Statistical Analysis and Recommendations for NSW Housing Project

This report presents a statistical analysis of housing prices in the coastal region of New South Wales (NSW), aiming to provide recommendations to a housing construction company. The analysis utilizes descriptive and inferential statistical techniques on a dataset considering dwelling types (house, unit), regions (Sydney, Wollongong, Newcastle), and ocean view. Descriptive statistics reveal that houses have higher average prices than units, and price variations exist across regions, with Sydney having the highest average price. Inferential statistics, including t-tests and ANOVA, confirm that houses command a price premium over units, ocean views increase prices, and significant price differences exist between regions. However, no significant price difference was found for units in Wollongong with or without an ocean view. The report recommends the construction company focus on building houses, especially in Sydney, and consider ocean views to maximize profitability, while also stressing the importance of cost considerations. The analysis is limited by a small sample size, potentially affecting the reliability of regional price preferences.

STATISTICS FOR ANALYTICAL DECISIONS
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Executive Summary
The objective of the given report is to provide recommendations to housing construction
company which wants to undertake a project in the coastal region of NSW. The sample
housing data is provided which considers the prices across dwelling type (house, unit), region
(Sydney, Wollongong, Newcastle) and ocean view. The technique deployed to undertake the
analysis involves both descriptive and inferential statistical techniques. Based on the
inferential statistics, it is highlighted that houses have higher prices as compared to units,
prices of houses vary across the regions and houses with ocean view tend to result in a price
premium. As a result, it makes sense for the construction company to consider the above
factors and ensure that higher focus should be on houses which are located in Sydney and
preferably with ocean view. However, corresponding cost considerations are also pivotal
which company must consider.
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Table of Contents
Business Problem.......................................................................................................................2
Statistical Problem.....................................................................................................................3
Analysis......................................................................................................................................3
Descriptive Statistics..............................................................................................................3
Inferential Statistics................................................................................................................5
General Conclusion....................................................................................................................9
Implications................................................................................................................................9
References................................................................................................................................11
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Business Problem
A firm which is involved in housing construction wants to undertake a major housing
development and needs to do analysis of the same for which information about the ongoing
pricing and preferences of the customers need to be considered. A sample data has been
performed in order to enable the analysis of the prices of houses and units that are located in
Wollongong, Sydney and New Castle. Through the analysis, the company can obtain vital
information in relation to the various combinations in terms of region, view and type which
can fetch higher prices and essentially can also narrow down on the existing prices.
Statistical Problem
The given sample lists down the price of houses and units. It takes into consideration the
region and also whether ocean view is available or not. For this data, descriptive statistics
tools need to be applied so as to highlight the key characteristics of the provided sample data.
Further, based on the sample data inferences need to be derived based on the population data
through the use of inferential statistics techniques such as hypothesis testing. Through this
statistical analysis a comparison needs to be facilitated between various parameters which
could highlight the prevailing price trends which could be then used by the company (Hair et.
al., 2015).
Analysis
Descriptive Statistics
The descriptive statistics aims to describe the characteristics of the sample data available
through the use of various measures of central tendency and dispersion as they provide
valuable information about the underlying shape and also helps in highlighting key trends
which further can be validated for the population using the inferential statistical tools.
Type of Dwelling
The descriptive statistics as per the dwelling type are as highlighted below.
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From the above, it is apparent that the average price of houses seems to be higher in
comparison to units. Also, there are certain houses which have quite high price leading to a
rightward tail as is apparent from a positive skew. On the contrary, unit prices have a slight
negative skew. Neither of the distributions would be normal owing to presence of skew.
Dispersion seems to be low to moderate for both the type of dwellings even though it is
slightly higher for houses in comparison to the units (Flick, 2015).
Region
The descriptive statistics as per the underlying region where the underlying dwelling is
located are as highlighted below.
It seems evident from the above that there seems a significant difference in average prices in
the various regions with Sydney having the maximum price and Newcastle having minimum
prices. Further, for all the regions there is a positive skew presence which highlights non-
normality and also presence of dwellings which have significantly high prices. The dispersion
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for the prices in various regions seems to be low when viewed in terms of mean which
implies that for each region there seems to a different price band with limited overlapping
(Hillier, 2006).
Ocean View
The descriptive statistics based on the presence or absence of the ocean view are as indicated
below.
From the above, it is apparent that there does not seem any significant difference in the price
of dwellings with or without an ocean view. A positive skew is observed for both which
implies a tail on the right and hence the underlying distribution would not be normal. The
dispersion as captured by standard deviation is quite comparable and remains moderate.
However, the range for the dwellings with ocean view seems higher than the dwellings which
lack ocean view. Thus, it might be possible that assuming everything else as the same, the
ocean view might add a premium to the price (Hastie, Tibshirani and Friedman, 2011).
Inferential Statistics
The inferential statistical techniques are deployed to derive information about the population
based on the given sample information. Various claims are made which need to be checked
based on the statistical data available from the sample through the application of hypothesis
testing. Using this technique, the various claims have been tested as highlighted below.
1) House Prices > Unit Prices
The requisite hypothesis to be tested is highlighted below.
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Null Hypothesis (H0): μHouse = μunit
Alternative Hypothesis (H1): μHouse > μunit
For the comparison of the means of the above two independent samples, the requisite test
would be T test since the standard deviation of the population is not known.
Considering the sample size is same for both the samples, equal variance option has been
chosen in excel for the performance t test. The relevant output obtained from excel is as
highlighted below.
Considering the alternative hypothesis has a > sign, it is apparent that the given hypothesis
test is single tail and hence the applicable p value would be one tail. The one tail p value has
been computed as 0. Assuming the level of significance as 5% or 0.05, it is evident that the
relevant p value is lower than this value which implies that the available evidence is ample
for rejecting the null hypothesis and thereby allows for acceptance of the alternative
hypothesis. Hence, it may be claimed with 95% confidence that the average house prices are
higher than the average unit prices (Flick, 2015).
2) Ocean view houses command premium
The requisite hypothesis to be tested is highlighted below.
Null Hypothesis (H0): μOceanView = μNoOceanView
Alternative Hypothesis (H1): μOceanView > μNoOceanView
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For the comparison of the means of the above two independent samples, the requisite test
would be T test since the standard deviation of the population is not known.
Considering the sample size is not the same for both the samples, unequal variance option has
been chosen in excel for the performance t test. The relevant output obtained from excel is as
highlighted below.
Considering the alternative hypothesis has a > sign, it is apparent that the given hypothesis
test is single tail and hence the applicable p value would be one tail. The one tail p value has
been computed as 0.043. Assuming the level of significance as 5% or 0.05, it is evident that
the relevant p value is lower than this value which implies that the available evidence is
ample for rejecting the null hypothesis and thereby allows for acceptance of the alternative
hypothesis (Hair et. al., 2015). Hence, it may be claimed with 95% confidence that the
average house prices with ocean view are higher than the average houses prices without the
ocean view.
3) Difference in house prices in different regions
The requisite hypothesis to be tested is as highlighted below.
Null Hypothesis (H0): μSydney= μWollongong = μNewCastle
Alternative Hypothesis (H1): The average prices of houses in atleast one region are different
from the others.
It is apparent that in the given case the average of more than two variables need to be
compared and hence t test would not be feasible. Hence, the one column ANOVA is a
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suitable choice to compare the means (Hastie, Tibshirani and Friedman, 2011). The relevant
output of this test obtained from Excel is as outlined below.
The requisite p value from the above output has come out as 0.00. Assuming the level of
significance as 5% or 0.05, it is evident that the relevant p value is lower than this value
which implies that the available evidence is ample for rejecting the null hypothesis and
thereby allows for acceptance of the alternative hypothesis (Hillier, 2006). Hence, it may be
claimed with 95% confidence that the average house prices in Sydney, Wollongong and New
Castle are not the same and a statistically significant difference does exist.
4) Units situated in Wollongong with ocean view demand a price premium
The requisite hypothesis to be tested is highlighted below.
Null Hypothesis (H0): μOceanView = μNoOceanView
Alternative Hypothesis (H1): μOceanView > μNoOceanView
For the comparison of the means of the above two independent samples, the requisite test
would be T test since the standard deviation of the population is not known.
Considering the sample size is not the same for both the samples, unequal variance option has
been chosen in excel for the performance t test. The relevant output obtained from excel is as
highlighted below.
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Considering the alternative hypothesis has a > sign, it is apparent that the given hypothesis
test is single tail and hence the applicable p value would be one tail. The one tail p value has
been computed as 0.203. Assuming the level of significance as 5% or 0.05, it is evident that
the relevant p value is higher than this value which implies that the available evidence is
insufficient for rejecting the null hypothesis and thereby does not allow for acceptance of the
alternative hypothesis (Hair et. al., 2015). Hence, it may be claimed with 95% confidence that
the average unit prices in Wollongong with ocean view are similar to the average unit prices
without the ocean view situated in Wollongong.
General Conclusion
Based on the results obtained from the statistical analysis carried above, it is apparent that the
average price of houses is higher in comparison to the units. Also, evidence from sample data
suggests that the houses having ocean view tend to command a price premium in comparison
to those which lack the same. Besides, it is also evident that the average prices in the various
regions (i.e. Sydney, Wollongong, Newcastle) are not comparable as they are significantly
different from each other. Finally, it has also been seen that for units situated in Wollongong,
the prices do not differ significantly with the presence or absence of an ocean view. However,
one limitation of this is that the sample size is very small and hence it would be preferable if
a larger sample size was available. The small sample size may be a problem especially for
region based preferences in price since the filtered sample tends to become quite small and
not very reliable.
Implications
Based on the above conclusion and the underlying objective of the study, it makes sense for
the housing construction company to consider the above trends and implement the same in
their choice of site and dwelling type constructed. It makes economic sense for the company
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to focus more on house construction rather than units since the former demands a price
premium over the latter. Also, considering the high regional differences in price, if possible
the company should look to undertake the project in Sydney as the price commanded by the
project would be the highest amongst the locations considered. Further, if possible, care
needs to be taken to provide ocean view considering the underlying financials as the presence
of ocean view could potentially bring in a price premium. However, it is essential that the
cost considerations of the above suggestions should be considered by the builder and a
suitable decision is undertaken by the construction company.
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References
Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research
project, 4th ed., New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015). Essentials
of business research methods, 2nd ed., New York: Routledge.
Hastie, T., Tibshirani, R. and Friedman, J. (2011). The Elements of Statistical Learning, 4th
ed., New York: Springer Publications.
Hillier, F. (2006), Introduction to Operations Research, 6th ed., New York: McGraw Hill
Publications
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