Analyse database using correlation analysis

The properties 'Number of addresses per square kilometre' and 'Number of houses per hectare' are very similar, which means that, possibly, only one should be used in the regression analysis. For this purpose correlation analysis is carried out prior to the regression analysis.

To determine whether a coefficient is meaningful to include in the regression, the following relationship holds (for derivation, see standard text books on statistics):

where:

r = correlation coefficient n = sample size

Z = coefficient depending on the chosen confidence level; for confidence level 95%, Z = 1.96

Table 12.1 shows the results of analysing the database to see which properties correlate to the return on investment. It shows that the property 'Number of addresses per square kilometre', correlates to the exploitation result much better than the property 'Number of houses per hectare' which is, therefore, not included in the regression analysis.

Before performing the regression analysis, the correlation between independent and dependent variables was analysed on multi-collinearity. This means two variables being so strongly related to each other, that only one should be included in the regression model. Part of the results of this analysis is shown in Table 12.2.

This correlation analysis is interesting because it shows that virtually every property relates to the type of house (apartment or non-apartment). This is called multi-collinearity. This means that regression analysis would not be useful because the influence of a particular property (i.e. floorspace) might be different for an apartment than it would be for a non-apartment. This is why the regression analysis is done per type of house.

1 Location vs return on investment

Property

Coefficient

Number of addresses per square kilometre

0.217

Number of houses per hectare

-0.007

Sample size: 293

Numbers in italics represent meaningful coefficients i

:|r|> °.1145 = -1293)

Table 12.2 Correlation analysis whole database

Property

ROI

MFU

SFU

Average Return on Investment

0,392

-0,392

Single family units (SFU)

0,392

-1,000

Multiple family units (MFU)

-0,392

-1,000

No. of houses the object consists of

-0,285

-0,067

0,067

Perc. of houses without rent restriction

0,085

0,230

-0,230

Houses with different no. of dwelling units

-0,156

-0,587

0,587

Subsidised

0,445

0,089

-0,089

Floorspace

0,083

0,573

-0,573

Houses with 2 dwelling units

-0,073

-0,350

0,350

Houses with 3 dwelling units

-0,082

-0,622

0,622

Houses with 4 dwelling units

0,043

0,229

-0,229

Houses with 5 dwelling units

0,098

0,487

-0,487

Reserved parking

-0,124

0,054

-0,054

Year of construction 1950-1959

-0,213

-0,271

0,271

Year of construction 1960-1969

-0,292

-0,154

0,154

Year of construction 1970-1979

-0,021

0,303

-0,303

Year of construction 1980-1989

0,523

0,185

-0,185

First five years of exploitation

0,216

-0,047

0,047

First ten years of exploitation

0,176

0,052

-0,052

First fifteen years of exploitation

-0,342

-0,001

0,001

Number of addresses per square kilometre

0,171

0,529

-0,529

Average family size

0,257

0,553

-0,553

Income per household

-0,237

-0,446

0,446

No. of primary schools in postcode area

0,048

0,235

-0,235

No. of supermarkets in postcode area

-0,162

-0,288

0,288

Built in densely populated provinces

-0,001

-0,193

Sample size: 130

Numbers in italics represent meaningful coefficients (|r| > 0.17 = ^HO) for the correlation of the variable concerned to the exploitation result

Table 12.3 Results of single variable regression analysis

Property

t-statistic

No. of houses the object consists of

-3.41

0,10

Perc. of houses without rent restriction

2.51

0.05

Subsidised

13.18

0.63

Year of construction 1960-1969

-2.07

0.03

Year of construction 1970-1979

-8.33

0.41

Year of construction 1980-1989

14.65

0.68

Floorspace

-0.07

-0.01

Houses with 4 dwelling units

4.15

-0,15

Houses with 5 dwelling units

-3.73

-0,12

Reserved parking

2.32

-0,04

Number of addresses per square kilometre

1.46

0.01

Average family size

2.93

-0,07

Income per household

0.18

-0.01

No. of primary schools in postcode area

-1.57

0.01

No. of supermarkets in postcode area

-2.22

0.04

Built in densely populated provinces

2.41

0,05

Numbers in italics are significant on a 5% level

Numbers in italics are significant on a 5% level

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