geostatistical analysis

P

2013

Prepared For:

Dr. Ian Smith

Prepared By:

Nobuhle Matanga, Lisa Atkinson and

Stephanie Korhonen

March 22, 2013

GISC 9303-Spatial Analysis D4b Geostatistical Analysis of Housing Sale Prices in St. Catharines Neighborhoods

135 Taylor Road, S.S #4

Niagara-on-the-lake, ON

Tel: 1-289-241-7627

Email: [email protected]

March 22, 2013

File: GISC93084b

Mr. Ian D. Smith

M.Sc., OLS, OLIP, EP

Post-Graduate Professor of Environmental Sciences and GIS

Niagara-on-the-lake Campus, Niagara College

Room E313

135 Taylor Road, S.S #4

On, L0S 1J0

Dear Mr. Smith:

Re: Submission of GISC93084b Please accept this letter as the formal submission of Deliverable 4b Geostatical Report for

GISC9308 – Spatial Analysis.

This geostatistical report outlines all intentions for undertaking the statistical investigation on the

Average Housing Sale Prices in St. Catharine Neighborhoods. The attached report beings by

highlights the study area, objectives, goals, methodologies and preliminary statistical assessment.

This report concludes with a comparison of the IDW and Kriging results created from the

obtained dataset. Supplemented material include: a summary of collected raw data, statistical

calculations, and graphing of the dataset. Overall it was determined that the IDW method

resulted in a better prediction surface.

Please do not hesitate to contact us for any additional information at 1-289-241-7627. Thank

you for your time and attention.

Sincerely,

Nobuhle Matanga, B.Sc.

GIS-GM Graduate Candidate

GIS Tek.

N.M. /

Enclosures: 1) [Geostatical Collection Report],

2) [Statistical Calculations and Graphing of Data Set].

Cc. Lisa Atkinson, BA

Stephanie Korhonen, BA

tel:1-289-241-7627

Geo Tek | Geostatistics Report i

March 22, 2013

Executive Summary

This geostatistical report begins by providing an in-depth summary of the study area,

objectives, goals methodologies and preliminary statistical assessment of the Housing Sale Prices

in St. Catharine Neighborhoods, for the obtained dataset. The geographic data is defined as

UTM Easting and Northing coordinates; whereas the z value is presented as housing cost.

Formal maps, displaying the housing locations and the study area extent are located within

Appendix A, and a full glossary of terms is located in Appendix B. The purpose of this

investigation is to determine the feasibility of this dataset for future geostatistical studies. The

St. Catharines housing price dataset can be summarized as follows; there are a total of 138

observations used in this study, the mean price is $367,270, the median price is $259,950, more

importantly there is a kurtosis of 22.14, skewness of 3.9814 and a standard deviation of 2188.1.

As a result of the positive skew in this dataset, a log transformation is required before spatial

importation can be conducted. The second half of this report discusses the prediction surfaces

created using both the kriging and IDW techniques. Although both surfaces provide adequate

representations of wealth zones in the St. Catharine’s area, the kriging results are more skewed

due to outliers. Therefore it was concluded that the IDW provides a more accurate classification

of poverty and affluence in St. Catharines area. As a result the information from the IDW results

will essentially allow contractors to maximize profit and minimize cost.

Geo Tek | Geostatistical Report ii

March 22, 2013

Table of Contents

Executive Summary ..................................................................................................................... i

1.0 Project Understanding ............................................................................................................ 1

1.1 Study Area ............................................................................................................................. 1

1.2 Project Goal ........................................................................................................................... 2

1.3 Objectives and Benefits of this Project this Project .............................................................. 2

2.0 Summary of Methodology ..................................................................................................... 2

2.1 Data Collection ...................................................................................................................... 2

2.2 Determining Sample Size ...................................................................................................... 2

2.3 Formatting and Displaying Data in ArcGIS .......................................................................... 3

2.3.1 Creation of a file Geodatabase ................................................................................... 3

2.3.2 Creating Metadata for file Geodatabase .................................................................... 3

2.3.3 Importing X, Y data into ArcGIS .............................................................................. 3

2.3.4 Projecting Data........................................................................................................... 3

2.3.4 Georeferencing Neighborhood Boundaries Data ....................................................... 3

2.4 Geostatistical Analysis of Data in ArcGIS ............................................................................ 4

2.4.1 Summary statistics ..................................................................................................... 4

2.4.2 Histogram ................................................................................................................... 6

2.4.3 Normal QQ Plots........................................................................................................ 8

2.5 Kriging Interpolation ........................................................................................................... 12

2.6 Inverse Distance Weighted (IDW) Interpolation ................................................................ 17

3.0 Results and Discussion ...................................................................................................... 19

3.1 Kriging vs. Inverse Distance Weighted (IDW) ................................................................... 19

3.1.1 Similarities ............................................................................................................... 19

3.1.2 Differences ............................................................................................................... 20

4.0 Conclusions ......................................................................................................................... 25

5.0 References ........................................................................................................................... 26

APPENDIX A (Formal Maps) ..........................................................................................................

APPENDIX B (Glossary of Terms and Parameters) ........................................................................ APPENDIX C (Raw Data)................................................................................................................

Geo Tek | Geostatistical Report iii

March 22, 2013

List of Figures

Figure 1 : Formal Map of Study Area ............................................................................................. 1

Figure 2 Summary Statistics Tool in ArcGIS, Image Source ArcGIS ........................................... 4

Figure 3: Summary statistics for Easting Observations, Image Source ArcGIS ............................. 5

Figure 4: Summary statistics for House Prices, Image Source ArcGIS .......................................... 5

Figure 5: Summary statistics for Northing Observations, Image Source ArcGIS .......................... 5

Figure 6 Northing Observations Histogram, Image Source ArcGIS.............................................. 6

Figure 7: House Prices Histogram, Image Source ArcGIS ............................................................. 7

Figure 8 Easting Observations Histogram, Image Source ArcGIS ................................................. 7

Figure 9 House Price Normal QQPlot, Image Source ArcGIS ....................................................... 8

Figure 11: Northing Observation QQPlot, Image Source ArcGIS .................................................. 9

Figure 10: Easting Observations QQPlot, Image Source ArcGIS................................................... 9

Figure 12 Normal QQ plot of Housing Prices with Log Transformation, Image Source ArcGIS10

Figure 13 Histogram of House Prices with Log Transformation, Image Source ArcGIS ............ 11

Figure 14 : Study Semivariogram, Image Source ArcGIS ............................................................ 12

Figure 15: Kriging Parameters Used In Study ............................................................................. 14

Figure 16: IDW Parameters Used In Study .................................................................................. 17

Figure 17: House Price Zone Classification, Image Source ArcGIS ........................................... 19

Figure 18: Real Estate Sale Prediction, St. Catharines, Ontario and Surrounding Area: Quadrant

1..................................................................................................................................................... 21


2..................................................................................................................................................... 22


3..................................................................................................................................................... 23


4..................................................................................................................................................... 24

Figure 22: Example of Spatial Interpolation, Image Source: Niagara College ............................. 2

Figure 23: Kriging Calculation, Image Source: Niagara College .................................................. 3

Figure 24: IDW Calculation, Image Source: Niagara College ...................................................... 4

List of Tables

Table 1 : Cross Validation Assessment of Kriging Results .......................................................... 15

Table 2:Cross Validation Assessment of IDW Results ............................................................... 18

March 22, 2013

1.0 Project Understanding

1.1 Study Area

The scope of this study is the St Catharines region. The study area is been divided into 54

subsections, encompassing 28 St Catharine's neighborhoods. A total of 138 observations are to

be assessed. The study area is defined by Figure 1, below:

Figure 1 : Formal Map of Study Area

Geo Tek | Geostatistical Report 2

March 22, 2013

1.2 Project Goal

The goal of this spatial statistical assessment is to determine areas of poverty and

affluence in St Catharine's, using sample residential housing sale prices.

1.3 Objectives and Benefits of this Project this Project

This project will allow for a practical assessment of future building projects, within a

specified neighborhood, in order to maximize profit, and minimize cost.

2.0 Summary of Methodology

2.1 Data Collection

The housing cost and address data is collected from the Relators® Canada Incorporated

website. This website is owned by the Canadian Real Estate Association and the National

Association of Realtors® (Realtors.ca, 2013). The data available on the website is provided by

realtors from across Canada, and is updated hourly (Realtors.ca, 2013). A Multiresolution

Seamless Image Database (MrSID) file, of the Niagara region and corresponding municipalities

boundaries, is provided by Niagara College. Subsequently, UTM NAD 83 Zone 17N Easting

and Northing coordinates are obtained via Google Earth. Google Earth is a real world

representation of superimposed images obtained from satellite imagery, aerial photography, and

GIS 3D globe. This platform is available at no cost to public users.

2.2 Determining Sample Size

All the sample data was collected on January 25, 2013. This dataset includes residential

houses that are for sale. On January 25, 2013 there were a total of 360 houses for sale in St

Catharines. However, in order to avoid large generalizations and minimize inaccuracies, the St.

Catharines region was divided into 54 equal area subsections. From these subsections

maximum, median and minimum values were obtained, therefore reducing the sample size to

138 observations.


March 22, 2013

2.3 Formatting and Displaying Data in ArcGIS

2.3.1 Creation of a file Geodatabase

The file geodatabase associated with this deliverable is created using ArcCatalog and is

set as the default geodatabase within the map document properties. This ensures a common

projection for all assessment products, and ensures products are exported to the correct

geodatabase, and finally, reduces project costs associated with data transfer.

2.3.2 Creating Metadata for file Geodatabase

Metadata (tags, summary, description, credits and use limitations) are created for the file

geodatabase using ArcCatalog. Metadata is essential for data management purposes; it provides

the user with information such as data source and data function.

2.3.3 Importing X, Y data into ArcGIS

An excel table composed of longitude, latitude and price values is transformed to a

shapefile via ArcGIS. The Easting coordinates are assigned as X values, the Northing

coordinates are assigned as Y values, and the price observations are assigned as Z values within

the attribute table.

2.3.4 Projecting Data

All of the imported data was reprojected into UTM Zone 17N, NAD 1983, this is the

desired format for all the data used in this study.

2.3.4 Georeferencing Neighborhood Boundaries Data

Georeferencing is the process of assigning raster data sets to a map coordinate, positional

reference, system (Smith, 2013). The purpose of this is to rectify data. Thus, a jpeg image of St

Catharine's neighborhood boundaries is correlated to the MrSID file of the Niagara Region, via

the Georeferencing tool in ArcGIS. This data management tool is used to allocate three control

point pairs to each image to warp the jpeg images to the MrSID referenced data. Control points

are geographic references, easily identifiable upon both the non-referenced image and the

referenced image. When georeferencing raster data, at least three, well distributed control points

must be established to ensure precise image warp effects.


March 22, 2013

2.4 Geostatistical Analysis of Data in ArcGIS

2.4.1 Summary statistics

Summary statistics (Count, Min, Max, Mean, Std. Dev., Range, Frequency and Sum) for

the St. Catharine's housing prices, Easting and Northing coordinates, are investigated utilizing

the Geostatistical Analyst tool bar in ArcGIS. The summary statistics for the housing prices,

Northing and Easting observations are displayed in Figures 2 to 5.

Figure 2 Summary Statistics Tool in ArcGIS, Image Source ArcGIS


March 22, 2013

Figure 4: Summary statistics for House Prices, Image Source ArcGIS

Figure 3: Summary statistics for Easting Observations, Image Source ArcGIS

Figure 5: Summary statistics for Northing Observations, Image Source ArcGIS


March 22, 2013

2.4.2 Histogram

Histograms for the St. Catharines housing prices, Easting and Northing coordinates are

created using the Geostatistical Analyst tool bar in ArcGIS. The number of bins used for our

histograms (12) is determined by rounding the square root of the sample size (138). This was

rounded because the square root of 138 is 11.74 and a decimal number cannot be used for the

number of bins. The histograms are used to assess the frequency distribution of the values

within the dataset. The presented histograms, display statistical analyses provided by the

Geostatistical Analyst tool such inclusing, skewness, kurtosis, median, 1-st Quartile and 3-rd

Quartile. The Northing observations are normally distributed while, the Easting values have a

negative skew and the price observations have a positive skew (Figures 6-8).

Figure 6 Northing Observations Histogram, Image Source ArcGIS


March 22, 2013

Figure 8 Easting Observations Histogram, Image Source ArcGIS

Figure 7: House Prices Histogram, Image Source ArcGIS


March 22, 2013

2.4.3 Normal QQ Plots

Normal QQ plots for the St. Catherines house prices, Easting and Northing coordinates, are

created utilizing the Geostatistical Analyst tool bar in ArcGIS. The standard normal distribution

quantile values are represented by the x-axis of a Normal QQ Plot, and the dataset quantile

values are represented by the y- axis. If data values are normally distributed they will be plotted

in proximity to a computed reference line. The Easting and Northing data (Figures 10-11) sets

are normally distributed, in contention with the pattern observed for the housing price data set

(Figure. 9).

Figure 9 House Price Normal QQPlot, Image Source ArcGIS


March 22, 2013

Figure 11: Easting Observations QQPlot, Image Source ArcGIS

Figure 10: Northing Observation QQPlot, Image Source ArcGIS


March 22, 2013

As previously stated, based on the QQ plots of the Easting and Northing data values, a normal

distribution exists, while the house prices are not normally distributed. The house prices appear

to have a positive skew. As a result a log transformation is applied to the price data to normalize

the data. The results of the log transformation are displayed in the normal QQPlot (Figure12)

and the histogram (Figure 13).

Figure 12 Normal QQ plot of Housing Prices with Log Transformation, Image Source ArcGIS


March 22, 2013

Figure 13 Histogram of House Prices with Log Transformation, Image Source ArcGIS


March 22, 2013

2.5 Kriging Interpolation

Before conducting the kriging technique a variography (structural analysis), must be

conducted on the dataset. This variography is conducted by created an empirical semivariogram.

An empirical semivariogram plots the relationship between distance and average semivariance.

Overall in this study’s empirical semivariogram proves that as distance increases the

observations become more variable. The semivariogram in this study follows the Gaussian

(hyperbolic) model, more specifically there is increase in semivariance with distance, shown in

figure 14 below:

Based on this graph it can be inferred that the housing price dataset for the city of St.

Catharines is very continuous at close distances. Additionally it be predicted that the prediction

surface created from this model would be very smooth, there would be a lot of gradual shifts

between price classes.

Figure 14 : Study Semivariogram, Image Source ArcGIS


March 22, 2013

Additionally the pre-kriging structural analysis determine that the housing price dataset

for St. Catharines is anisotropic (directional). Housing price is depends on direction and distance.

The reason for this is that houses that are closer together generally cost the same. Moreover

housing cost is also depended on geographic location, for example housing cost tends to increase

going towards waterfront properties and decreases the inner city, and this is illustrated in both the

IDW and Kriging surface results

In order to interpolate the housing cost across a surface, ordinary kriging is employed to

display the housing cost variance. For this investigation, ordinary kriging is utilized, so that the

constant mean is assumed as unknown, as is a common best practice of geostatistical analysis

(Smith, 2013). The Kriging results depend on the semivariogram model. This technique

classifies data using the semivariogram and relative distance. Additionally, kriging settings are

enforced, via the interactive kriging tool window. These settings are summarized by Figure 15,

shown below:


March 22, 2013

Figure 15: Kriging Parameters Used In Study


March 22, 2013

The input parameters above, summarized as Figure 14 , creates a data depiction utilizing

semivariogram; comparing data points, in terms of local neighbours, and similarity of housing

cost, based on distance to neighboring data points (Smith, 2013). The cross validation graphs are

important tools to understand the predictability of a data set, or investigation. For this

discussion, the cross variance outputs, and interpretations, are summarized by Table 1:

Table 1 : Cross Validation Assessment of Kriging Results

Cross Validation Depiction Interpretation

Prediction

This graph displays the

prediction of a normal

distribution in grey. However,

the blue line represents the

predictability of the housing

cost data presented in this

study. While not a perfect

model of prediction, this data

is not displayed as random

either. Within the confines of

the investigation, the

prediction trend is logical for

housing costs.

Error

Due to the presence of a

selection of extremely high

housing costs, the majority of

data points appear clustered.

This in turn, affects the

prediction model for the entire

surface being examined.

However, these points are not

outliers, as they represent lake

front properties.

Standard Error

The standard error is also a

measurement of the success of

a prediction model, such as

kriging. Again, the data

points appear clustered due to

extreme housing costs for lake

front properties. Therefore,

the ability to predict housing

costs accurately, across the

entire study area is affected,

and may contains errors.


March 22, 2013

Normal QQ Plot

The predicted surface for the

kriging result, based on the

localization of data points,

among the normal distribution

line, will result in an accurate,

and normal, prediction

surface.


March 22, 2013

2.6 Inverse Distance Weighted (IDW) Interpolation

As a supplementary check, on the predictability of the surface, a second method of

creating a predicability surface model is completed. This model will display the housing cost

variance over a surface. Where Kirging appears to give a more smooth transition of data values

avoiding the bull’s eye effect and gives a standard error, IDW is more simplified, requiring less

user input parameters to produce a result (Smith, 2013). The IDW is completed for the cost

variable of this study. IDW settings are enforced, via the interactive geostatistical wizard tool

window. These settings are summarized by Figure 16, shown below:

Figure 16: IDW Parameters Used In Study


March 22, 2013

The input parameters above, summarized by Figure 16, creates a data depiction,

comparing data points, in terms of local neighbours, and similarity of housing cost, based on

distance to neighbouring data points. The cross validation graphs, for the IDW results, are

important tools to understand the predictability of a data set, or investigation. For this

discussion, the cross variance outputs, and interpretations, are summarized by Table 2:

Table 2: Cross Validation Assessment of IDW Results

Cross Validation Depiction Description

Predicted

This graph displays the prediction

of a normal distribution in grey.

However, the blue line represents

the predictability of the housing

cost data presented in this study.

While not a perfect model of

prediction, this data is not

displayed as random either.

Within the confines of the

investigation, the prediction trend

is logical for housing costs.

Error

Due to the presence of a selection

of extremely high housing costs,

the majority of data points appear

clustered. This in turn, affects the

prediction model for the entire

surface being examined. However,

these points are not outliers, as

they represent lake front

properties. Further, as compared

to the Kriging results, there is less

of a data distribution stretch, due to

the bull-eye nature, of this method.


March 22, 2013

3.0 Results and Discussion

3.1 Kriging vs. Inverse Distance Weighted (IDW)

3.1.1 Similarities

The kriging and IDW methods produce surface covers that categorize St. Catharines into

different zones based on housing price. These zones are classified according to the parameters

outlined in Figure 17, below:

Both the Kriging and the IDW surfaces show a decrease in housing prices towards the

core of the city, downtown St. Catharines, as well Riverview. Additionally, both surfaces display

an increase in housing prices towards the greater Louth area, Western Hill, Burleigh Hill and

lake front properties, as shown in Appendix A. Both surfaces have excellent coverage and no

data daps, or holes are present in the data.

Figure 17: House Price Zone Classification, Image Source ArcGIS


March 22, 2013

3.1.2 Differences

In the Kriging surface there is a more pronounced presence of extreme housing prices,

both high and low. In comparison to the IDW results, a more gradual transition between areas of

high housing costs and low housing costs is present. Due to the generalization of the IDW

results there is a larger error for predicting housing cost, as opposed to the Kriging results, which

show a greater amount of localized detail. For a better assessment of the differences the larger

study area, is divided into quadrants.


March 22, 2013

In quadrant 1, the differences between the two interpolation methods are most apparent in

the Martindale neighborhood, particularly the area surrounding the $2,150,000.00 Martindale

home. In the IDW results there is a gradual increase in price towards the center of the

neighborhood where a ‘bulls-eye’ effect occurs. In comparison, the kriging results predict that

the majority of the houses in Martindale will be expensive and not just those within in the direct

vicinity of the $2,150,000.00 dollar Martindale home. However based on the dataset, delineating

housing costs around the $400,000 cost, the IDW results appear to be more accurate for this

quadrant. These comparisons are shown by Figure 18, below:

Figure 18: Real Estate Sale Prediction, St. Catharines, Ontario and Surrounding Area: Quadrant 1


March 22, 2013

In quadrant 2 both the kriging and the IDW results are relatively similar. The only

notable difference is that the IDW results tend to account for average housing prices, whereas the

kriging result are highly influenced by the more extreme values. However, as indicated by the

original dataset figures, houses in and around the North End are relevantly cheap in comparison,

with the exception of waterfront property. In this particular quadrant the kriging results appear

to be more correct. These comparisons are displayed by Figure 19, below:



March 22, 2013

In quadrant 3, there are differences in the prediction for the Louth neighborhood

(located in the southwest region of the maps below). In the kriging results, there is a smaller area

for houses with extremely high prices, whereas this area is expanded in the IDW results.

Moreover, there is larger area for moderately high housing costs, in comparison this area is a lot

smaller in the IDW results. In this quadrant it appears that the outlier, the $1,995,000 house,

greatly skews the IDW results. Therefore, in this quadrant the kriging results are more accurate.

These comparisons are displayed by Figure 20, below:



March 22, 2013

In quadrant 4, the only major difference between the kriging results and the IDW is the

increase of designation of areas as extremely low cost housing in the kriging results. Overall

both of these results are fair and give an accurate prediction of housing costs of this area. These

comparisons are displayed by Figure 21, below:


Overall the IDW results give a more accurate prediction of the housing cost in the study area.


March 22, 2013

4.0 Conclusions

To conclude, an in-depth summary of the study area, objectives, goals, methodologies

and preliminary statistical assessment of the House Sale Prices in St. Catharine Neighbors study

dataset was outlined in the beginning of this report. Based on the results of the statistical

assessment, the dataset was declared suitable for a geostatistical analysis. A geostatistical

analysis, utilizing both kriging and IDW interpolation methods, was conducted on this study

area. Both of these methods produced prediction surfaces that divided St. Catharines into

different zones based on housing price. A comparison of these two surfaces reveals that the

IDW results is less skewed towards outliers and is therefore the more representative surface. In

turn the IDW results correctly determine areas of poverty and affluence in St. Catharines which

will influence of the location of future building project in this city. The IDW surface will

essentially allow contractors to maximize profit and minimize cost.


March 22, 2013

5.0 References

5.1. Lectures

Smith, Ian. Week 1- Introduction to Stats. GISC9308-Spatial Analysis. Niagara

College. PDF.

Smith, Ian. Week 2- Multivariate Statistics. GISC9308-Spatial Analysis. Niagara

College. PDF.

Smith, Ian. Week 3- Sampling. GISC9308-Spatial Analysis. Niagara College. PDF.

Smith, Ian. Week 4- Introduction to Spatial Analyst. GISC9308-Spatial Analysis.

Niagara College. PDF.

Smith, Ian. Week 7- Regression and Interpolation. GISC9308-Spatial Analysis.

Niagara College. PDF.

Smith, Ian. Week 8- Geostatistical Analyst. GISC9308-Spatial Analysis. Niagara

College. PDF.

5.2 Software

ArcGIS (2008) ArcGIS Desktop Education Edition (Version 10). Computer program.

Available at http://www.esri.com/products 5,Sept, 2012

5.3 Terms of Reference

"Assignment4- Geostatistical Analysis of Student Collected Spatial Data."

GISC9308-Spatial Analysis. Niagara College. Web.

5.4 Textbook

Ormsby , Napoleon , Burke , Carolyn Groessl and, Laura Bowden. Getting to Know

ArcGIS Desktop; for ArcGIS 10. Redlands: Esri press. 2010. Print.

5.5 Websites

"ArcGIS Resources." ArcGIS. Esri, n.d. Web. 20 Jan 2013.

http://www.esri.com/products

http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&field-author=Tim%20Ormsby&ie=UTF8&search-alias=books&sort=relevancerank

http://www.amazon.com/s/ref=ntt_athr_dp_sr_2?_encoding=UTF8&field-author=Eileen%20J.%20Napoleon&ie=UTF8&search-alias=books&sort=relevancerank

http://www.amazon.com/s/ref=ntt_athr_dp_sr_3?_encoding=UTF8&field-author=Robert%20Burke&ie=UTF8&search-alias=books&sort=relevancerank

http://www.amazon.com/s/ref=ntt_athr_dp_sr_4?_encoding=UTF8&field-author=Carolyn%20Groessl&ie=UTF8&search-alias=books&sort=relevancerank

http://www.amazon.com/s/ref=ntt_athr_dp_sr_5?_encoding=UTF8&field-author=Laura%20Bowden&ie=UTF8&search-alias=books&sort=relevancerank


March 22, 2013

<http://resources.arcgis.com>.

"Realtors.ca." The Canadian Real Estate Association. Web. 20 Jan 2013.

<http://www.realtor.ca/>.

March 22, 2013

APPENDIX A (Formal Maps)

March 22, 2013

A.1 Real Estate Sale Prediction, St. Catharines, Ontario and Surrounding Area: Study Area


March 22, 2013

A.2 Real Estate Sale Prediction, St. Catharines, Ontario and Surrounding Area: Kriging Results


March 22, 2013

A.3 Real Estate Sale Prediction, St. Catharines, Ontario and Surrounding Area: Inverse Distance Weighting Results

March 22, 2013

APPENDIX B (Glossary of Terms)


March 22, 2013

B.1 Spatial Interpolation

Spatial Interpolation is the process of using known values (kernels) to mathematically

compute unknown values. In the ArcGIS geostatistical extension this can be used to create

prediction surfaces incorporating known and predicted z-values. The example, shown in

figure 22, below shows use the z- values of 4 data points are interpolated and used to compute

12 predicted z-values.

This study will seek to use 138 kernels to compute predicted z-values for the entire city

of St. Catharines. Additionally, this study will compare the results of two different spatial

interpolation methods available in ArcGIS geostatistical extension, the kriging technique and the

IDW technique. Before conducting either of these spatial interpolation methods, a data analysis

must be conducted. Based on the histogram, QQ plot of the St. Catharines, housing price

dataset it was determined that the house prices appear to have a positive skew. As a result a log

transformation was undertaken on the price data to normalize the data. It was also noted that

there are directional influences on the data and therefore the neighborhoods were not divided in

to sectors. This information will be incorporated in the interpolation of this dataset.

Figure 22: Example of Spatial Interpolation, Image Source: Niagara College


March 22, 2013

B.2 Kriging Technique

The kriging technique creates surfaces were by predicted z-values are based statistical

relationships between kernels; this is referred to as the autocorrelation method. This method is

based on the following equation. Before conducting the kriging technique a variography

(structural analysis), must be conducted on the dataset. This variography is conducted by created

an empirical semivariogram. An empirical semivariogram plots the relationship between

distance and average semivariance. Overall in this study’s empirical semivariogram proves that

as distance increases the observations become more variable. The empirical semivariogram is

this study follows a Gaussian trend. The equation for this method is outline in figure 23.

In ArcGIS there are two different kriging methods available, the ordinary and the

universal. The ordinary method is to be used on data that is variable, whereas the universal

method is used on data that follows a trend. The ordinary kriging method is used is this study in

order not to bias results, more specifically this technique was conducted under the assumption

that the dataset is trendless. The kriging method is more applicable for datasets that are highly

variable.

Figure 23: Kriging Calculation, Image Source: Niagara College


March 22, 2013

B.3 Inverse Distance Weighted (IDW) Technique

The IDW technique creates surfaces were by predicted z-values are directly based on

surrounding kernels; this is referred to as the deterministic method. This method is based on the

following equation. The equation for this method is outline in figure 24.

Additionally, the IDW method is more applicable for datasets were distance greatly effects

influence.

Figure 24: IDW Calculation, Image Source: Niagara College

March 22, 2013

APPENDIX C (Raw Data)

March 22, 2013

Grid Number Neighbourhood Price Address Easting Northing

1 North End $2,799,000.00 15 Lantana Circle , St Catharines 643553.52 4786445.99

1 North End $339,900.00 5 lakebreeze Crescent , St Catharines 643761.79 4786315.68

1 North End $364,900.00 1 Warrington Place, St Catharines 643433.92 4785962.26

1 North End $689,900.00 39 Royal York Road, St Catharines 643188.45 4786135.16

2 North End $102,500.00 11 Grandview Drive, St Catharines 644447.55 4787008.56

2 North End $189,900.00 78 Melody Trail, St Catharines 644698.48 4786792.85

2 North End $269,900.00 103 Arthur Street, St Catharines 644376.37 4786942.22

3 Port Weller $189,500.00 9 Shoreham Street, St Catharines 645284.67 4787223.03

3 Port Weller $329,900.00 6 Moes Crescent, St Catharines 645564.06 4787138.55

3 Port Weller $569,000.00 4 Yonge Street, St Catharines 645093.33 4787070.34

4 Port Dalhousie $179,000.00 65 Main Street, St Catharines 640511.41 4784479.55

4 Port Dalhousie $299,500.00 10 Ann Street, St Catharines 640464.39 4784434.50

4 Port Dalhousie $260,000.00 94 Dalhousie Avenue , St Catharines 640327.44 4784526.88

4 Port Dalhousie $294,000.00 99 DalhousieAvenue , St Catharines 640261.58 4784467.25

5 Michigan Beach $1,599,900.00 14 Shore Boulevard, St Catharines 641820.34 4785262.42

5 Michigan Beach $559,900.00 5 Xavier Court, St Catharines 642478.20 4785079.13

5 Michigan Beach $589,900.00 3 Cricket Hallow Road, St Catharines 642107.59 4785154.62

5 Port Dalhousie $274,900.00 27 Simpson Road, St Catharines 642143.90 4784860.87

6 North End $799,000.00 164 A Lakeshore Road, St Catharines 643081.77 4785220.63

6 North End $209,000.00 25 Murray Street, St Catharines 643747.83 4785657.60

6 North End $299,000.00 13 Costen Boulevard, St Catharines 643807.56 4785198.63

7 North End $189,900.00 584 Bunting Road, St Catharines 645313.51 4785289.58

7 North End $244,900.00 20 Pearce Avenue, St Catharines 644903.32 4785637.49


March 22, 2013

7 North End $269,900.00 23 The Cedars Street, St Catharines 644084.73 4784853.23

7 North End $229,900.00 7 Glencairn Drive, St Catharines 644635.60 4784870.30

9 Louth $750,000.00 1214 Lakeshore Road, St Catharines 637485.61 4782754.12

10 Martindale $2,150,000.00 1010 Lakeshore Road, St Catharines 638997.96 4783300.55

10 Martindale $448,500.00 28 Dalemere Crescent, St Catharines 639311.53 4783366.76

10 Martindale $439,900.00 12 Courtland Road, St Catharines 639702.77 4782845.76

10 Port Dalhousie $229,000.00 22 Corbett Avenue, St Catharines 639679.00 4784137.55

11 Port Dalhousie $869,000.00 36 Scullers Way, St Catharines 640042.62 4783692.17

11 Port Dalhousie $244,900.00 8 Pawling Street, St Catharines 6396221.34 4784235.33

11 Port Dalhousie $399,900.00 22 Johnston Street, St Catharines 640064.39 4784119.82

12 North End $315,000.00 13 Bluespruce Court, St Catharines 641655.93 4784010.92

12 North End $189,900.00 27 Prince Paul Crescent, St Catharines 642088.98 4784237.02

12 North End $219,900.00 32 Ernest Street, St Catharines 641472.57 4782888.61

13 North End $349,000.00 511 Vine Street, St Catharines 643676.59 4784374.65

13 North End $179,900.00 37 Ghent Street, St Catharines 642974.03 4783323.08

13 North End $249,900.00 540 Geneva Street, St Catharines 642821.44 4784247.01

14 North End $199,900.00 19 Chatham Road, St Catharines 644819.32 4783147.20

14 North End $339,000.00 413 Niagara Street, St Catharines 644148.39 4783197.67

14 North End $229,900.00 10 Champa Drive, St Catharines 644394.53 4783701.95

14 North End $225,000.00 473 Scott Street, St Catharines 644605.89 4783658.68

15 North End $167,500.00 363 Bunting Road, St Catharines 645439.79 4782888.95

15 North End $219,900.00 13 Gormley Crescent, St Catharines 645269.55 4782862.16

15 North End $315,900.00 1A SunnyLea Drive, St Catharines 645079.26 4782743.87

15 North End $209,400.00 3 Ennismore Court, St Catharines 646032.96 4782894.36

17 Louth $519,900.00 1451 Fifth Street, St Catharines 638227.79 4781917.22


March 22, 2013

18 Martindale $350,000.00 56 Henley Drive, St Catharines 640455.75 4782190.58

18 Martindale $639,900.00 1 Brooklyn Court, St Catharines 639889.22 4782250.50

19 Martindale $279,000.00 70 Scott Street, St Catharines 646839.12 4784794.59

19 Martindale $166,000.00 104 Ventura Drive, St Catharines 641388.35 4781674.62

19 Martindale $219,900.00 118 Haig Street, St Catharines 641521.65 4781748.97

19 Orchid Park $214,900.00 11 Fonthill Court, St Catharines 641979.42 4782457.18

20 Orchid Park $269,900.00 11 Kingsway Crescent, St Catharines 643354.16 4781780.11

20 Orchid Park $177,000.00 11 Hill Park Lane, St Catharines 643412.50 4782160.41

20 Fitzgerald $169,900.00 21 Sandown Street, St Catharines 643525.30 4781880.17

20 Orchid Park $132,000.00 222 Carlton Street, St Catharines 642801.30 4781675.35

21 Facer $229,900.00 68 Parkview Road, St Catharines 644413.60 4781881.45

21 Facer $164,900.00 50 Parkview Road, St Catharines 644454.89 4781775.37

21 Facer $159,900.00 54 Cosby Avenue, St Catharines 644376.99 4781807.82

21 North End $117,500.00 110 Garnett Street, St Catharines 644587.06 4782301.41

22 Bunting $190,000.00 24 Huntley Crescent, St Catharines 645907.72 4782612.61

22 Bunting $229,900.00 15 Rendale Avenue, St Catharines 646017.00 4782802.31

23 Louth $629,900.00 1665 Gregory Road, St Catharines 637008.61 4780897.32

25 Martindale $629,900.00 40 Tulip Tree Common, St Catharines 640599.05 4781227.53

25 Martindale $149,900.00 6 Barton Street, St Catharines 640599.53 4780431.14

25 Martindale $359,900.00 5 Inglis Circle, St Catharines 640144.49 4779930.68

26 Haig $119,900.00 153 Pleasant Avenue, St Catharines 642095.95 4781014.32

26 Haig $259,900.00 44 Chicory Crescent, St Catharines 641354.83 4781289.07

26 Haig $174,900.00 21 Taylor Avenue, St Catharines 641891.45 4780930.48

27 Fitzgerald $77,900.00 173 Vine Street, St Catharines 643841.79 4781353.66

27 Fitzgerald $226,900.00 56 Maple Street, St Catharines 643011.45 4780915.30


March 22, 2013

27 Fitzgerald $154,900.00 42 McGhie Street, St Catharines 642705.71 4781574.66

27 Fitzgerald $154,900.00 59 Vine Street, St Catharines 643870.98 4780723.05

28 Queenston $99,794.00 30 Parkview Road, St Catharines 644430.96 4781628.54

28 Queenston $204,900.00 62 Chelsea Street, St Catharines 644804.36 4780530.40

28 Queenston $155,000.00 25 Berryman Avenue, St Catharines 644171.39 4780463.24

28 Queenston $159,900.00 17 Berryman Avenue, St Catharines 644178.28 4780425.61

29 Kernahan $89,500.00 23 Emmett Road, St Catharines 646401.30 4780417.82

29 Queenston $224,900.00 97 Bunting Road, St Catharines 645575.73 4780266.74

29 Queenston $179,900.00 25 Lorne Street, St Catharines 644976.29 4780278.76

29 Kernahan $160,000.00 31 Emmett Road, St Catharines 646418.58 4780362.62

30 Lock 3 $538,800.00 15 MacKenzie King Avnue, St

Catharines

646576.55 4780191.10

31 Louth $649,000.00 2098 Seventh Street, St Catharines 637672.50 4778582.77

33 Vansickle $309,900.00 66 Elderwood Drive, St Catharines 640673.75 4779794.27

33 Vansickle $435,000.00 53 West Farmington Drive, St

Catharines

640468.37 4779775.04

33 Vansickle $389,900.00 74 Sawmill Road, St Catharines 641140.93 4779810.22

33 Vansickle $359,900.00 228 First Street, St. Catharines 640108.41 4779939.54

34 Western Hill $549,900.00 29 Yates Street, St. Catharines 642391.57 4779453.21

34 Western Hill $649,900.00 14 Trafalgar Street, St. Catharines 642447.13 4779513.39

34 Western Hill $749,900.00 10 Norris Place, St. Catharines 642152.28 4779680.03

34 Western Hill $1,350,000.00 55 Yates Street, St. Catharines 642104.50 4779564.31

35 Western Hill $289,900.00 63 Glenridge Avenue, St. Catharines 643105.28 4779041.31

35 Western Hill $374,800.00 54 Highland Avenue, St. Catharines 643297.83 4779404.20

35 Western Hill $149,900.00 23 Hainer Street, St. Catharines 642523.17 4779029.04

35 Glenridge $650,000.00 43 Highland Avenue, St. Catharines 643290.53 4779546.38


March 22, 2013

36 Glenridge $139,000.00 6 Phelps Street, St. Catharines 644589.87 4779059.90

36 Glenridge $239,900.00 2 Marren Street, St. Catharines 644266.91 4779394.41

36 Oakdale $189,900.00 298 Oakdale Avenue, St. Catharines 644029.78 4779967.80

37 Secord Woods $357,500.00 28 Woodrow Street, St. Catharines 645790.40 4779806.49

37 Oakdale $132,900.00 27 Battersea Avenue, St. Catharines 645473.22 4779559.71

37 Secord Woods $174,900.00 37 Greenwood Avenue, St. Catharines 645849.50 4779719.24

37 Secord Woods $159,900.00 52 Greenwood Avenue, St. Catharines 645943.29 4779720.40

38 Secord Woods $329,900.00 3 Alex Grant Place, St. Catharines 646621.41 4779921.26

39 Louth $1,995,000.00 3420 Ninth Street, St. Catharines 636907.27 4777505.39

39 Louth $569,900.00 1673 St. Paul Street, St. Catharines 637937.85 4777679.81

41 Vansickle $349,900.00 15 Consiglia Drive, St. Catharines 640886.08 4777726.63

41 Vansickle $359,900.00 52 Strada Blvd., St. Catharines 641083.64 4777791.16

42 Vansickle $114,000.00 48 Church Hill Street, St. Catharines 641797.25 4778145.97

42 Western Hill $224,000.00 28 Cumming Street, St. Catharines 642267.18 4778061.14

42 Vansickle $165,000.00 35 Lloyd Street, St. Catharines 641915.16 4778243.01

43 Western Hill $254,900.00 45 Rivercrest Drive, St. Catharines 643041.78 4778346.23

43 Western Hill $399,999.00 111 South Drive, St. Catharines 643231.63 4778819.56

43 Western Hill $449,900.00 47 Hillcrest Avenue, St. Catharines 642967.70 4778852.48

43 Glenridge $369,900.00 25 Riverview Blvd., St. Catharines 642888.28 4777800.39

44 Glenridge $275,000.00 71 Village Road, St. Catharines 643832.64 4777690.53

44 Glenridge $379,000.00 27 Adelene Crescent, St. Catharines 643763.57 4778099.34

44 Glenridge $144,000.00 168 Oakdale Avenue, St. Catharines 644579.04 4778896.22

45 Secord Woods $219,500.00 16 Rampart Drive, St. Catharines 645808.10 4778756.05

45 Merritton $103,900.00 20 Chestnut Street, St. Catharines 645265.43 4777841.19

45 Merritton $349,900.00 368 Merritt Street, St. Catharines 645263.62 4778087.06


March 22, 2013

B.1 Raw Data of Neighborhoods, House Prices, Addresses and Coordinates in St.

Catharine’s

49 Vansickle $545,000.00 68 McCaffery Crescent, St. Catharines 640915.76 4776246.53

49 Vansickle $186,900.00 218 Rykert Street, St. Catharines 640805.07 4777428.80

49 Vansickle $369,800.00 93 McBride Drive, St. Catharines 640843.90 4777354.35

50 Powerglen $99,900.00 198 Pelham Road, St. Catharines 641973.92 4777220.88

50 Riverview $599,000.00 280 Riverview Blvd., St. Catharines 642970.97 4778096.75

50 Powerglen $334,900.00 259 Pelham Road, St. Catharines 641759.54 4776895.80

51 Riverview $349,900.00 2 Parklane Crescent, St. Catharines 642717.47 4776976.48

51 Marsdale $389,000.00 12 Valerie Drive, St. Catharines 643591.71 4777061.70

52 Brockview $389,000.00 6A Pearl Ann Drive, St. Catharines 644300.64 4776809.85

52 Glenridge $254,900.00 16 Glengarry Road, St. Catharines 644756.71 4777608.79

52 Glenridge $234,900.00 10 Brookdale Avenue, St. Catharines 644859.36 4777633.17

53 Merritton $725,000.00 46 Ridge Point Drive, St. Catharines 645174.02 4776881.33

53 Burleigh Hill $132,900.00 68 Queen Street, St. Catharines 642267.02 4779903.42

53 Burleigh Hill $194,900.00 64 Rose Street, St. Catharines 640824.33 4780720.23

54 Merritton $175,000.00 54 Welland Avenue, St. Catharines 642151.79 4780291.92

54 Merritton $279,900.00 57 Welland Avenue, St. Catharines 642205.43 4780310.28

geostatistical analysis

Documents

geostatistical report

catharines area

obtained dataset

b geostatical report

geostatical collection

statistical calculations

housing locations

statistical investigation