandsSouth[N] 1.94
This now means that the fitted model is able to
explain 87% of the spatial variation in home
ownership, based on the explanatory variables.
With only one explanatory variable
($NorthMidlandsSouth) used, the model
can only explain 2.7% of the spatial variation in
home ownership, meaning that the remaining 4
explanatory variables increase the accuracy of
the model by over 84%.
> summary(lm(Owner_occupied ~ Nort
hMidlandsSouth, data=census))$r.sq
uared
[1] 0.02767543
> 0.027*100
[1] 2.7
The model can also be checked using AIC
which eliminates the issue of the R2
value
automatically increasing for each variable
added to the model.
> AIC(model)
[1] 1871.359
> AIC(lm(Owner_occupied ~ NorthMid
landsSouth, data = census))
[1] 2582.018
This shows that increasing the complexity of the
model reduces the AIC score from 2582 to 1871
meaning that the additional complexity is
statistically significant and worthwhile.
Figure 2 – a residual plot of the fitted model
with R2
value of 0.87
To validate the model thus far, the model
residuals were checked to ensure normal
distribution. Figure 3 shows the model residuals
plotted as a graph, displaying very slight
positive skewness. This can be calculated:
> skew(model$residuals)
[1] 0.04953776
The skewness value for this model is calculated
as 0.04, which is so slight that the distribution is
essentially a symmetric distribution.
A ‘QQ’ plot was also generated to check the
skewness of the model. Rodríguez (2016)
states that a QQ plot showing curvature would
indicate skew distributions. The QQ plot
generated for this model is shown in Figure 4.
The plot is slightly curved at each end, but
ENVS450 – Assignment 3 200923027
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broadly follows a straight line across the
majority of the points within the dataset
suggesting only minimal skew. Given the equal
mirrored curvature at each end of the graph in
Figure 4, this largely cancels, resulting in only a
slight overall positive skew, which is what the
graph in Figure 3 and the skew calculations
previously discussed indicate. This gives
reasonable confidence to move on to the next
stage in validating the model which is to check
for constancy in error variance.
Figure 3 – model residuals plotted to show the
skewness of the model. The model is
symmetrically distributed
Figure 4 – a QQ plot of the model showing
minimal positive overall skew
The constancy was checked using a ‘spread-
level’ plot which is displayed in Figure 5.
Figure 5 shows a near-horizontal line of best fit
and no clear curvature in the scatter plot (the
few points in the bottom right are not significant
compared to the bulk of points above), together
these two properties show a constant error
variance.
Figure 5 – a spread-level plot of the model
residuals showing a near-horizontal line of best
fit suggesting constant error variance
Next, the multicollinearity of the model is tested.
This checks whether the explanatory variables
used in the model are strongly correlated in
combination. To check the multicollinearity of
the model, the following code was run:
> sqrt(mean(car:::vif(model)))
[1] 1.417898
This value is well within the safe range
described by Kabacoff (2015), who describes
sqrt(VIF) values greater than 2.0 as concerning.
Next, the Ordinary Least Squares Regression
assumes that the relationship between each of
the explanatory variables and the outcome
variable are linear. A partial residual plot was
generated in Figure 6.
ENVS450 – Assignment 3 200923027
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Figure 6 – partial residual plots of the model
With the exception of the $Professionals
plot, each plot appears linear, accounting for
limited noise such as that in $Age_65plus.
However, on closer inspection the large
deviation from linearity in $Professionals is
caused by a single outlier (City of London
district) which has a much higher than average
rate of professional workers. This is hardly
surprising, and as it is only a single point, the
red line of best fit follows the expected trajectory
of the green line to the point of deviation. It can
therefore be said that there is no obvious
departure from linearity from any of the
explanatory variables in the model.
Given all of the checks made, the model
appears to be robust and statistically sound.
The model output was then used to conduct a
multivariate principle components analysis in
PAST, shown in Figure 7 and larger in Appendix 3
Figure 7 – a multivariate principle component analysis of the model, conducted in PAST
Figure 7 shows each of the 348 districts within
the census dataset plotted according to their
residuals on axis 4 and 5 ($Owner_occupied
and $Professionals) of Model 5. It shows
ENVS450 – Assignment 3 200923027
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how the districts are seated in relation to each
other and the variables of the model, colour-
coded by the region of the UK to which they
belong, as defined in the model design
($NorthMidlandsSouth).
It is clear from Figure 7 that there is a lot of
overlap amongst the districts from each region,
which is to be expected. The interesting regions
are those which extend away from the central
cluster, as these are the ones that move away
from the “average” and begin to define the wider
region.
Focussing first on the North, the districts are
pulled toward the right and down, suggesting a
greater influence from $illness and
$No_Cars than the other regions. Figure 8A
shows that the North does indeed have the
highest average rate of no-car ownership.
However, Figure 8B shows that the Midlands
has a higher rate of illness, with a peculiar
positive linear relationship between $illness
and home ownership in the South which defies
empirical thought and goes against the
negative relationship of the North and Midlands.
The North also experiences a fairly significant
pull upwards by $Age_65plus, which is aligns
with Figure 8D which shows that the North has
2nd
highest rate of people aged over 65, though
in Figure 7 a lot of those districts influenced by
a high rate of older people also see strong
influences from professional workers.
Next, the South appears to have a much
broader spread than the other two regions, but
with 184 districts, it is exactly twice the size of
the North (largely owing to the higher
population and therefore larger number of
districts). Figure 7 shows that the South has a
large cluster positioned toward the left of the
graph, which appears to traverse the length of
Figure 8 – separate regression models for each
explanatory variable against the outcome var.
A
B
C
D
ENVS450 – Assignment 3 200923027
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the Y-axis, suggesting strong influences from
an aging population, home ownership and no-
car ownership, with little impact from the rate of
illness and rate of professionals in each district.
Figure 7 is backed up by Figure 8D which
shows that the South has the largest range in
the variable $Age_65plus of any of the
explanatory variables. Figure 8A shows that the
rate of no-car ownership has the largest impact
on the South, while Figure 8C shows – perhaps
counter-intuitively – that increased rate of
professional employees within a district leads to
lower rates of home ownership. However, this
is most-likely a result of people living and
working within London districts, where house
prices are high and workers may rent
accommodation as they may be expecting to
move in line with work commitments.
Nevertheless, 8C supports Figure 7’s apparent
lack of influence from $Professionals.
Finally, Figure 7 shows that there is a pull to the
right side of the graph with the Midlands region.
This suggests high rates of illness and high
rates of professionals in the workforce. Figures
8B & 8C support this, showing that the Midlands
has the highest average rates of both illness
and professional workforce.
Conclusion
This study has found a number of key points:
 The final model (Model 5 in Table 1) was
statistically significant and the model
validation steps show this.
 There are great disparities between the
North and South across all variables
except $No_Cars, where each of the 3
regions had very well correlated plots,
such as that in Figure 8A.
 The Midlands often aligns very closely with
the North, as Figure 8 shows well. Figure
7 displays a lot of overlap between the
Midlands and the North – much more so
than any region does with the South.
 Home ownership in the South is impacted
differently to what the literature suggests,
and what may be reasonably expected –
for example: higher rate of professionals in
a district = lower rate of home ownership.
This indicates that the South is subject to
different pressures and factors than the
North when it comes to home ownership.
Given that the Midlands aligns so closely with
the North rather than the South, it would make
sense to group the two regions together, as the
report by ‘e-moov’ did. This would not only
serve to increase the statistical significance of
the North (by giving this region a similar number
of districts to the South), but it would also make
logical sense given that this study has proven
the districts classified as “Midlands” to actually
be statistically similar to those classified as
“North”.
What this essentially means is that there is
indeed a north-south property divide in England
and Wales. The boundary is clear: from Bristol
in the west, across Warwickshire and
Gloucestershire, across to Leicestershire and
Norfolk in the east – as stated by ‘e-moov’ in
their 2016 report.
Obviously, this study did not look at the spatial
economics of homeownership in a statistical
sense, though empirically it is understood and
respected that property costs more in the
South. This study instead focused on just a few
social variables from the 2011 census in order
to draw this conclusion. A future study would
benefit from greater complexity in the modelling
ENVS450 – Assignment 3 200923027
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(increased number of social variables) as well
as incorporating some economic factors to
paint a much clearer picture of the wider issues
that we as a nation face when it comes to home
ownership and house prices.
References
e-moov, 2016. The North-South Property
Divide Defined, Brentwood: e-moov.
Fraser, I., 2016. This map shows just how stark
the north-south property divide is. The
Telegraph, 30 November.
Gregoriou, A., Kontonikas, A. & Montagnoll, A.,
2014. Aggregate and regional house price to
earnings ratio dynamics in the UK. Urban
Studies, 51(13), pp. 2916-2927.
Kabacoff, R., 2015. R in Action: Data Analysis
and Graphics with R. 2nd ed. Greenwich, CT:
Manning.
Land Registry, 2017. House Price Index for
United Kingdom; January 2006 to January
2016. [Online]
Available at:
http://landregistry.data.gov.uk/app/ukhpi/explor
e
[Accessed 1 January 2017].
Lynch, R., 2015. North-South divide in house
prices is highest ever. The Independent, 30
December.
Milligan, B., 2016. North-South house price
divide hits record high. BBC News Business, 1
April.
Montagnoli, A. & Nagayasu, J., 2013. An
Investigation of Housing Affordability in the UK
Regions, Glasgow: Scottish Institute for
Research in Economics.
Office for National Statistics, 2011. 2011
Census: Key Statistics for England and Wales,
March 2011. [Online]
Available at:
https://www.ons.gov.uk/peoplepopulationandc
ommunity/populationandmigration/populatione
stimates/bulletins/2011censuskeystatisticsfore
nglandandwales/2012-12-11#key-points
[Accessed 26 December 2016].
Office for National Statistics, 2016. UK
Perspectives 2016: Housing and
homeownership in the UK. [Online]
Available at: http://visual.ons.gov.uk/uk-
perspectives-2016-housing-and-home-
ownership-in-the-uk/
[Accessed 25 December 2016].
Osborne, H., 2016. Home ownership in
England at lowest level in 30 years as housing
crisis grows. The Guardian, 2 August.
Rodríguez, G., 2016. Generalized Linear
Models. [Online]
Available at:
http://data.princeton.edu/wws509/notes/c2s9.h
tml
[Accessed 1 January 2017].
Shaw, V., 2016. Buyers vs sellers – the new
north-south divide on house prices. Mirror, 17
October.
ENVS450 – Assignment 3 200923027
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Appendix 1 :: R Code
###########################################################
#### Assignment 3 ####
### "England’s North-South Divide: exploring the impact of socio-
demographic variables on the rate of home-ownership by geographic location"
###
###########################################################
## Load Libraries & Data ##
source("functions.R")
load(file = "2011 Census.RData")
load(file = "QLFS.RData")
library(plyr)
load.package("mosaic")
load.package("reshape2")
load.package("ggplot2")
load.package("car")
load.package("scales")
load.package("MASS")
load.package("pls")
###########################################################
## Dataset to be 2011 Census ##
## Output variable chosen to be $Owner_occupied ##
## Explanatory vars to be $Professionals, $Age_65plus, $No_Cars and
$illness ##
## (explanatory vars chosen from literature and logic) ##
# Insert the vars into an array for later use #
explan.vars <- c("Professionals","Age_65plus","illness","No_Cars")
###########################################################
### Explore the relationship between outcome and explan. vars ###
## Function to generate a scatter plot with best fit line ##
generateXbyY <- function(inputX, inputY){
return(ggplot(data=census) +
geom_point(aes_string(x="Owner_occupied", y=inputY) ) +
geom_smooth(method = "lm",fullrange=TRUE,
aes_string(x="Owner_occupied", y=inputY)) +
theme_bw() +
geom_vline(xintercept = 0) +
geom_hline(yintercept = 0) +
theme(axis.line = element_line(colour = "black"),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
panel.background = element_blank()))
}
ENVS450 – Assignment 3 200923027
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# Output a scatter for each explan. var #
for (i in explan.vars) {
generateXbyY("Owner_occupied",i)
}
## Function to generate skew plots for explan. vars ##
generateSkew <- function(inputY) {
return(qplot(inputY, data=census, geom="histogram", binwidth=1))
}
# Output a skew graph for each explan. var #
for (i in explan.vars) {
generateSkew(i)
}
###########################################################
## Up to now, all vars appear to be suitable, though the ##
## Skewness indicates that Spearman's Rank must be used ##
## in place of Pearson's correlation coefficient ##
###########################################################
### Build the model; assess statistical significance ###
## Start with 1 var ($NorthMidlandsSouth - spatial) ##
## and then add consecutive explan. vars ##
model1 <- lm(Owner_occupied ~ NorthMidlandsSouth, data=census)
model2 <- lm(Owner_occupied ~ NorthMidlandsSouth + Age_65plus, data=census)
model3 <- lm(Owner_occupied ~ NorthMidlandsSouth + Age_65plus + No_Cars,
data=census)
model4 <- lm(Owner_occupied ~ NorthMidlandsSouth + Age_65plus + No_Cars +
Professionals, data=census)
model5 <- lm(Owner_occupied ~ NorthMidlandsSouth + Age_65plus + No_Cars +
Professionals + illness, data=census)
# Check whether there is stat. sig. between each model #
anova(model1,model2,model3,model4,model5)
# Check that AIC is reducing from one model to the next #
AIC (model1,model2,model3,model4,model5)
###########################################################
## Everything looks good, so adopt the most complex model ##
## as --the-- model for the study ##
model <- model5
###########################################################
### Begin the validation of the model - check it is ###
### actually statistically significant ###
## Output the coefficents and obtain R-sq. value ##
coefficients(model)
summary(model)$r.squared
#-- R-sq. = 0.87 #
ENVS450 – Assignment 3 200923027
Page 12
## Don't take R-sq. at face value - check residuals are ##
## distributed evenly! ##
plot(resid(model))
abline(0,0)
#-- Residuals appear evenly distributed about the horizon #
#-- all seems good so far #
summary(model)$r.squared*100
#-- 87.67 #
#-- this means that >87% of the variation is explained by the model #
summary(model1)$r.squared*100
#-- 2.76 #
#-- model1() only explains 2.67% of variation - model() is much better! #
AIC(model)
#-- 1871.359 #
AIC(model1)
#-- 2582.018 #
#-- This shows a great reduction from model1() to model() meaning #
#-- that additional model complexity = greater stat. sig. #
## Next, the skewness of the model can be checked. Given that the checks ##
## made up to now indicate a good model, skewness should be limited at most
##
skew(model$residuals)
#-- 0.049.. - basically negligible; points to symmetric distribution #
## Next generate a QQ-plot to check skewness ##
#-- expect to find good fit to line given skew value of 0.04 #
p2<-ggplot(model, aes(qqnorm(.stdresid)[[1]], .stdresid))+geom_point(na.rm
= TRUE)
p2<-p2+geom_abline(aes(qqline(.stdresid)))+xlab("Theoretical
Quantiles")+ylab("Standardized Residuals")
p2<-p2+ggtitle("Normal Q-Q")+theme_bw()
p2
#-- Indeed, all but a few points appear to follow the line #
## Spread-level plot to show residual fit when studentized ##
car:::spreadLevelPlot(model)
#-- the near-horizontal line of best fit is good as it shows a good
linearity #
#-- also the lack of curvature in the scatter indicates good distribution
of residuals #
## Multicollinearity ##
# Check whether the explan. vars are strongly correlated in combination #
sqrt(mean(car:::vif(model)))
#-- 1.41 ... this is good according to Kabacoff(2015 -- see References) #
#-- Kabacoff says >2.0 is concerning #
## OLS expects linear relationship of explan. vs. outcome ##
# Plot partial residual plots to check this #
car:::crPlots(model)
#-- good, as no obvious departure from linearity in any explan. var #
ENVS450 – Assignment 3 200923027
Page 13
###########################################################
## Model appears good; export data to PAST and plot fixed slopes ##
## to check each var in relation to each region simultaneously ##
###########################################################
## Function to generate fixed slope scatters of all regions for any explan.
var ##
generateFixedSlope <- function(inputX) {
ggplot(data=census) +
geom_point( aes_string(x=inputX, y="Owner_occupied",
colour="NorthMidlandsSouth") ) +
geom_smooth(method = "lm", se = FALSE, aes_string(x=inputX,
y="Owner_occupied", colour="NorthMidlandsSouth")) +
theme_bw() +
geom_vline(xintercept = 0) +
geom_hline(yintercept = 20) +
theme(axis.line = element_line(colour = "black"),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
panel.background = element_blank())
}
# Output a fixed slope for each explan. var #
for (i in explan.vars) {
generateFixedSlope(i)
}
###########################################################
ENVS450 – Assignment 3 200923027
Page 14
Appendix 2 :: Output to PAST
0 $illness $Age_65plus $No_Cars $Owner_occupied $Professionals
Midlands 0.85722 7.8872 -0.20675 -3.177 3.5413
Midlands 7.0449 7.8189 -0.46525 0.68677 3.0232
Midlands 3.6226 3.5087 -2.6487 -2.7353 1.0627
Midlands 8.0847 2.9307 1.7398 -2.3016 0.55221
Midlands 11.396 -4.9062 -2.1232 -0.18976 0.59395
Midlands 1.0382 4.2181 -2.0911 2.5569 -0.33778
Midlands 0.27413 7.3475 -1.4628 -0.51751 2.8294
Midlands -11.045 2.215 -0.28043 -2.7259 -1.4466
Midlands 7.2488 2.8637 3.7624 -3.5941 -0.54167
Midlands 1.3298 6.1872 -0.67978 -3.0022 1.1709
Midlands 4.6799 3.5683 -2.0605 2.6072 0.82615
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ENVS450 – Assignment 3 200923027
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ENVS450 – Assignment 3 200923027
Page 16
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ENVS450 – Assignment 3 200923027
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ENVS450 – Assignment 3 200923027
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ENVS450 – Assignment 3 200923027
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ENVS450 – Assignment 3 200923027
Page 20
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South 18.733 -11.635 4.0124 -3.1947 1.0936
South -53.776 -6.6146 8.5886 4.6679 0.79874
South 5.728 -2.017 -3.1428 2.236 -0.6914
South 0.96073 -1.6202 -5.2604 -4.1717 -1.1096
South 12.739 -8.1378 1.1425 1.1522 0.52633
South 11.567 -10.558 0.66026 1.7655 2.645
South 1.9793 -6.8395 -6.1936 -1.8674 -0.16077
South -3.4207 -6.4703 -3.2157 -1.6712 -0.0054187
South 9.6436 -5.5921 -0.50932 1.6979 0.45826
South 10.592 -11.834 3.6683 -0.2431 2.3942
South 9.972 -4.8239 -1.4161 -0.65227 -0.3212
South 7.8213 -10.618 -0.10802 2.3535 1.1876
South 6.8263 -4.2303 -2.32 2.2128 0.45182
South -0.88866 4.6184 -0.58191 2.5633 -0.0086849
South 7.9825 -9.5221 1.1806 -0.99352 0.99509
South 10.517 -6.2951 -1.7931 2.1132 0.02828
South 1.6544 2.9521 3.3628 0.4669 -0.849
South -0.060084 -3.2732 -2.0307 -2.6568 -0.25603
South 9.9679 -8.1541 0.85484 2.0034 1.0795
ENVS450 – Assignment 3 200923027
Page 21
Appendix 3 :: Large-scale PCA graph

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England's North-South Divide on Home Ownership

  • 1. ENVS450 – Assignment 3 200923027 Page 1 England’s North-South Divide: exploring the impact of socio-demographic variables on the rate of home-ownership by geographic location Introduction The “north-south divide” is a widely debated social phenomena in the UK, and is often used to describe the cultural, social, political and economic differences between the two halves of the country, with the south generally determined to be “out-performing” the north. This has been officially recognised by the current Conservative government with the instatement of the Northern Powerhouse project, which aims to re-balance economic disparity between the north and south. However, house prices between the north and south differ enormously, with the average house price in the south far-exceeding the wages of all but the most senior employees, making the prospect of mortgages completely unrealistic for most the workforce. Several factors were identified which would realistically impact home ownership across the whole of the UK. These were taken from a list of census variables and include: rate of professional employment, rate of households without a car, rate of residents aged 65 plus, rate of illness and location within the UK. Given the nature of the census dataset, each variable has 348 instances, existing once for each district in England and Wales. These variables were then used to determine whether there is in fact a clear north-south divide in home ownership in the UK. Literature Review Home-ownership in the United Kingdom is somewhat hegemonic; there is a widely held cultural expectation and desire to own a home. This is despite the average house price increasing by some 35% in the last 10 years to over £216,000 (The Land Registry, 2017). Because of this, home ownership has decreased in the last 30 years as younger people are “priced out” of the housing market (Osborne, 2016). The Office for National Statistics states that in 1991 36% of 16-24 year olds owned their own home, falling to 9% in 2014. The 35-44 age group has also seen a drastic fall from 1991 to 2014, from 78% ownership to 59%. By contrast, home ownership amongst older age groups has increased. However, Osborne (2016) found that overall, the proportion of ownership has fallen across every part of the UK since the early 2000s and as of publication, England was seeing the lowest levels of home ownership in 30 years. Throughout 2016 there were multiple news articles published highlighting the deepening north-south divide in the UK as defined by house prices (Fraser, 2016; Milligan, 2016; Shaw, 2016; Lynch, 2015). Research conducted by ‘e-moov’, an online estate agent, defined the north-south divide based on a “clear boundary” which snaked across the Midlands from Bristol to Norfolk. Along this boundary, the difference in average house prices is as much as £160,000 between neighbouring counties (e- moov, 2016). This disparity has led to the claim that “house prices may permanently diverge from earnings” causing increasingly unaffordable houses (Gregoriou, et al., 2014). However, given the complexity of the national social demographic, and the additional complexity of factors affecting home ownership
  • 2. ENVS450 – Assignment 3 200923027 Page 2 rates across the country, the research best describes the factors as “heterogenic” as they vary from one part of the country to another depending on a web of other variables (Montagnoli & Nagayasu, 2013). Methodology A census subset used was taken from the 2011 census – a survey of England and Wales which determined a resident population of 56.1 million people (Office for National Statistics, 2011). The dataset is not raw data, but rather a rate of variable occurrence within the population of each of the 348 districts in England and Wales. An Ordinary Least Squares Regression analysis was used in alignment with the standard demographic approach to analyse only variables that were statistically significant to the model. The explanatory variables chosen at the start of the study are as follows:  Rate of professional employment $Professionals  Rate of households which do not own a car $No_Cars  Rate of residents Aged 65 or more $Age_65plus  Rate of Illness $illness  Location within England and Wales $NorthMidlandsSouth The statistical significance of these variables was not known when they were selected, so some may be subject to dismissal during the statistical analysis. These variables were selected based on sparse literature surrounding factors concerning home ownership $Owner_occupied (Montagnoli & Nagayasu, 2013), as well as using empirical reasoning. All the explanatory variables are continuous, except for $NorthMidlandsSouth which is categoric. This variable was created by grouping districts based on their region in the UK. The categories are: North, Midlands, South; with Midlands encompassing the area along the north-south boundary described by ‘e-moov’ which lacks some clarity. It is hoped that by the end of the analysis, the Midlands category will identify more with either North or South, rather than existing as its own unique region, as this would suggest that there is indeed a “north-south divide” when it comes to house prices. Results Before the main regression analysis can begin, it is important to gain some understanding of the relationship between the outcome variable $Owner_occupied and the continuous explanatory variables. Each of the 4 continuous explanatory variables was plotted against $Owner_occupied, with a second graph plotted to assess Skewness. Figure 1 shows the graphs. From Figure 1, it is evident that all variables except $Age_65plus are not normally distributed. Pearson’s correlation requires normal distribution, so Spearman’s Rank correlation coefficient must be used instead to establish the correlation between the variables. The rs results from the Spearman’s Rank calculations are included on each graph. The results from Figure 1 are perhaps not surprising, apart from that of $Professionals, which shows weak correlation between the explanatory and outcome variables. However, this is not yet cause for concern as this analysis does not
  • 3. ENVS450 – Assignment 3 200923027 Page 3 consider spatial distribution of the districts within each region at this stage. Figure 1 – the relationship of each explanatory variable in relation to the outcome variable, and their Skewness Next, a Multivariate Linear Regression Model was fitted to establish the variance between the variables. The following code was run in R: > lm(Owner_occupied ~ No_Cars + Pr ofessionals + illness + Age_65plus + NorthMidlandsSouth, data=census) This model was developed by creating 5 progressively more complex models, each one incorporating an additional variable from the 5 explanatory variables. Table 1 shows how each model fared in increasing the model’s statistical significance using Akaike’s Information Criterion (AIC). For AIC, the smaller the value, the more significant the model is. Table 1 – multiple regression model output of AIC results for each progressive model Model Additional Variable AIC 1 $NorthMidlandsSouth 2582.018 2 $Age_65plus 2381.025 3 $No_Cars 1894.315 4 $Professionals 1889.316 5 $illness 1871.359 Table 1 shows the AIC reducing with each additional variable, but the reduction in AIC gets smaller and smaller, particularly between models 3 and 4 where there is only a 5 point reduction in AIC. However, the reduction still contributes to the understanding and outcome of the model, even if it does increase the complexity by 20%. Therefore, model 5 will become the model used for this study. From this model, the coefficients can be examined to write the fitted model in readable terms: > coefficients(model) The output of the above code is displayed in Table 2, the data from which was used to write the fitted model: % Home Owners = 67.37 – 0.82 + 0.37 + 0.64 + 0.13 – 1.17 + 1.94 The R2 of the model can also be obtained: > summary(model)$r.squared [1] 0.8767051 The R2 value of 0.87 suggests that the model has a good fit. However, such a high R2 value
  • 4. ENVS450 – Assignment 3 200923027 Page 4 does not necessarily mean that the fit is good. The residuals must be considered to check how the data is distributed about the horizon. > plot(resid(model)) This outputs the graph in Figure 2, which shows that the residuals are fairly evenly distributed throughout the plot, suggesting that there is in fact a good fit within this model, and that the R2 value of 0.87 can be respected. Table 2 – coefficients of the fitted linear regression model of all predictor variables Variable Coefficient (Intercept) 67.37 $No_Cars -0.82 $Professionals 0.37 $illness 0.64 $Age_65plus 0.13 $NorthMidlandsSouth[S] -1.17 $NorthMidlandsSouth[N] 1.94 This now means that the fitted model is able to explain 87% of the spatial variation in home ownership, based on the explanatory variables. With only one explanatory variable ($NorthMidlandsSouth) used, the model can only explain 2.7% of the spatial variation in home ownership, meaning that the remaining 4 explanatory variables increase the accuracy of the model by over 84%. > summary(lm(Owner_occupied ~ Nort hMidlandsSouth, data=census))$r.sq uared [1] 0.02767543 > 0.027*100 [1] 2.7 The model can also be checked using AIC which eliminates the issue of the R2 value automatically increasing for each variable added to the model. > AIC(model) [1] 1871.359 > AIC(lm(Owner_occupied ~ NorthMid landsSouth, data = census)) [1] 2582.018 This shows that increasing the complexity of the model reduces the AIC score from 2582 to 1871 meaning that the additional complexity is statistically significant and worthwhile. Figure 2 – a residual plot of the fitted model with R2 value of 0.87 To validate the model thus far, the model residuals were checked to ensure normal distribution. Figure 3 shows the model residuals plotted as a graph, displaying very slight positive skewness. This can be calculated: > skew(model$residuals) [1] 0.04953776 The skewness value for this model is calculated as 0.04, which is so slight that the distribution is essentially a symmetric distribution. A ‘QQ’ plot was also generated to check the skewness of the model. Rodríguez (2016) states that a QQ plot showing curvature would indicate skew distributions. The QQ plot generated for this model is shown in Figure 4. The plot is slightly curved at each end, but
  • 5. ENVS450 – Assignment 3 200923027 Page 5 broadly follows a straight line across the majority of the points within the dataset suggesting only minimal skew. Given the equal mirrored curvature at each end of the graph in Figure 4, this largely cancels, resulting in only a slight overall positive skew, which is what the graph in Figure 3 and the skew calculations previously discussed indicate. This gives reasonable confidence to move on to the next stage in validating the model which is to check for constancy in error variance. Figure 3 – model residuals plotted to show the skewness of the model. The model is symmetrically distributed Figure 4 – a QQ plot of the model showing minimal positive overall skew The constancy was checked using a ‘spread- level’ plot which is displayed in Figure 5. Figure 5 shows a near-horizontal line of best fit and no clear curvature in the scatter plot (the few points in the bottom right are not significant compared to the bulk of points above), together these two properties show a constant error variance. Figure 5 – a spread-level plot of the model residuals showing a near-horizontal line of best fit suggesting constant error variance Next, the multicollinearity of the model is tested. This checks whether the explanatory variables used in the model are strongly correlated in combination. To check the multicollinearity of the model, the following code was run: > sqrt(mean(car:::vif(model))) [1] 1.417898 This value is well within the safe range described by Kabacoff (2015), who describes sqrt(VIF) values greater than 2.0 as concerning. Next, the Ordinary Least Squares Regression assumes that the relationship between each of the explanatory variables and the outcome variable are linear. A partial residual plot was generated in Figure 6.
  • 6. ENVS450 – Assignment 3 200923027 Page 6 Figure 6 – partial residual plots of the model With the exception of the $Professionals plot, each plot appears linear, accounting for limited noise such as that in $Age_65plus. However, on closer inspection the large deviation from linearity in $Professionals is caused by a single outlier (City of London district) which has a much higher than average rate of professional workers. This is hardly surprising, and as it is only a single point, the red line of best fit follows the expected trajectory of the green line to the point of deviation. It can therefore be said that there is no obvious departure from linearity from any of the explanatory variables in the model. Given all of the checks made, the model appears to be robust and statistically sound. The model output was then used to conduct a multivariate principle components analysis in PAST, shown in Figure 7 and larger in Appendix 3 Figure 7 – a multivariate principle component analysis of the model, conducted in PAST Figure 7 shows each of the 348 districts within the census dataset plotted according to their residuals on axis 4 and 5 ($Owner_occupied and $Professionals) of Model 5. It shows
  • 7. ENVS450 – Assignment 3 200923027 Page 7 how the districts are seated in relation to each other and the variables of the model, colour- coded by the region of the UK to which they belong, as defined in the model design ($NorthMidlandsSouth). It is clear from Figure 7 that there is a lot of overlap amongst the districts from each region, which is to be expected. The interesting regions are those which extend away from the central cluster, as these are the ones that move away from the “average” and begin to define the wider region. Focussing first on the North, the districts are pulled toward the right and down, suggesting a greater influence from $illness and $No_Cars than the other regions. Figure 8A shows that the North does indeed have the highest average rate of no-car ownership. However, Figure 8B shows that the Midlands has a higher rate of illness, with a peculiar positive linear relationship between $illness and home ownership in the South which defies empirical thought and goes against the negative relationship of the North and Midlands. The North also experiences a fairly significant pull upwards by $Age_65plus, which is aligns with Figure 8D which shows that the North has 2nd highest rate of people aged over 65, though in Figure 7 a lot of those districts influenced by a high rate of older people also see strong influences from professional workers. Next, the South appears to have a much broader spread than the other two regions, but with 184 districts, it is exactly twice the size of the North (largely owing to the higher population and therefore larger number of districts). Figure 7 shows that the South has a large cluster positioned toward the left of the graph, which appears to traverse the length of Figure 8 – separate regression models for each explanatory variable against the outcome var. A B C D
  • 8. ENVS450 – Assignment 3 200923027 Page 8 the Y-axis, suggesting strong influences from an aging population, home ownership and no- car ownership, with little impact from the rate of illness and rate of professionals in each district. Figure 7 is backed up by Figure 8D which shows that the South has the largest range in the variable $Age_65plus of any of the explanatory variables. Figure 8A shows that the rate of no-car ownership has the largest impact on the South, while Figure 8C shows – perhaps counter-intuitively – that increased rate of professional employees within a district leads to lower rates of home ownership. However, this is most-likely a result of people living and working within London districts, where house prices are high and workers may rent accommodation as they may be expecting to move in line with work commitments. Nevertheless, 8C supports Figure 7’s apparent lack of influence from $Professionals. Finally, Figure 7 shows that there is a pull to the right side of the graph with the Midlands region. This suggests high rates of illness and high rates of professionals in the workforce. Figures 8B & 8C support this, showing that the Midlands has the highest average rates of both illness and professional workforce. Conclusion This study has found a number of key points:  The final model (Model 5 in Table 1) was statistically significant and the model validation steps show this.  There are great disparities between the North and South across all variables except $No_Cars, where each of the 3 regions had very well correlated plots, such as that in Figure 8A.  The Midlands often aligns very closely with the North, as Figure 8 shows well. Figure 7 displays a lot of overlap between the Midlands and the North – much more so than any region does with the South.  Home ownership in the South is impacted differently to what the literature suggests, and what may be reasonably expected – for example: higher rate of professionals in a district = lower rate of home ownership. This indicates that the South is subject to different pressures and factors than the North when it comes to home ownership. Given that the Midlands aligns so closely with the North rather than the South, it would make sense to group the two regions together, as the report by ‘e-moov’ did. This would not only serve to increase the statistical significance of the North (by giving this region a similar number of districts to the South), but it would also make logical sense given that this study has proven the districts classified as “Midlands” to actually be statistically similar to those classified as “North”. What this essentially means is that there is indeed a north-south property divide in England and Wales. The boundary is clear: from Bristol in the west, across Warwickshire and Gloucestershire, across to Leicestershire and Norfolk in the east – as stated by ‘e-moov’ in their 2016 report. Obviously, this study did not look at the spatial economics of homeownership in a statistical sense, though empirically it is understood and respected that property costs more in the South. This study instead focused on just a few social variables from the 2011 census in order to draw this conclusion. A future study would benefit from greater complexity in the modelling
  • 9. ENVS450 – Assignment 3 200923027 Page 9 (increased number of social variables) as well as incorporating some economic factors to paint a much clearer picture of the wider issues that we as a nation face when it comes to home ownership and house prices. References e-moov, 2016. The North-South Property Divide Defined, Brentwood: e-moov. Fraser, I., 2016. This map shows just how stark the north-south property divide is. The Telegraph, 30 November. Gregoriou, A., Kontonikas, A. & Montagnoll, A., 2014. Aggregate and regional house price to earnings ratio dynamics in the UK. Urban Studies, 51(13), pp. 2916-2927. Kabacoff, R., 2015. R in Action: Data Analysis and Graphics with R. 2nd ed. Greenwich, CT: Manning. Land Registry, 2017. House Price Index for United Kingdom; January 2006 to January 2016. [Online] Available at: http://landregistry.data.gov.uk/app/ukhpi/explor e [Accessed 1 January 2017]. Lynch, R., 2015. North-South divide in house prices is highest ever. The Independent, 30 December. Milligan, B., 2016. North-South house price divide hits record high. BBC News Business, 1 April. Montagnoli, A. & Nagayasu, J., 2013. An Investigation of Housing Affordability in the UK Regions, Glasgow: Scottish Institute for Research in Economics. Office for National Statistics, 2011. 2011 Census: Key Statistics for England and Wales, March 2011. [Online] Available at: https://www.ons.gov.uk/peoplepopulationandc ommunity/populationandmigration/populatione stimates/bulletins/2011censuskeystatisticsfore nglandandwales/2012-12-11#key-points [Accessed 26 December 2016]. Office for National Statistics, 2016. UK Perspectives 2016: Housing and homeownership in the UK. [Online] Available at: http://visual.ons.gov.uk/uk- perspectives-2016-housing-and-home- ownership-in-the-uk/ [Accessed 25 December 2016]. Osborne, H., 2016. Home ownership in England at lowest level in 30 years as housing crisis grows. The Guardian, 2 August. Rodríguez, G., 2016. Generalized Linear Models. [Online] Available at: http://data.princeton.edu/wws509/notes/c2s9.h tml [Accessed 1 January 2017]. Shaw, V., 2016. Buyers vs sellers – the new north-south divide on house prices. Mirror, 17 October.
  • 10. ENVS450 – Assignment 3 200923027 Page 10 Appendix 1 :: R Code ########################################################### #### Assignment 3 #### ### "England’s North-South Divide: exploring the impact of socio- demographic variables on the rate of home-ownership by geographic location" ### ########################################################### ## Load Libraries & Data ## source("functions.R") load(file = "2011 Census.RData") load(file = "QLFS.RData") library(plyr) load.package("mosaic") load.package("reshape2") load.package("ggplot2") load.package("car") load.package("scales") load.package("MASS") load.package("pls") ########################################################### ## Dataset to be 2011 Census ## ## Output variable chosen to be $Owner_occupied ## ## Explanatory vars to be $Professionals, $Age_65plus, $No_Cars and $illness ## ## (explanatory vars chosen from literature and logic) ## # Insert the vars into an array for later use # explan.vars <- c("Professionals","Age_65plus","illness","No_Cars") ########################################################### ### Explore the relationship between outcome and explan. vars ### ## Function to generate a scatter plot with best fit line ## generateXbyY <- function(inputX, inputY){ return(ggplot(data=census) + geom_point(aes_string(x="Owner_occupied", y=inputY) ) + geom_smooth(method = "lm",fullrange=TRUE, aes_string(x="Owner_occupied", y=inputY)) + theme_bw() + geom_vline(xintercept = 0) + geom_hline(yintercept = 0) + theme(axis.line = element_line(colour = "black"), panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.border = element_blank(), panel.background = element_blank())) }
  • 11. ENVS450 – Assignment 3 200923027 Page 11 # Output a scatter for each explan. var # for (i in explan.vars) { generateXbyY("Owner_occupied",i) } ## Function to generate skew plots for explan. vars ## generateSkew <- function(inputY) { return(qplot(inputY, data=census, geom="histogram", binwidth=1)) } # Output a skew graph for each explan. var # for (i in explan.vars) { generateSkew(i) } ########################################################### ## Up to now, all vars appear to be suitable, though the ## ## Skewness indicates that Spearman's Rank must be used ## ## in place of Pearson's correlation coefficient ## ########################################################### ### Build the model; assess statistical significance ### ## Start with 1 var ($NorthMidlandsSouth - spatial) ## ## and then add consecutive explan. vars ## model1 <- lm(Owner_occupied ~ NorthMidlandsSouth, data=census) model2 <- lm(Owner_occupied ~ NorthMidlandsSouth + Age_65plus, data=census) model3 <- lm(Owner_occupied ~ NorthMidlandsSouth + Age_65plus + No_Cars, data=census) model4 <- lm(Owner_occupied ~ NorthMidlandsSouth + Age_65plus + No_Cars + Professionals, data=census) model5 <- lm(Owner_occupied ~ NorthMidlandsSouth + Age_65plus + No_Cars + Professionals + illness, data=census) # Check whether there is stat. sig. between each model # anova(model1,model2,model3,model4,model5) # Check that AIC is reducing from one model to the next # AIC (model1,model2,model3,model4,model5) ########################################################### ## Everything looks good, so adopt the most complex model ## ## as --the-- model for the study ## model <- model5 ########################################################### ### Begin the validation of the model - check it is ### ### actually statistically significant ### ## Output the coefficents and obtain R-sq. value ## coefficients(model) summary(model)$r.squared #-- R-sq. = 0.87 #
  • 12. ENVS450 – Assignment 3 200923027 Page 12 ## Don't take R-sq. at face value - check residuals are ## ## distributed evenly! ## plot(resid(model)) abline(0,0) #-- Residuals appear evenly distributed about the horizon # #-- all seems good so far # summary(model)$r.squared*100 #-- 87.67 # #-- this means that >87% of the variation is explained by the model # summary(model1)$r.squared*100 #-- 2.76 # #-- model1() only explains 2.67% of variation - model() is much better! # AIC(model) #-- 1871.359 # AIC(model1) #-- 2582.018 # #-- This shows a great reduction from model1() to model() meaning # #-- that additional model complexity = greater stat. sig. # ## Next, the skewness of the model can be checked. Given that the checks ## ## made up to now indicate a good model, skewness should be limited at most ## skew(model$residuals) #-- 0.049.. - basically negligible; points to symmetric distribution # ## Next generate a QQ-plot to check skewness ## #-- expect to find good fit to line given skew value of 0.04 # p2<-ggplot(model, aes(qqnorm(.stdresid)[[1]], .stdresid))+geom_point(na.rm = TRUE) p2<-p2+geom_abline(aes(qqline(.stdresid)))+xlab("Theoretical Quantiles")+ylab("Standardized Residuals") p2<-p2+ggtitle("Normal Q-Q")+theme_bw() p2 #-- Indeed, all but a few points appear to follow the line # ## Spread-level plot to show residual fit when studentized ## car:::spreadLevelPlot(model) #-- the near-horizontal line of best fit is good as it shows a good linearity # #-- also the lack of curvature in the scatter indicates good distribution of residuals # ## Multicollinearity ## # Check whether the explan. vars are strongly correlated in combination # sqrt(mean(car:::vif(model))) #-- 1.41 ... this is good according to Kabacoff(2015 -- see References) # #-- Kabacoff says >2.0 is concerning # ## OLS expects linear relationship of explan. vs. outcome ## # Plot partial residual plots to check this # car:::crPlots(model) #-- good, as no obvious departure from linearity in any explan. var #
  • 13. ENVS450 – Assignment 3 200923027 Page 13 ########################################################### ## Model appears good; export data to PAST and plot fixed slopes ## ## to check each var in relation to each region simultaneously ## ########################################################### ## Function to generate fixed slope scatters of all regions for any explan. var ## generateFixedSlope <- function(inputX) { ggplot(data=census) + geom_point( aes_string(x=inputX, y="Owner_occupied", colour="NorthMidlandsSouth") ) + geom_smooth(method = "lm", se = FALSE, aes_string(x=inputX, y="Owner_occupied", colour="NorthMidlandsSouth")) + theme_bw() + geom_vline(xintercept = 0) + geom_hline(yintercept = 20) + theme(axis.line = element_line(colour = "black"), panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.border = element_blank(), panel.background = element_blank()) } # Output a fixed slope for each explan. var # for (i in explan.vars) { generateFixedSlope(i) } ###########################################################
  • 14. ENVS450 – Assignment 3 200923027 Page 14 Appendix 2 :: Output to PAST 0 $illness $Age_65plus $No_Cars $Owner_occupied $Professionals Midlands 0.85722 7.8872 -0.20675 -3.177 3.5413 Midlands 7.0449 7.8189 -0.46525 0.68677 3.0232 Midlands 3.6226 3.5087 -2.6487 -2.7353 1.0627 Midlands 8.0847 2.9307 1.7398 -2.3016 0.55221 Midlands 11.396 -4.9062 -2.1232 -0.18976 0.59395 Midlands 1.0382 4.2181 -2.0911 2.5569 -0.33778 Midlands 0.27413 7.3475 -1.4628 -0.51751 2.8294 Midlands -11.045 2.215 -0.28043 -2.7259 -1.4466 Midlands 7.2488 2.8637 3.7624 -3.5941 -0.54167 Midlands 1.3298 6.1872 -0.67978 -3.0022 1.1709 Midlands 4.6799 3.5683 -2.0605 2.6072 0.82615 Midlands 11.076 0.31235 1.9994 1.6027 1.9106 Midlands 7.2012 -2.1536 0.064575 -2.8973 -1.2668 Midlands 4.3592 4.4369 -1.1857 -0.5565 1.3601 Midlands 3.1302 0.78879 -0.17583 -2.3434 -0.81525 Midlands -17.455 1.9164 -1.1694 -2.2336 -0.1411 Midlands 1.8093 4.1508 0.11173 -1.1229 -0.31587 Midlands 3.6002 3.5304 0.19376 -3.9051 -0.5915 Midlands 6.0664 -2.8024 -0.54453 -0.41755 -0.29223 Midlands 13.134 1.1216 -0.61859 0.93446 0.10251 Midlands 12.771 -5.951 5.7046 -1.0329 1.3068 Midlands 0.43999 4.5494 -4.5913 2.1363 -0.85498 Midlands 4.5735 3.07 1.989 -3.2174 -0.62703 Midlands 5.7082 0.57761 4.1684 -2.0652 0.44927 Midlands 9.624 1.5892 -1.8575 -1.0755 0.28713 Midlands 4.3786 8.4122 1.7571 3.7242 0.65657 Midlands -7.9642 1.4878 -0.62237 -1.511 0.12019 Midlands -6.2405 1.758 -4.0558 -3.228 -0.97438 Midlands 10.911 -0.7855 1.9958 3.27 0.54515 Midlands 16.966 -1.2754 2.0902 -4.7941 -1.895 Midlands 4.8783 7.1719 0.93778 -2.849 3.0232 Midlands -3.4763 5.4239 -0.64911 0.46544 2.5852 Midlands -10.055 -1.6308 -0.89229 -1.225 1.7948 Midlands 11.9 -0.0087905 1.6115 5.4292 0.96268 Midlands -1.4853 7.0442 -1.1299 -1.7502 2.0754 Midlands 16.939 -1.7578 3.8806 -1.0166 0.29292 Midlands 5.919 5.3949 -1.0926 3.7939 1.7093 Midlands 7.0402 10.086 -0.59193 5.6425 1.3653 Midlands -14.584 5.7582 -2.3034 -1.1967 -0.18489 Midlands 3.671 6.5465 -0.33861 1.5849 1.5402 Midlands 13.444 -0.8145 1.4154 0.063341 0.386 Midlands 8.2544 3.9283 -2.8718 4.4755 0.62074 Midlands 6.2035 -0.25805 1.5182 -2.215 0.36223 Midlands 16.142 -5.0745 2.4476 -2.0736 -0.71925 Midlands 13.14 -0.73057 1.0734 -2.6159 -0.85977 Midlands -4.8926 5.9385 -0.35997 0.95351 1.8206 Midlands -7.0815 10.777 -2.0678 -0.026287 3.5797 Midlands 0.71766 -1.3987 -3.8304 -2.2365 0.34461 Midlands 6.0893 5.9568 -2.3418 2.6846 0.68412
  • 15. ENVS450 – Assignment 3 200923027 Page 15 Midlands 0.093701 9.5176 2.1611 -4.296 2.8829 Midlands -22.322 0.95001 -4.915 -1.3708 -0.58205 Midlands 12.449 -2.1623 -0.99777 -3.7387 1.1898 Midlands 10.799 -2.6951 -2.4105 -1.4055 -0.13825 Midlands 8.6589 2.0363 -1.209 -2.2758 0.32404 Midlands -5.1849 3.9255 0.089491 -1.7258 0.81823 Midlands 4.8803 -0.82347 -1.6839 -2.201 -0.28188 Midlands 6.6028 1.4045 1.7853 -1.1955 1.6868 Midlands 6.8225 4.5027 0.33878 1.4156 1.1534 Midlands 7.7809 -0.47876 1.1022 0.34882 0.34635 Midlands 15.4 4.3482 2.5443 -2.1768 0.16168 Midlands 3.3583 -7.0793 1.2601 1.4438 1.2562 Midlands 0.0047059 10.858 0.4322 -1.4582 4.3125 Midlands 11.079 -4.1772 -0.73601 3.6817 -0.58698 Midlands 6.2861 2.2432 -0.060552 -0.1042 1.0742 Midlands 12.05 -3.4347 1.3945 4.112 0.42075 Midlands 2.5827 3.5057 0.28451 -1.0372 0.90234 Midlands 9.4137 -0.6944 -0.82755 -1.5248 0.65771 Midlands -4.0762 -1.7966 -3.1284 -2.7721 -0.74593 Midlands -12.915 1.4963 -5.1367 0.31482 -0.007617 Midlands -6.9007 5.1684 -1.1571 -0.94378 -0.21108 Midlands -30.219 2.32 -3.0388 -0.41093 -0.63442 Midlands 10.599 2.2798 -0.54801 1.0874 0.26623 Midlands 14.293 1.3184 4.7247 -4.6321 -2.049 Midlands 7.6681 0.48406 -1.6533 2.625 -0.090925 Midlands 2.3573 0.63114 -2.992 -3.6131 -0.13278 Midlands 7.688 -0.75256 4.4136 -1.1712 0.13171 Midlands -10.675 6.7207 -2.6714 -1.211 1.2511 Midlands 9.7302 -2.5774 -0.58345 -0.49786 -1.235 Midlands 1.2834 0.59254 -2.4249 -1.293 -0.40145 Midlands -5.6941 10.345 0.090669 -2.6144 3.6039 Midlands 6.4888 1.0423 -2.0991 3.4694 -0.36354 Midlands 11.132 4.5904 -1.943 1.8193 -0.7215 Midlands 6.9715 -0.95387 -1.1454 1.0355 -0.40557 Midlands -14.459 5.1513 -1.7368 0.13161 -0.3469 Midlands -1.3043 -2.1972 -2.066 -1.519 -0.23061 Midlands 16.474 -6.7513 -0.50122 -1.6305 -0.075186 Midlands -1.4012 2.8479 -3.6156 0.47228 1.3671 Midlands 12.232 -1.4241 -0.046089 2.6708 -0.018333 Midlands -0.34502 6.7089 -1.5408 -0.40247 2.6271 Midlands 13.92 0.58579 0.68329 0.30561 -0.033436 Midlands 6.817 3.1234 -0.12141 1.1573 -0.36052 Midlands -0.72782 -0.35183 -4.6582 -1.0239 1.434 North -7.8809 7.4498 1.7201 -3.5949 0.42461 North -13.026 1.8574 0.45911 -0.52291 -0.084095 North 8.23 -3.6087 1.4286 1.3348 -0.66338 North -7.2554 4.5527 3.5381 -1.688 -0.036439 North -3.3339 1.161 1.7622 -2.8299 -0.64405 North 3.9622 4.4673 -0.13255 1.1737 -0.23739 North -3.3211 6.8286 0.62698 -0.92847 1.9673 North -7.7484 3.821 -0.29431 -5.3392 0.67704 North -5.8618 6.5516 1.197 -3.1696 -2.8284
  • 16. ENVS450 – Assignment 3 200923027 Page 16 North 6.3927 -0.55523 1.295 -0.10294 0.86619 North 10.244 1.0229 -2.1926 2.9926 -1.3174 North -21.308 3.1781 -2.6221 1.2724 1.5302 North -5.3213 4.1457 -2.0752 -2.5954 1.579 North -0.031442 9.8502 6.0892 -4.8552 0.93375 North 10.703 8.6536 5.8213 0.36562 -0.13425 North 14.538 -2.02 1.9413 -0.2539 -0.52159 North -24.652 5.4288 -3.1079 -0.46966 -1.2904 North 1.1605 1.3174 1.4268 -3.3493 0.28558 North 9.7587 -2.512 -1.0836 4.3552 -0.18127 North 0.77944 3.1613 -0.51552 2.2117 0.73842 North -17.174 8.7293 1.9935 0.30763 0.1773 North 10.69 -2.1375 3.0501 -0.29188 0.66823 North -3.3897 5.7566 -0.68991 -1.1961 0.81749 North -1.8884 6.5686 1.0405 -1.7429 1.3517 North -7.4073 4.5071 0.8503 -4.6437 -0.69125 North 13.649 0.65322 2.1896 -4.4117 -0.49794 North -5.9798 2.9731 -0.19977 -2.3726 0.45242 North 0.91013 3.3373 1.7956 -1.766 -0.6935 North -4.6057 3.4063 1.0607 -1.1303 -0.40757 North -12.626 -0.71898 0.15325 -0.80081 -0.61615 North -7.1365 1.8338 0.58505 -5.5867 -1.5062 North -13.264 8.3648 0.76303 -1.1534 0.78331 North 3.032 4.6019 2.2481 -1.6276 0.60602 North -15.125 6.6122 2.1555 0.11071 0.37637 North -10.253 1.3063 -0.56733 -2.8691 -0.15742 North 11.172 1.7095 1.7615 3.9047 -1.1446 North 7.0423 2.8108 1.5953 -1.7759 0.26043 North 9.6327 1.0041 2.5025 2.1853 -1.5301 North -13.422 9.9311 2.15 -3.769 1.1499 North -4.1581 7.0359 -1.0243 -0.88945 2.2533 North 10.076 -0.16815 1.3811 -3.5699 0.73702 North -1.1134 2.8908 0.69327 -4.0474 -0.55098 North -13.259 8.3907 0.77427 -1.3868 0.44286 North 7.5224 0.3356 -2.6927 5.9153 -1.3315 North -3.3825 8.892 2.64 2.3264 -1.7344 North 2.6149 -3.2825 2.7744 -1.5984 1.3606 North -0.47485 7.6566 5.2905 -1.3242 -0.20468 North 2.8569 1.5006 -0.29617 -3.1158 1.5106 North -4.1917 6.1199 -0.44441 -2.2239 0.24013 North 8.8618 3.0917 5.6435 3.5791 1.5599 North -17.052 6.5641 -0.10681 -2.4857 -0.77503 North -6.9047 4.8908 -0.16762 -2.7512 0.40725 North -3.3465 8.0196 1.3826 -0.99052 -0.1818 North 0.28182 3.9858 0.57414 -1.5863 -1.5121 North -3.2623 6.2094 0.68813 -4.2265 0.40577 North 5.5312 0.35318 4.4097 -2.5804 0.21928 North -1.6677 4.9241 0.87111 -3.9477 0.28087 North 5.1941 -4.1168 -6.9796 3.1549 -0.40347 North -30.224 6.6451 0.30403 0.31901 1.2065 North 10.497 2.8193 2.3772 -0.37842 -1.1506 North -2.5165 5.899 3.3676 -0.83496 1.1842
  • 17. ENVS450 – Assignment 3 200923027 Page 17 North -4.7217 5.2261 -1.2272 -0.80211 1.3532 North -25.486 1.956 0.38786 0.39356 0.089853 North 11.4 -2.091 0.050659 -3.0121 -0.37198 North -2.54 1.1982 0.69049 -3.6545 -0.82012 North 5.8962 -1.7484 1.0452 -2.8474 0.61831 North 3.7468 3.1396 -1.4652 -1.5445 -0.71136 North -9.6177 4.7145 -0.52152 -3.0678 0.69444 North -12.682 11.724 2.8419 -0.85638 0.70203 North -0.47589 4.7122 -0.56021 -2.8709 1.1118 North -36.095 -0.96715 -5.6901 1.8557 1.5731 North -2.5213 -1.7216 2.2797 -1.3729 -1.9281 South 7.54 4.7281 2.9998 -0.15212 -1.4056 South 7.3243 2.8118 3.8967 1.6581 -0.84937 South -59.864 -2.4794 -0.36867 1.744 -1.0082 South 9.2908 6.4423 4.0592 3.5155 -2.0735 South 16.206 -9.1746 1.6847 -1.572 0.0034213 South 6.6346 -2.6097 -2.9085 -0.17008 -0.27122 South 10.002 -7.0599 -1.5919 -1.9677 -0.012059 South 10.771 -0.42903 -0.67348 2.3313 -0.99594 South -26.496 0.94165 -5.7972 -1.6471 -1.5876 South -10.69 -6.5271 0.25768 0.12042 0.35562 South 12.89 5.4295 3.9689 5.7793 -1.6779 South 20.703 2.6484 4.9173 4.5553 -1.2756 South 0.30056 -0.19718 -1.8464 -1.4254 -0.37725 South 6.102 -8.4196 -1.5521 -0.6541 0.98166 South 4.0662 2.618 0.8537 1.7115 -0.71166 South 1.0376 -2.5178 1.3044 0.72508 -0.63566 South 1.0899 -2.821 -1.5596 -0.70808 -0.17891 South 3.378 0.81261 2.0371 -5.3711 -2.8315 South 6.8167 -5.2459 -2.4536 -1.5263 -0.65103 South 11.722 -4.3956 -0.6801 -1.8046 -0.086247 South -12.367 -8.2204 -1.8682 -0.17426 0.49931 South 12.339 -12.008 2.8357 0.52453 1.4501 South 7.2745 -1.246 0.4097 7.292 -0.74076 South 16.12 -8.389 3.9692 0.67445 0.10347 South 13.172 -6.6384 3.5076 -3.0908 -0.7991 South 11.484 7.2755 5.347 6.7764 -1.5085 South -8.2107 0.46908 -3.422 3.4983 0.42126 South 7.2679 -10.073 -2.8193 -2.1854 0.87723 South 6.4608 5.0765 -2.3491 0.53842 -0.28057 South 6.1948 -2.34 -3.0653 -0.49012 -0.15642 South 7.6702 2.7588 -3.1563 3.1697 -0.49242 South -31.171 -2.5687 -3.1438 0.14611 -1.516 South 12.011 -4.4308 3.341 -0.32743 -0.069939 South -25.948 -0.92758 -1.3735 -3.8121 -2.4177 South -20.426 -1.6244 1.6252 -0.9115 -0.27376 South -13.303 -3.9947 -2.9012 1.378 1.9547 South 17.922 1.9153 1.3991 -0.17174 -1.1593 South 2.5937 -3.5408 4.8448 -2.503 -1.0892 South 3.3625 -6.37 -3.0441 1.4273 0.78318 South 8.1898 -1.044 -1.0321 -3.8575 -2.4247 South 2.6959 -2.6679 -3.4572 -2.7588 -1.1329
  • 18. ENVS450 – Assignment 3 200923027 Page 18 South 11.496 -2.6812 0.55832 0.73662 0.05806 South -35.471 -2.7889 0.1355 -1.2506 -1.2471 South 8.5646 2.6049 -1.1715 0.92475 -0.24449 South 12.971 1.5116 0.18261 3.6569 0.60732 South -21.222 -10.937 0.11263 3.7818 2.4333 South -51.496 -5.6324 7.2799 3.7347 0.60125 South -40.553 -3.3704 0.68246 -0.88085 -1.2399 South 0.126 1.0347 0.023304 0.75547 -0.81469 South 8.778 -5.4703 -2.6841 1.2012 0.77123 South -1.6656 -5.3462 0.892 -1.9825 0.10859 South 18.548 -10.865 2.237 -1.6315 0.54464 South 16.007 5.0284 4.4933 -4.174 -2.8853 South 10.825 -5.2566 -1.7844 -2.1488 -0.40696 South 8.7774 -0.25862 -2.0553 1.1869 -0.29848 South 4.9793 2.2017 2.9023 -4.2647 -2.5009 South 9.6182 -4.9672 0.91964 -1.9853 -0.69094 South -0.67476 -4.0494 -0.06196 0.67015 -0.50909 South -6.1905 5.9116 1.2827 4.0472 -1.2675 South -2.8277 -4.1828 -3.3757 -2.5637 -0.86226 South 14.737 -0.60503 0.049943 1.5637 -0.19498 South 13.836 -5.727 1.4813 1.0345 -0.14612 South -13.365 -1.5882 -0.95717 -2.9414 -1.3597 South 9.4648 -3.2561 0.042826 -0.41164 -0.54324 South 11.046 -7.0472 1.1097 -1.2167 0.23224 South -10.419 0.12186 -4.2932 0.72975 -0.11099 South -50.154 -12.487 27.345 2.7023 1.3509 South 1.2909 -2.672 -1.6446 -0.98163 -0.53065 South -34.781 5.251 1.5626 7.8282 -9.3456 South -56.749 -4.609 6.2474 2.7423 1.6552 South -1.8933 -4.3076 -10.782 4.9763 -0.28185 South 6.5923 4.3591 -1.9122 2.7858 0.44269 South 8.0945 -4.11 -2.4243 7.0365 -0.031126 South 0.27156 4.6968 -0.16261 1.1827 -0.24375 South -4.0347 -8.3559 1.9403 -2.4036 -0.18502 South 0.50802 -0.046856 -1.6952 -3.4118 -1.0458 South -5.2337 -4.0291 -6.0861 -0.97866 -0.4116 South -13.431 -2.709 1.0024 -3.5485 -1.4417 South -3.752 8.1809 -0.47334 1.4481 -0.81998 South -30.22 -3.3927 -2.609 0.47206 -0.078893 South 8.017 -10.075 -0.15719 0.54286 0.85539 South -8.7632 3.2849 -3.2348 0.72342 0.7453 South 12.087 0.56606 0.94489 3.4189 -0.61833 South 9.5005 -9.0901 -1.5463 0.017507 0.87741 South 5.0635 -5.3254 -1.1132 0.10625 0.12788 South -46.172 -8.2145 4.1236 2.3598 0.4291 South 12.26 -5.7491 1.6117 -0.67833 -0.67606 South 7.7055 -2.7471 -1.3727 -0.98896 -0.67005 South -20.037 -4.9437 -1.575 -1.2408 -0.24694 South 6.3169 8.1932 -0.50041 9.767 -0.3582 South -21.623 -9.3199 -2.7184 2.3891 0.73715 South 14.684 -5.5249 1.6705 -0.572 -0.08763 South 13.931 -5.5454 0.41797 1.1623 -0.081845
  • 19. ENVS450 – Assignment 3 200923027 Page 19 South 10.679 -8.5895 -0.36968 -1.1079 0.41524 South 16.815 -1.5917 4.4074 -2.026 -1.145 South 7.1368 0.6266 0.37842 1.4136 -0.32629 South -12.715 -7.3019 3.2046 -2.9311 -0.52436 South -45.234 -8.6857 7.8954 4.5482 0.021086 South 14.787 -1.6107 -0.90513 0.36724 -0.98727 South 7.7705 4.9231 -2.1081 3.6707 -0.23816 South 10.429 -6.6296 1.0904 -0.67274 0.47366 South -2.3061 -7.9794 -6.0167 -1.0049 1.5667 South -17.848 -5.7346 -4.5941 -0.25605 -0.068009 South 9.7414 -5.3244 -1.6995 -1.0192 0.23409 South 9.4581 0.474 -1.4239 2.9923 -0.69181 South 14.167 2.1207 1.8813 4.0134 -1.0272 South -7.5996 -1.0936 -1.6848 0.16648 -0.48612 South 16.957 0.11996 3.2016 0.76791 -1.4609 South -3.9027 2.0975 1.4115 -0.76103 -0.90479 South -44.756 -1.4542 -5.9923 -1.2762 -2.4249 South -15.866 -0.55368 -2.1895 -1.0953 -1.4038 South 12.099 2.2699 -0.48109 0.32164 -0.10535 South -23.03 -1.1689 -6.7352 5.9611 1.7568 South -8.5883 -1.1157 -4.7855 -3.9163 -1.9562 South -31.419 -11.209 5.5789 -0.54757 0.88828 South 4.0708 -6.8281 -0.7482 2.4658 1.3571 South -0.59451 0.97358 -1.8594 -0.70336 -1.1569 South -1.3879 0.34122 -2.8082 -1.2143 -1.1672 South 9.5657 8.0522 0.20796 8.1 -0.87 South 9.3038 0.69364 2.3677 1.1972 0.3791 South -14.937 5.7817 -2.0641 1.782 1.0019 South 7.3244 -8.3505 0.74959 3.8874 1.5049 South -4.4835 -6.1971 -5.5319 3.4364 0.32761 South -51.629 -5.4447 0.85644 1.8578 -0.19459 South 8.6709 -0.4564 -2.8355 2.5584 -0.84374 South -7.0718 8.1393 0.81037 2.5919 0.26613 South 9.6343 2.2243 -1.1459 5.5876 -0.72791 South 11.99 -5.5835 1.1623 0.80349 -0.043382 South -8.629 -0.52834 -6.4861 1.5637 -0.34187 South 13.186 -6.2539 2.5837 2.6092 -0.059444 South -10.872 -6.6588 -10.114 -0.92491 0.33159 South -0.27127 5.8836 0.88999 1.3182 -0.19982 South 1.1132 -0.22966 -2.5938 -4.274 -1.2416 South -58.552 -5.671 0.46232 1.8906 0.1714 South 4.1035 7.4376 2.3335 2.602 -0.55031 South 12.68 -3.7682 -0.3536 -2.1697 -0.20056 South 6.4823 12.194 4.6682 2.921 -0.78352 South 17.482 1.1807 4.2063 -4.5088 -2.4685 South 5.1822 4.0379 -1.2283 2.7486 -1.5047 South 10.966 -0.70149 -3.2025 3.8826 -0.63932 South 9.7961 7.9835 4.7826 5.9302 -0.56049 South -6.3952 -3.9165 0.76719 -4.3655 -0.29645 South 7.9643 -6.1518 -1.3874 0.058428 -0.57293 South -0.16255 9.2046 1.7153 3.0055 -0.032512 South 8.6553 -8.0598 -1.2907 -0.14913 0.0088773
  • 20. ENVS450 – Assignment 3 200923027 Page 20 South 9.438 5.5952 -1.2386 2.8557 -1.0674 South 13.339 -7.9592 2.7238 2.033 0.31773 South -6.7679 -1.43 -4.7896 -0.92938 -0.034011 South 3.3758 -6.3384 -1.4128 1.3802 0.036944 South -16.56 -2.532 -6.9377 2.2663 0.28796 South 11.906 0.32787 0.78569 4.8858 0.36567 South 12.175 -2.2527 0.57359 0.90106 -0.59699 South 0.18568 -3.7319 0.99078 -3.6448 -1.4083 South 9.133 2.9424 0.9827 7.3467 -0.58589 South 3.3251 1.5949 -2.2414 -1.8452 -0.20945 South 15.973 -0.42868 1.5921 -1.4274 -0.76102 South -5.7153 -3.3558 -5.4322 0.78313 0.11554 South -49 -6.0153 2.6788 0.34451 -0.71214 South 3.9929 7.7397 0.81378 2.8599 -1.1173 South 14.485 -8.2704 1.5214 2.2369 0.60427 South 4.8022 0.13152 -2.1374 2.7657 -0.10114 South -3.8735 -12.738 5.4333 0.032493 1.6126 South 11.003 3.6242 1.5529 2.5141 -0.19556 South 12.809 -8.0206 -1.8314 0.87171 0.44008 South 10.205 -3.6382 -0.38013 -1.3852 -1.1585 South 18.733 -11.635 4.0124 -3.1947 1.0936 South -53.776 -6.6146 8.5886 4.6679 0.79874 South 5.728 -2.017 -3.1428 2.236 -0.6914 South 0.96073 -1.6202 -5.2604 -4.1717 -1.1096 South 12.739 -8.1378 1.1425 1.1522 0.52633 South 11.567 -10.558 0.66026 1.7655 2.645 South 1.9793 -6.8395 -6.1936 -1.8674 -0.16077 South -3.4207 -6.4703 -3.2157 -1.6712 -0.0054187 South 9.6436 -5.5921 -0.50932 1.6979 0.45826 South 10.592 -11.834 3.6683 -0.2431 2.3942 South 9.972 -4.8239 -1.4161 -0.65227 -0.3212 South 7.8213 -10.618 -0.10802 2.3535 1.1876 South 6.8263 -4.2303 -2.32 2.2128 0.45182 South -0.88866 4.6184 -0.58191 2.5633 -0.0086849 South 7.9825 -9.5221 1.1806 -0.99352 0.99509 South 10.517 -6.2951 -1.7931 2.1132 0.02828 South 1.6544 2.9521 3.3628 0.4669 -0.849 South -0.060084 -3.2732 -2.0307 -2.6568 -0.25603 South 9.9679 -8.1541 0.85484 2.0034 1.0795
  • 21. ENVS450 – Assignment 3 200923027 Page 21 Appendix 3 :: Large-scale PCA graph