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1 Quantitative Methods (M) Semester 1, 2020 Major Project (individual project) 1. Instructions 1) This is an individual assignment. 2) The maximum score is 50 points. 3) All numerical analysis, all...

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1
Quantitative Methods (M) Semester 1, 2020
Major Project (individual project)
1. Instructions
1) This is an individual assignment.
2) The maximum score is 50 points.
3) All numerical analysis, all tables and figures need to be done using Excel or Stata.
4) Please retain your Stata code and Excel file and make sure that they are user-friendly (use
comments where necessary). Using your submitted analysis file, one should be able to produce
all your results, tables, and figures.
5) The presentation of your write-up is important. Poorly presented work may result in loss of
marks (up to 20 marks out of 50).
6) Please retain a copy of the project that is submitted.
7) You would need to submit:
a) Stata code (if you use it)
) Excel file with analysis (if you use it)
c) the report (in doc, docx, or pdf format) with ‘Assignment Cover Sheet’, which must be
signed (electronic signature is okay) and dated before submission; the report should be
properly formatted and be similar to business report.
8) Lecturer can refuse to accept assignments, which do not have a signed acknowledgment of
the University’s policy on plagiarism.
9. Any suspected plagiarism will be severely punished. This includes any student that submits
copied work or any student that allows their work to be copied.
10. You must acknowledge any external material you use in your answers, e.g., material from
websites, textbooks, academic journals and newspaper articles.
11. All queries for this project should be directed to Lecturer.
12. The submission deadline for the problem set is 6pm, Wednesday the 10th of June, 2020.
13. The submission must be done through MyUni.
14. Late submission will be penalized 5 points (out of 50 points) per day.
2
2. Agenda
Assume that now it is the end of March 2018, and you are a real estate consultant in Melbourne.
The Melbourne real estate data for the XXXXXXXXXXperiod was downloaded from the following
website:
https:
www.kaggle.com/anthonypino/melbourne-housing-market.
The data set includes the following variables:
Variable Description
Subu
Subu

Address Address
Rooms Number of bedrooms
Type H - House; U - Unit; T - Townhouse
Price Price in Australian dollars
Method Sale method:
PI - property passed in (property not sold yet);
S - property sold in auction;
SA - sold after auction;
SP - property sold prior;
VB - vendor bid (property not sold yet)
PN - sold prior not disclosed;
SN - sold not disclosed;
NB - no bid (property not sold yet);
W - withdrawn prior to auction (property not sold yet).
SellerG Real estate agent
Date Date sold
Distance Distance from CBD in Kilometres
Postcode Postcode
Bedroom2 Number of bedrooms
Bathroom Number of bathrooms
Car Number of car spots
Landsize Land size in sq. metres
BuildingArea Building size in sq. metres
YearBuilt Year the house was built
CouncilArea Governing council for the area
Lattitude Latitude
Longtitude Longitude
Regionname General region (West, North West, North, North East etc.)
Propertycount Number of properties that exist in the subu
Given that there are two variables for the number of rooms (Rooms and Bedroom2), please use
Rooms in the analysis and ignore Bedroom2.
You got a client who would like to better understand real estate market and purchase the
property. Your tasks are listed below.
https:
www.kaggle.com/anthonypino/melbourne-housing-market
3
Task #1: Market conditions (7 points)
Your client would like to know more about the market conditions about the real estate market
in Melbourne (including all subu
s). Please provide the time series graphs for quarterly sale
volume (the number of sold properties) as well as mean and median sold price for the 2016-
2018 period.
Has the average property price increased in the first quarter of 2018 compared to the last quarter
of 2017?
Have the mean and median property price increased in the first quarter of 2018 compared to
the first quarter of 2017? Which measure (mean or median) is more suitable to use to describe
the property price evolution?
Discuss the results, including the limitations of the tests.
Task #2: Descriptive statistics (7 points)
Discuss
iefly your sample, including the number of observations, outliers. Provide the
descriptive statistics of the sample. How you choose to do this is entirely at your discretion.
However, it is recommended that you consider using both summary statistic and graphical
methods while also noting any peculiarities within the data set. In addition, your client would
like to see:
 the histogram of the sold price for the entire sample1
 and the histograms of sold price for the year 2016 and the year 2017 on the same figure.
Task #3: Property price estimation (13 points)
Your client would like to purchase the following property:
 Subu
: Balwyn North
 Distance: 9.2
 Rooms: 4
 Type: House
 Car: 2
 Bathroom: 3
 Landsize: 700
 BuildingArea: 220.
You are expected to build a regression model of house prices. In doing so, make sure that you
use an appropriate number of predictors to develop your estimates. Once you have constructed
an appropriate model, use it to obtain:
 A point prediction of the expected property price

1 You may refer to the textbook on how to determine the optimal bin width.
4
 A 90% interval prediction for this price.
Discuss the significance of the independent variables in your model. Suppose your client is
flexible and he can drop the requirement for house are to be 220 sq. meters. Please compute:
 A point prediction of the expected property price
 A 90% interval prediction for this price.
Compare the obtained results with the previous findings.
Your client’s friend is a builder, and he told your client that it is possible to extend a 3-bedroom
house to a 4-bedroom house for $150,000. Would you recommend your client to buy a 3-
edroom house and then renovate it rather than to buy a 4-bedroom house (assuming that after
enovation the 3-bedroom house will become equivalent to a 4-bedroom house)?
Your client expects that property price increases with the number of rooms (controlling for
many other factors) and would like to know whether this positive relation is impacted by the
number of bathrooms.
Task #4: Hypothesis testing (7 points)
You client hear that property prices in Brighton are higher than in Balwyn North. Develop the
appropriate hypotheses and test them using t-test and regression analysis. Discuss the results.
Task #5: Buying property (9 points)
Your client would like to know whether property price depends on the sale method. Would you
ecommend your client to purchase property prior to the auction, or in the auction, or after the
auction, given the empirical data?
Your client has been told that large real estate agencies are able to sell properties at higher
prices. You are asked to check this statement. Assume the following agent types:
 big (market share over the sample period in terms of number of sold properties >= 6%)
 medium (1% <= market share over the sample period in terms of number of sold
properties < 6%), and
 small (market share over the sample period in terms of number of sold properties <
1%).
Would you recommend your client to take into account the agent type when buying the
property?
Task #6: Limitations of the analysis (7 points)
Discuss the limitations of the analysis and how they affect your recommendations to your
client.
5
Additional information
Our sample is likely to contain missing values, outliers and be subject to other imperfections.
You may need to consider them prior to starting the analysis. Further, the sample includes
properties that were not sold. You should drop those observations.
To ensure that regression residuals “behave well,” you may need to scale or transform one or
more variables. For example, to use a natural logarithm value of the variable instead of its raw
value.
Good luck!
Answered Same Day Jun 13, 2021

Solution

Sudharsan.J answered on Jun 14 2021
130 Votes
Melbourne Housing
Assignment
Task-1
Plot-1
    Yea
    Quarte
     Mean
    Median
    2016
    Qt-1
    933572.581
    890000
    
    Qt-2
    1040925.96
    850000
    
    Qt-3
    1046924.12
    886000
    
    Qt-4
    1094654.66
    910000
    2017
    Qt-1
    1125863.21
    931000
    
    Qt-2
    1080965.33
    906500
    
    Qt-3
    1008621
    850000
    
    Qt-4
    1023868.11
    850000
    2018
    Qt-1
    1001258.31
    835000
The table shows the mean and median of price of house in Austrialia (in dollars) for each quarter. It’s is found that quarter-4 in 2016 has the highest mean pricing of $10946544.66, followed by quarter-2 in 2017, mean pricing of $1080965.33.
    Yea
    Mean
    AVG
    2017
    Qt-4
    1023868
    2018
    Qt-1
    1001258
Comparing the last quarter of 2017 with first quarter of 2018, there was reduction in the mean property price, it shows that there is decrease in property value when compared to quarter-1 of 2018 with quarter-4 of 2017.
    9.20241E-08
    * P-value
Here we used unpaired t-test to compare mean property pricing of first quarter between 2018 and 2017. There was statistically significant difference noted between 2018 and 2017.
Task-2
    Outliers
    1278
Plot-2

    House Type
    Frequency
    Percentage
    House
    23980
    68.80%
    Town house
    3580
    10.27%
    Unit
    7297
    20.93%
    Grand Total
    34857
    100.00%
Overall population consists of 68.8% of house, whereas 20.1% has town house and remaining Unit type of house.
Plot-3
    Sale Method
    Frequency
    Percentage
    PI
    4850
    13.91%
    PN
    308
    0.88%
    S
    19744
    56.64%
    SA
    226
    0.65%
    SN
    1317
    3.78%
    SP
    5095
    14.62%
    SS
    36
    0.10%
    VB
    3108
    8.92%
    W
    173
    0.50%
    Grand Total
    34857
    100.00%
It is noted that, more than half of the property were sold in auction its about 56%, followed by property sold in prior and property passed was about 14% respectively.
    Region Name
    Average of Price
    Min of Price
    Max of Price
    Eastern Metropolitan
    1108723.00
    288000
    5000000
    Eastern Victoria
    714328.20
    337000
    2300000
    Northern Metropolitan
    861484.05
    121000
    6500000
    Northern Victoria
    619051.20
    296000
    1430000
    South-Eastern Metropolitan
    877682.68
    266000
    9000000
    Southern Metropolitan
    1395928.33
    112000
    11200000
    Western Metropolitan
    837615.32
    85000
    4020000
    Western Victoria
    432606.77
    280000
    1152000
    Grand Total
    1050173.345
    85000
    11200000
Based on the region wise segregation, Southern metropolitan has the highest average pricing property with $1395928.33, followed by eastern metropolitan and southern eastern metropolitian.
    Su
u
    Average of Price
    Average of Landsize
    Cante
ury
    2386270.59
    710.53
    Middle Park
    2232148.15
    224.21
    Malvern
    2087618.64
    407.26
    Deepdene
    2001785.71
    979.71
    Brighton
    1984226.93
    466.02
    Albert Park
    1927650.54
    198.23
    Balwyn
    1893712.05
    614.96
    Camberwell
    1861132.86
    607.78
    Kew
    1796676.04
    530.76
    Balwyn North
    1786108.75
    933.17
    Ivanhoe East
    1769047.62
    749.37
    Kooyong
    1698875.00
    677.08
    Kew East
    1674408.16
    737.86
    Ashburton
    1660385.32
    623.79
    Toorak
    1655193.61
    495.48
Plot-4
Plot-5
Task-3
Regression Output:
Inference:
Inference:
The model.1 is run with explanatory variable(Rooms, Type, Distance, Bathroom, Car, Landsize and Building area. Before running the analysis the Type variable is recoded as following, H-1, U-2 and T-3. the above table says that there is a strong negative relationship between type and positive relationship between rooms, distance, car, bathroom, Landsize and building area. There was a statistically significance difference noted between all explanatory variables except car and landsize. Based on the test of significance and adjusted R-squared value it is found that above model does not fit the dependent variable, seem to be a poor model with adj-R square (0.4548).
The fitted equation of the best model is:
 Price= -3059660+ 179728.2*room - 293287*type + 456099.9*Distance + 103062.7*Bathroom + 7536.317*Car +7.4150*Land size + 1002.86*Building Area
Plot-6
Task-4
· Null hypotesis: property pricing of Brighton are not higher than Balwyn North
· Alternative hypothesis: property pricing of Brighton are higher than in Balwyn North
    Su
u
    
    Price
    
    max
    min
    mean
    P-value
    Brighton
    11200000
    290000
    1984227
    0.0106
    Balwayn North
    4050000
    555500
    1786109
    
There was statistically significant difference between Brighton and Balwayn North.Since the p-value is less than 0.05, and, hence we reject our null hypothesis. Hence, it is concluded that property pricing of Brighton are higher than in Balwyn North.
Task-5
    Real State Agent
    Sum of price
     
    Percentage
    
    S
    SA
    SP
    Grand Total
    S %
    SA %
    SP...
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