Data Collection

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 .  

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 Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	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

Data 1 missing

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.

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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.  

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.  

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.

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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.

We need data1 so that it can be compared with data 2.

References

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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].

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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].