BUS708 Statistics and Data Analysis: Property Data dataset
Overview Of The Assignment
This assignment will test your skill to collect and analyse data to answer a specific business problem. It will also test your understanding and skill to use statistical methods to make inferences about business data and solve business problems, including constructing hypotheses, test them and interpret the findings.
Suppose you work in a company that provide services for people worldwide who are moving to Australia either permanently or temporarily (e.g. international students). One of the services it provides is to assist clients with choosing accommodation. Your task is to analyse the rent in different suburbs in Sydney Metro, specifically 4 different suburbs: Sydney, Randwick, Parramatta, and Auburn and analyse the rent that international students currently pay.
TaskDescription:
Before you proceed, you need to have Dataset 1 and Dataset 2 ready:
Dataset 1: Collect data on international students’ weekly rent (in Australian Dollars). There is no requirement about sampling methods and sample size, but you need to justify your approaches in Section 1 (see below).
Dataset 2: You will receive an email about the instruction to download the Rental Bond Board Property Data dataset that has been edited and allocated to you. This is a subset of NSW Rental Bonds data published by the Department of Finance, Services and Innovation. The original dataset can be obtained from https://data.nsw.gov.au/data/dataset/formal-gipa-access-application-2016-2017-fa-13
Both datasets should be saved in an Excel file (one file, separate worksheets). All data processing should be performed primarily in Excel, or by using Statkey tool (http://www.lock5stat.com/StatKey).
Section 1: Introduction
- Give a brief introduction about the assignment
- Dataset 1: Explain how you collect the data and discuss whether or not your sample is biased. Is this primary or secondary data? What type of variable(s) is involved? You don’t need to display your data in this section.
- Dataset 2: Give a short description about this dataset. Is this primary or secondary data? What type of variable(s) is involved? Display the first 5 cases of your dataset.
Section 2: International Students’ Weekly Rent Use Dataset 1
- Present your data using a suitable graphical display and numerical summary.
- Make a short comment about the distribution of your data (e.g. the shape, centre, spread, outlier, and any interesting point).
Section 3: Rental Bond Board Property Data – Dwelling Type Use Dataset 2
- Examine just the data relating to Dwelling Type. Describe the data using a suitable graphical display and numerical summary.
- Is there enough evidence that the proportion of House dwelling type is less than 10%? Perform a suitable hypothesis test at a 5% level of significance.
- Describe the relationship between the variables Dwelling Type and Suburb using suitable graphical display and numerical summary.
- What suggestions can you give for clients who would prefer to rent a house instead of a flat, in terms of their options?
Section 4: Rental Bond Board Property Data – Weekly Rent Use Dataset 2
- By considering residential with 2 bedrooms only, compare the weekly rentamong the different suburbs using a suitable graphical display and numerical summary.
- By considering residential with 2 bedrooms only, is there any evidence of the difference in weekly rent among the different suburbs? Perform a suitable hypothesis test at a 5% level of significance.
- What suggestions can you give for clients who are deciding to rent in one of those suburbs, in terms of the Weekly Rent?
Section 5: Bond Amount Use Dataset 2
- Examine the relationship between the variables Weekly Rent and Bond Amount, using a suitable graphical display.
- Calculate the correlation coefficient and make comments, including any outliers that may present and what suggestions can you give to clients regarding bond amount.
Section 6: Conclusion
- What can you conclude about the weekly rent currently paid by international students and the weekly rent of properties on the market?
- Give suggestion for future research
Answer:
Section 1
This report looks into rented properties in 4 suburbs of Australia and targets only students. It uses information on not just weekly rents paid but also on other aspects of the accommodation. These aspects include- type of dwelling, number of bedrooms in the accommodation , suburb chosen, and bond amount of the property rented .
Data 1 Is Missing
The secondary data is taken from the website of Department of Finance, Services and Innovation as part of Rental Bond Board Property Data. A sample size of 500 is chosen. The table below is snapshot of this data:
|
BondAmount |
WeeklyRent |
DwellingType |
NumberBedrooms |
Postcode |
Suburb |
|
$2,900 |
$725 |
Flat |
3 |
2031 |
RANDWICK |
|
$2,480 |
$620 |
Flat |
1 |
2031 |
RANDWICK |
|
$1,960 |
$490 |
Flat |
2 |
2150 |
PARRAMATTA |
|
$2,200 |
$550 |
Flat |
2 |
2031 |
RANDWICK |
|
$2,280 |
$570 |
Flat |
2 |
2031 |
RANDWICK |
Section 2
Data 1 missing
Section 3:
Looking at the secondary data , we focus on the categorical variable - Dwelling Type. It has two options - flat and house. We provide a pivot tale for a 2*2 classification where the 2 attributes are dwelling type and suburb. We can observe the following:
- Most students live in flats – 462 /500 or 92.4%.
- Most of them prefer to live in Parammatta, while least number in Auburn, despite lowest rents here.
- Sydney has no student sin houses.
|
Row Labels |
Flat |
House |
|
AUBURN |
38 |
19 |
|
PARRAMATTA |
151 |
12 |
|
RANDWICK |
117 |
7 |
|
SYDNEY |
156 |
|
|
Grand Total |
462 |
38 |
The above information is visually seen below. The high blue bars for flats show their dominance over houses.
We ten turn to hypothesis testing to check is the proportion of houses is less than 10%
required sample proportion = p = 38/500 = 0.076
Ho: p= 0.1
H1: p < 0.1
Using the left tail hypothesis test with z distribution we get
Test value = (0.076 – 0.1)/ SE where
SE = (0. 1 *.9 /500)^.5 = 0.0134
The z test value = ( 0.076 0.1)/ 0.0134 = -1.789. The test value is more than critical value for 95% confidence ( -1.645) in absolute terms. This leads to the conclusion that that at a 5% level of significance or 95% confidence level, we DO NOT ACCEPT the null hypothesis. There is statistical evidence that proportion of houses in rented dwellings is less than 10%.
This means that flats are dominant in a systematically important way. It is no chance that this sample has rejected the null hypothesis. However if we choose a 99% confidence then we will be accepting the null hypothesis. This is because the critical value will be -2.33. thus, the idea that houses are less than 10% of al rented places for students can be debated depending on the confidence level and the precision level we choose.
Section 4:
We turn to the next parameter which is no of bedrooms – looking at flats and houses with 2 bedrooms only. The table and chart use the same information on average weekly rents across suburbs. Auburn is the cheapest suburb among the 4 , with rent of $393.17on weekly basis. Sydney is expectedly the most expensive with a rent of more than double Auburn rents - $840.74
|
Row Labels |
Average of WeeklyRent |
|
AUBURN |
393.167 |
|
PARRAMATTA |
474.159 |
|
RANDWICK |
608.278 |
|
SYDNEY |
840.738 |
The difference seen above can be challenged in statistical terms. Using ANOVA for checking the significance in differences, we conclude that differences in average weekly rents across suburbs are statistically different. The F test value is 261.9, which has p value of zero. This p value automatically supports differences in rent argument.
|
Anova: Single Factor |
|
|
|
|
| |
|
SUMMARY |
|
|
|
|
|
|
|
Groups |
Count |
Sum |
Average |
Variance |
|
|
|
Column 1 |
113 |
53580 |
474.159292 |
4371.832 |
|
|
|
Column 2 |
79 |
48054 |
608.278481 |
11073.23 |
|
|
|
Column 3 |
61 |
51285 |
840.737705 |
14925.7 |
|
|
|
Column 4 |
30 |
11795 |
393.166667 |
2290.489 |
|
|
|
ANOVA |
|
|
|
|
|
|
|
Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
|
Between Groups |
6522098.798 |
3 |
2174032.93 |
261.9743 |
8.15E-81 |
2.63696 |
|
Within Groups |
2315322.976 |
279 |
8298.64866 |
|
|
|
|
Total |
8837421.774 |
282 |
|
|
|
|
This result is helpful to pick and choose a suburb based on how much has been allocated for rent or what student can pay as rent. These average values area good guide to rents in each suburb, and help to avoid looking at all suburbs when rent constraint exists.
Section 5:
The scatterplot tells us:
- A strong positive association between weekly Rent and Bond Amount exists, as shown by upward sloping regression line.
- The value of R2 is 0.953- so that 95.3% of variation in weekly rent is explained by variation in bond amount.
- We can see 2 outliers visually as depicted.
- The coefficient of correlation is .953^.5 = 0.972, which is very high.
Association. This proves that bond prices are a good indicator/ proxy for weekly rent Any information on bond amount can help to guess the rent level quite accurately.
Section 6
We need data1 so that it can be compared with data 2.
References
Anon., n.d. Hypothess testing. [Online] Available at: https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/ [Accessed 12 Sep 2017].
Anon., n.d. Mean, median, mode. [Online] Available at: https://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/measuresofaveragerev6.shtml [Accessed 13 Sep 2017].
Home.iitk.ac.in, n.d. Regression analysis. [Online] Available at: https://home.iitk.ac.in/~shalab/regression/Chapter2-Regression-SimpleLinearRegressionAnalysis.pdf [Accessed 6 Sep 2017].
Learn,bu.edu, n.d. The 5 steps in Hypothesis testing. [Online] Available at: https://learn.bu.edu/bbcswebdav/pid-826908-dt-content-rid-2073693_1/courses/13sprgmetcj702_ol/week04/metcj702_W04S01T05_fivesteps.html [Accessed 5 Sep 2017].
Rgs.org, n.d. Sampling techniques. [Online] Available athttps://www.rgs.org/OurWork/Schools/Fieldwork+and+local+learning/Fieldwork+techniques/Sampling+techniques.htm [Accessed 15 Sep 2017].
stat.ualberta.ca, n.d. What isa P value. [Online] Available at: https://www.stat.ualberta.ca/~hooper/teaching/misc/Pvalue.pdf [Accessed 9 Sep 2017].
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