Datasets On Rented Properties

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Question:

Discuss about the Datasets On Rented Properties.

Answer:

This report looks at two datasets on rented properties taken by students in Australia. It uses primary and secondary data to determine a few determinants of rent paid by students, in terms of the chosen suburb, the number of bedrooms as a proxy for size, type of property (flat or house) and bond amount paid for the property. As we are using a sample its usefulness is limited by the sampling technique, and the data collected.

Section 1

We first consider a primary dataset, obtained by an interview with students to know their weekly rent. This dataset is problematic as

It is very small (only 5 points in it)
It is not comparable to other secondary data that provides information on suburb, the number of bedrooms, category - flat or house, and bond amount paid.

The other data is a secondary data- with 500 observations. It is rich in terms of additional information and can be used to make estimates campus wise or to determine association among variables. It can also be used for regression purposes to determine what affects rents in a significant way. Such conclusions can help students search for the right property based on their own requirements. A snapshot of this set is as follows:

Bond Amount	Weekly Rent	Dwelling Type	Number Bedrooms	Postcode	Suburb
$2,700	$675	Flat	3	2031	RANDWICK
$3,000	$750	Flat	2	2031	RANDWICK
$1,540	$385	Flat	2	2144	AUBURN
$2,360	$590	House	3	2144	AUBURN
$2,600	$650	Flat	1	2000	SYDEY

Section 2

We now use the primary data, to give a snapshot with numerical and visual help.

weekly rent
Mean	160
Standard Error	24.2899156
Median	150
Mode	#N/A
Standard Deviation	54.31390246
Sample Variance	2950
Kurtosis	-1.952887101
Skewness	0.327662152
Range	130
Minimum	100
Maximum	230
Sum	800
Count	5

It can be seen that the highest rent is $230, while the lowest is $120 only0 almost half of the maximum. The mean rent is $160 while median is $150. The data is limited, but a little skewed to the right.

Section 3

Next we consider dataset2, and look at the variable - Dwelling Type. The following points are clear:

Most students prefer to live in flats- 474/500 or 94.8% in the sample.
Parramatta is the most preferred location- 156/500 = 33.2% stay here
The most dominated suburb is Sydney in terms of flats, with just 1/167 =0.5% staying in a house here. The other suburbs have a % of 17.8% , 5.7% and 2.9% staying in houses.
The difference in flat and house residency is seen more starkly in a bar chart below.

SUBURB	Flat	House	Grand Total
AUBURN	60	13	73
PARRAMATTA	147	9	156
RANDWICK	101	3	104
SYDNEY	166	1	167
Grand Total	474	26	500 .

We move to check the hypothesis that houses are preferred by less than 10% of students. = sample proportion of students in houses = 26/500 = 0.052

Ho: p= 0.1

H1: p < 0.1 ( left tail test)

Z test value = (0.052 – 0.1)/ SE where SE = (0.052 *.948 /500)^.5 = 0.01

Test value = - 0.042 /0.01 = -4.834. Using a 95% confidence level, the critical z value is -1.645. The p value of the test value is P (z < -4.834) = 0 as p value < 0.05, we conclude that we cannot accept the null hypothesis. There is statistical evidence that proportion of Houses is less than 0.1.

This conclusion proves the data shown above in true in a statistical sense. It is not mere luck/sampling problem that share of flats is so high. The low share of houses is systematic, and may have deeper reasons which we are unable to see in this assignment. ?

Section 4

Next we move on to dwellings with 2 bedrooms only- flat and houses, irrespective of the suburb. To compare them we segregate them on the basis of suburbs and use average mean as the comparison metric. The table shows that Auburn has the lowest average rent of $404.67, while Sydney is at the other extreme of $838.04. A visual description is shown for easier comparison.

Row Labels	Sum of Average of WeeklyRent
AUBURN	404.67
PARRAMATTA	461.31
RANDWICK	618.04
SYDNEY	838.04

Once again, like we tested for statistical significance of the houses proportion, we can check if the differences in average rent are amatter of luck/ design of the sample chosen or sysematic. For testing this we use ANOVA test.

The null hypothesis is

Ho: µ1 = µ2 = µ3 =µ4 ( 1, 2,3 4 refer to suburbs)

The alternative hypothesis is

H1: µ1 ≠ µ2 ≠ µ3 ≠ µ4

Using the ANOVA function in Excel we get the following table. Using the F test we note that p value is zero as P( F > 456.9) = 0. This implies that the differences are statistically different. Accordingly a student must decide on the suburb to choose after considering these mean values as important and real enough.

Source of Variation	SS	df	MS	F
Between Groups	7640126.16	3	2546709	456.9565
Within Groups	1616227.32	290	5573.198

Total	9256353.49	293

Section 5

Lastly, we consider the relation between two quantitative variables- weekly Rent and Bond Amount in a scatterplot. ?

We can see that most datapoints lie on the regression line (red line) of are very close to. This shows up as very strong association, with virtually zero outliers. The value of coefficient of determination = 0.985. The correlation coefficient is 0.992= .958^.5 is extremely high. So the bond amount can act as a very good and reliable guide to the value of rent. Lower bond amount properties are likely to have lower rents.

Section 6

To conclude we can say that the secondary data is richer and more useful. It can still be validated with use of primary data. However we need more details on the primary data, so that we can make it more comparable with secondary data.

The data can be improved to include more parameters that affect rents – size of dwelling in square feet, shared or single occupancy, provision of kitchen can be some examples.

References

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