Ýêîíîìè÷åñêèå íàóêè/8.
Ìàòåìàòè÷åñêèå ìåòîäû â ýêîíîìèêå
Nurpeissova Zh.S.
A.Baitursynov Kostanai State University, Kazakhstan
Application of correlation-regression analysis in the
formation of real estate prices
In economical
research to determine level and
dinamics of economical processes generally we determine factors by solving problem. Solution
of this problem generally solving by analyzing correlation, regression and factors.
In this
process affected factors
can be divided into 2 groups: basic (determines level of process) and additional. Generally additional
factors defined as random factors.
The relation
between basic and additional factors determines changes in process. It`s
important to show relationship between this factors to determine exact state of
economical process,
and although it`s not all about showing them, but also calculate their value.
The
problem of house is one of the most important problems in our lifes. And one of
the consequence of this problem is determination of factors which forms the
flat`s price. Prices of flats in 1st
market term are much higher then prices of flats in 2nd market term, according to the
values of affected factors. That`s why, it`s
recommended to analyze
flats in 2nd market term to determine dependence of different factors
to the price of flat.
In our
research we analyzed Kostanay city`s houses. We took
information about 50 one-roomed, two-roomed, three-roomed, four-roomed flats
which were written in different newspapers such as («Øàíñ», «Âàêàíñèÿ», «Êîñòàíàéñêèå
íîâîñòè». On the basis of this information we build the regression model by using different
factors which were having influence on the prices of this 50 flats.
Model
of plural regression: Y = a + ∑bixi+
ε
There
are:
Y – dependent variables (Price);
à – empty variable;
b – coefficient of õi;
õ³ – independent variable;
ε – random value.
In case
of Independent variables – Price
of apartment (dollars of USA).
Independent
variables:
― Õ1- Number of rooms (1, 2, 3, 4);
–
Õ2 – Region;
–
Õ3 - Area
(ì2);
–
Õ4 - Floor;
–
Õ5 - Number of house`s floor;
–
Õ6 - Repair works (0 – not repaired, 1 – repaired);
–
Õ7 - Construction project (0 – not improved, 1 – improved).
Table 1 – Initial data
|
Price, Ó |
Number of rooms, Õ1 |
Region, Õ2 |
Area, Õ3 |
Floor, Õ4 |
Number
of house`s floor, Õ5 |
Repair works, Õ6 |
Construction project, Õ7 |
|
35 000 |
1 |
4 |
36 |
4 |
6 |
1 |
0 |
|
27 000 |
1 |
4 |
34,2 |
2 |
6 |
1 |
1 |
|
23 500 |
1 |
4 |
34 |
1 |
5 |
1 |
0 |
|
15 000 |
1 |
1 |
27,4 |
2 |
5 |
0 |
1 |
|
16 000 |
1 |
1 |
32 |
3 |
5 |
1 |
0 |
|
17 500 |
1 |
1 |
21,2 |
5 |
5 |
1 |
0 |
|
16 000 |
1 |
3 |
26 |
1 |
5 |
1 |
0 |
|
20 000 |
1 |
3 |
35 |
1 |
9 |
0 |
1 |
|
28 000 |
1 |
3 |
42 |
2 |
5 |
1 |
1 |
|
20 000 |
1 |
2 |
30 |
2 |
5 |
0 |
0 |
|
22 000 |
1 |
2 |
33 |
5 |
10 |
1 |
1 |
|
30 000 |
1 |
2 |
35 |
5 |
9 |
0 |
0 |
|
22 000 |
1 |
5 |
30 |
5 |
5 |
0 |
0 |
|
30 000 |
1 |
5 |
32 |
4 |
5 |
1 |
1 |
|
40 000 |
1 |
5 |
34 |
1 |
5 |
1 |
1 |
|
28 000 |
2 |
4 |
52 |
10 |
10 |
1 |
0 |
|
33 000 |
2 |
4 |
53 |
7 |
10 |
1 |
0 |
|
42 000 |
2 |
4 |
54,7 |
3 |
10 |
1 |
1 |
|
37 000 |
2 |
4 |
49,9 |
7 |
9 |
0 |
1 |
|
21 000 |
2 |
1 |
44 |
2 |
3 |
0 |
0 |
|
23 000 |
2 |
1 |
47 |
3 |
5 |
1 |
0 |
|
25 000 |
2 |
1 |
46 |
2 |
5 |
1 |
0 |
|
25 000 |
2 |
1 |
47 |
1 |
5 |
0 |
0 |
|
23 000 |
2 |
3 |
38 |
4 |
6 |
0 |
1 |
|
28 000 |
2 |
3 |
43 |
4 |
5 |
0 |
1 |
|
31 000 |
2 |
3 |
44,1 |
5 |
5 |
1 |
1 |
|
40 000 |
2 |
3 |
53 |
4 |
6 |
1 |
1 |
|
21 000 |
2 |
2 |
44 |
2 |
5 |
0 |
0 |
|
25 000 |
2 |
2 |
48 |
3 |
5 |
0 |
0 |
|
28 000 |
2 |
2 |
44 |
2 |
5 |
1 |
0 |
|
45 000 |
2 |
2 |
48 |
3 |
5 |
1 |
1 |
|
30 000 |
2 |
5 |
47 |
3 |
4 |
1 |
0 |
|
35 000 |
2 |
5 |
56 |
8 |
9 |
1 |
0 |
|
45 000 |
2 |
5 |
53 |
4 |
5 |
1 |
0 |
|
55 000 |
2 |
5 |
63 |
5 |
5 |
1 |
1 |
|
40 000 |
3 |
4 |
68 |
5 |
5 |
1 |
0 |
|
40 000 |
3 |
4 |
60 |
5 |
5 |
1 |
0 |
|
22 000 |
3 |
1 |
58,2 |
1 |
4 |
0 |
0 |
|
36 000 |
3 |
1 |
62 |
4 |
5 |
1 |
0 |
|
45 000 |
3 |
3 |
68 |
2 |
9 |
1 |
0 |
|
65 000 |
3 |
3 |
69,2 |
4 |
9 |
1 |
1 |
|
40 000 |
3 |
2 |
61,8 |
5 |
5 |
0 |
0 |
|
45 000 |
3 |
2 |
65 |
4 |
5 |
1 |
1 |
|
50 000 |
3 |
5 |
69,5 |
10 |
10 |
0 |
1 |
|
80 000 |
3 |
5 |
64,4 |
5 |
5 |
1 |
1 |
|
78 000 |
4 |
4 |
82 |
5 |
5 |
1 |
0 |
|
30 000 |
4 |
1 |
62 |
5 |
5 |
1 |
0 |
|
65 000 |
4 |
3 |
83 |
5 |
5 |
1 |
0 |
|
45 000 |
4 |
2 |
62 |
3 |
5 |
0 |
0 |
|
80 000 |
5 |
5 |
83 |
1 |
6 |
1 |
0 |
Table 2 – Multicollinear
problem
|
|
Price, Ó |
Number of rooms, Õ1 |
Region, Õ2 |
Area, Õ3 |
Floor, Õ4 |
Number
of house`s floor, Õ5 |
Repair works, Õ6 |
Construction project, Õ7 |
|
Price, Ó |
1 |
|
|
|
|
|
|
|
|
Number of rooms, Õ1 |
0,7098 |
1 |
|
|
|
|
|
|
|
Region, Õ2 |
0,4719 |
0,0284 |
1 |
|
|
|
|
|
|
Area, Õ3 |
0,8163 |
0,9212 |
0,2078 |
1 |
|
|
|
|
|
Floor, Õ4 |
-0,2308 |
0,1749 |
0,3418 |
0,2897 |
1 |
|
|
|
|
Number of house`s floor, Õ5 |
-0,0986 |
-0,0633 |
0,2668 |
0,0965 |
0,5018 |
1 |
|
|
|
Repair works, Õ6 |
0,3210 |
0,0829 |
0,2728 |
0,1950 |
0,0707 |
0,0224 |
1 |
|
|
Construction project, Õ7 |
0,1362 |
-0,2191 |
0,2330 |
-0,1111 |
0,0621 |
0,2375 |
0,0070 |
1 |
To determine multicollinear problem by using
selected data, we
open MS Excel program and then use option “ Data analysis -> Correlation” and so by doing it we build matrix. In
this matrix we saw that Õ1 and Õ3 are strongly related,
that`s why in this correlation model we can not define the factor Õ1
as affected factor.
On the basis of this facts we make correlation-regression
analysis.
Table 3 – Regression
solution
|
Statistics of regression |
|
|
|
|
|
|
Plural R |
0,8983 |
|
|
|
|
|
R-square |
0,8070 |
|
|
|
|
|
Normalized/restricted R-square |
0,7800 |
|
|
|
|
|
Standard error |
7602,10 |
|
|
|
|
|
Observation |
50 |
|
|
|
|
|
|
|
|
|
|
|
|
Dispersion analysis |
|
|
|
|
|
|
|
df |
SS |
MS |
F |
Value F |
|
Regression |
6 |
10392064374 |
1732010729 |
29,96973611 |
7,65309E-14 |
|
Remainder |
43 |
2485055626 |
57791991,31 |
|
|
|
Result |
49 |
12877120000 |
|
|
|
|
|
Coefficients |
Standard error |
t-statistics |
P-value |
Bottom 95% |
Top 95% |
|
Y-intercetion |
-14889,26719 |
4972,8569 |
-2,9941 |
0,0045 |
-24917,98 |
-4860,54 |
|
Region, Õ2 |
3232,597172 |
871,0294 |
3,7112 |
0,0005 |
1475,99 |
4989,19 |
|
Area, Õ3 |
832,6470715 |
76,5099 |
10,8828 |
6,22345E-14 |
678,35 |
986,94 |
|
Floor, Õ4 |
-647,1780657 |
629,9167 |
-1,0274 |
0,3099 |
-1917,52 |
623,17 |
|
Number of house`s floor, Õ5 |
-457,7868931 |
673,2498 |
-0,6799 |
0,5001 |
-1815,52 |
899,95 |
|
Repair works, Õ6 |
3290,564859 |
2429,2976 |
1,3545 |
0,1826 |
-1608,58 |
8189,71 |
|
Construction project, Õ7 |
5783,097775 |
2365,0469 |
2,4452 |
0,0186 |
1013,52 |
10552,66 |
Defined plural regression model:
Ó=
- 14889,3 + 3232,6∙õ2 + 832,6∙õ3 – 647,2∙õ4 – 457,8∙õ5
+ 3290,6∙õ6 +5783,1∙õ7
To sum up, equality which came out during the
research we done is statistically valued, because: Ffactor > Ftable.
Let`s see how this model
works. For example, let`s calculate the price of one-roomed flat which is located at KSK
region in 2-floor of 5-floored house which area is 44 m2 and which is repaired well but not with
construction project with using this model. By doing so we calculate that the
price of this flat is 32.495,5 $ and the price of one metre square of this
flat is 738,5 $ (when we calculate the price of the flat we
must pay attension not only for given factors but also for coefficient of
inflation).
We can use
the buit-up model in differet ways:
·
to calculate the price of flat by using given data;
·
to chek if given price is correct;
·
to define which factor is the most and the least effect to the price of
flat;
·
to define factors as they are increasing or decreasing when we
predicting price of flat, if it was given data in different periods.