## 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) |

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
Numbers in italics are significant on a 5% level Numbers in italics are significant on a 5% level |

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