Analyzing Rental Market Data

This assignment analyzes real estate rental market data to understand the relationship between bond amounts and rental prices. Students utilize secondary data sources, employing descriptive statistics (mean, median, mode, range) and measures of dispersion (standard deviation, variance) to summarize the data. Regression analysis is used to examine the correlation between bond amount and rent, with the coefficient of determination (R-squared) and correlation coefficient (r) providing insights into the strength of the association. The assignment concludes by discussing the limitations of secondary data and suggesting improvements for future analyses.

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 SYDNEY
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.
a.
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.

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