JP5145933B2 - A device that evaluates standard housing land by regression analysis to eliminate "multi-collinearity" and interactive adjustment of price vs. price formation factors - Google Patents

Description

  The present invention is an apparatus for evaluating an appropriate disparity of a standard residential land and determining its price formation factor evaluation criteria by a regression analysis technique that eliminates multicollinearity.

  The transaction case comparison method, which is the main method of appraisal evaluation of residential land, obtains the price of the target site by comparing the transaction case price in the neighborhood with the price formation factor. However, the parties to buying and selling residential land are not familiar with the land market, and because it depends on individual circumstances, the established price often deviates from the price deemed appropriate for the residential land. Therefore, it is not possible to expect an appropriate price gap for the transaction case price.

  The “land price comparison table” is published as a price disparity evaluation standard, and further, annual land price announcements by the Land Price Public Notice Act and land price surveys by the National Land Use Planning Act Enforcement Ordinance are being used as a guideline for evaluation. . However, these public evaluations are price indications only, and although there is a guarantee of the price as a result of an expert appraisal by an expert appraiser, it is objective and rational due to price formation factors regarding price differences between standard sites. The grounds are not specified.

  The price disparity must be balanced based on the price formation factors of the residential land, but no matter what the disparity evaluation criteria of the adopted factors are, the price disparity as such can be adjusted appropriately. You can make an order. Therefore, there is no guarantee of validity just by the evaluation based on the price difference evaluation standard based on the price formation factor.

  Based on the above circumstances, in order to determine the appropriate price gap between multiple and many residential land, as in the standard housing land evaluation for housing land taxation, the price formation factor is used as an explanatory variable, and the price that is primarily evaluated A multiple regression analysis with the objective variable is performed.

  In the appraisal of a single brush, the disparity rating standard for price formation factors is used for each application and for each application. However, in a large number of standard residential land evaluations, it is desirable to use a single standard in order to obtain a unified and unified price gap. For this reason, a rating standard that can be applied to a wide range and a means for complementing it are necessary.

  The multiple correlation coefficient indicates the extent to which the explanatory variables that are correlated with each other can explain the objective variable as a whole group. In the multiple regression equation, each explanatory variable independently represents the objective variable. It is not aimed at how much you can explain.

  However, in appraisal evaluation of residential land, we would like to find out how much explanatory power the price formation factors, which are individual explanatory variables, have with respect to land prices, which are objective variables. However, since price formation factors, which are social phenomena, have a high correlation with each other, the multiple regression coefficient of each factor indicating the extent to which the land price that is the objective variable can be explained deviates from the value of practical experience of appraisal evaluation. "Linearity" problem arises. This tendency is further strengthened in standard residential land evaluation in which the number of explanatory variables is large and, in practice, a high multiple correlation coefficient of about 0.93 is required. An extreme example is a partial regression coefficient that is contrary to theories and common sense that “the wider the width, the lower the land price”.

To solve “multicollinearity”, one of the two explanatory variables with a high correlation coefficient can be omitted. However, in the evaluation of residential land, it is not possible to omit one of the price formation factors selected by theory and experience. If that is the main factor, it is not acceptable. In addition, there is a method in the following paper that adds a certain number to the diagonal elements of the correlation matrix to obtain a stable partial regression coefficient.
Arthur E.M. Hoer and Robert W. Kennard “Ridge regression”

  The criteria for evaluating the price-forming factors that indicate the utility of land vary by region, region, and use. The “Land Price Ratio” also stipulates the residential land, commercial land, industrial land, prospective land, etc. according to the purpose of use, such as better, standard, mixed, creation, farm village, villa land. . A single grading standard is preferred and a means of complementing this is needed to achieve an overall price balance for a wide range of standard housing estates.

In the present invention, the price of standard residential land with representativeness that divides the entire municipality into residential, commercial, and industrial uses, and further divides each usage into situation-similar areas, and the price formation factor of each standard residential land is large, such as street conditions. Each item is classified into a main factor with a large explanatory power and a subordinate factor with a small explanatory power. A method for creating a database by inputting the rating value in% units based on the rating standard into the computer together with the measured value,
The price formation factor is a means of adding 1 as the reference value to the total value of the rating value for each condition of the large item to (1 + total value), and taking a logarithm for each standard residential land price and condition,
In the multiple regression analysis with the logarithmic price as the objective variable and the price formation factor for each logarithmic condition as the explanatory variable, a means to standardize the variable and create a correlation matrix of the normal equation,
The non-diagonal search rij of the correlation matrix is changed to rij (1-RiRj) using the single correlation coefficients Ri and Rj for the prices of the i and j factors, and the apparent correlation part of price mediation is removed. By reducing the correlation coefficient value of rij, the numerical value of the partial regression coefficient bi is brought close to the numerical value of Ri that is expected from the evaluation experience, the “multicollinearity” is eliminated, and the appropriate price formation factor Means for obtaining a partial regression coefficient bi which is a specific gravity and calculating a regression price by reducing the logarithm of a price which is an objective variable;
A device for evaluating a standard residential land, characterized by comprising means for creating a numerical price ascending order list of the set price, regression price and price formation factor based on the opening rate of the set price and the regression price and all the main factors About.

ここで、
Ｒｉ ：要因ｉの目的変数ｙに対する単相関係数
Ｒｊ ：要因ｊの目的変数ｙに対する単相関係数
ｒｉｊ：相関行列の非対角要素 （ｉ≠ｊ）
ｂｉ ：標準化後の係数 ｂ’ｉ ：標準化前の係数
σｙ ：目的変数ｙの標準偏差
σｉ ：説明変数ｉの標準偏差
なお、標準化前後のｂ’ｉ、ｂｉの関係は次のとおりである。
ｂ’ｉ＝ｂｉ（σｙ／σｉ） （２）Perform multiple regression analysis with price as objective variable and price formation factor as explanatory variable. (Example of two variables)
From the normal equation, variables are standardized to obtain a normal equation in the form of a correlation matrix.
Standardization of variables: (variable-average of variables) / standard deviation of variables

here,
Ri: Single correlation coefficient for objective variable y of factor i Rj: Single correlation coefficient for objective variable y of factor j rij: Non-diagonal element of correlation matrix (i ≠ j)
bi: coefficient after standardization b′i: coefficient before standardization σy: standard deviation of objective variable y σi: standard deviation of explanatory variable i The relationship between b′i and bi before and after standardization is as follows.
b′i = bi (σy / σi) (2)

この処理により、ｒ’ｉｊの数値が低く抑えられるので、“多重共線性”が解消される。The explanatory variable is a factor that can explain the land price that is the objective variable, and the explanatory variable is selected with high explanatory power. As a result, the single correlation coefficient between the explanatory variable and the land price becomes high. For this reason, although there is no original correlation between the selected explanatory variables, the apparent explanatory variable is mediated by the land price. Mutual correlation increases. Since this tendency is considered to be proportional to the single correlation coefficient between the explanatory variable and the land price, the following processing is performed to remove this land price-mediated correlation part.
r′12 = r12 (1-R1R2) (3)
Therefore, Equation (3) is as follows.

By this processing, the numerical value of r′ij can be kept low, so that “multiple collinearity” is eliminated.

  This correlation between explanatory variables for price mediation is not only in the case where there is a high correlation between explanatory variables such as “multicollinearity”, but if there is a slight correlation, that correlation will be generated. This removal process is incorporated into the system regardless of the level of correlation.

  In an evaluation that seeks reasonable prices for a variety of housing lots, there are various housing lots with different forms in the same usage, apart from the use of housing, commerce, and construction. In order to make a disparity, it must be a single evaluation standard, but an adjustment means to complement this is necessary.

The correction is made by the following means.
1. Create a number of ascending arrangements arranged from small numbers to large ones based on the opening ratio with the regression line price, the main factors such as width, distance to the center, environment, etc. To do.
2. In the arrangement of the opening rate with the regression line price, for example, + plus or minus minus 10% or more of standard residential land (unsuitable residential land) is color-coded or marked.
3 In the arrangement table by factor, the following items will be corrected and corrected by examining the characteristics of the unsuitable residential land for the factor and conducting individual field surveys.
Correction of rating standard
Correction of grade function
Increase or decrease the number of rating ranks
Increase / decrease of rating constant value (including suitability between price range and rating range)
(B) Correction of rank rating c Correction of price

  By removing the objective variable-mediated correlation part from rij which is a non-diagonal element of the correlation matrix, "multi-collinearity" is eliminated, and pricing criteria for pricing factors that can be adapted to a wider area are set. This makes the difference in land prices at multiple points appropriate, and is also an effective standard for single-stroke appraisals.

Fig. 2 is a table of set prices, price formation factor ratings, and their logarithms. In the appraisal evaluation, the residential land serving as a reference for comparison is set to 1, and the percentage of the utility of the target land is compared to the lower or higher, so the evaluation formula has the form (1 + xi). Therefore, even when comparing multiple points, the ratio is as follows and is not a difference. Therefore, when applying regression analysis in a linear format, the variable is made logarithm.
(Y1 / y2) = (1 + x1) / (1 + x2)
Logarithm log (y1 / y2) = log (y1) −log (y2)
Where y1: Evaluation target site
y2: Evaluation reference site

  The set price is obtained by the ordinary appraisal method.

Related to Figure 3 The inequality criteria for price formation factors applied to the multiple regression analysis are initially set empirically. However, adjustments will be made to correct deficiencies in disparity assessment standards.

  The multiple regression analysis to find the price difference at multiple points is not only to obtain the rating value of the price forming factor that supports the evaluation, but also to verify the validity of the price itself and the rating standard.

The calculation of the multiple regression analysis related to FIG. 4 is not particularly different from the correlation coefficient rij between the explanatory variables, except that the apparent correlation portion mediated by the objective variable is removed.

Relevant to Figure 5 Regression analysis calculations give a recurring price that has a theoretical character based on price-forming factors, but it is not possible to immediately determine where this should be corrected. In addition, this correction needs to be performed comprehensively for all the main factors.

FIG. 6 is an ascending arrangement table of price difference rate criteria and distance criteria to the center for regression price, set price, and price formation factor. The distance standard to the center of this figure has a feature that the return price of the remote area is lower than the set price, and the rating standard is particularly modified to reduce the rate of decline due to the remote distance. In particular, if there are no unacceptable circumstances as a group, we will investigate and correct each item with a large difference between the return price and the set price.

FIG. 7 is a table of interactive adjustment results of price vs. price formation factors. The reduction rate of the return price in the remote area has been improved because the rate reduction rate of the distance rating standard to the center has been greatly reduced. In addition, the housing land with a large difference between the return price and the set price was reviewed individually, and the environmental factors and the set price of the price formation factor were reviewed to improve the open range. It rose from 0.84 to 0.96.

  Multiple regression analysis of "multicollinearity" cancellation and interactive adjustment flowchart of set price versus price formation factor   Set price, price formation factor rating value and its logarithm   Main factor price inequality rating criteria   Multiple regression analysis calculation   Return price   Recurring price opening ratio and center distance standard ascending order   Results of interactive adjustment of price vs. price formation factors

Claims (1)

The price of standard residential land with representativeness that divides the entire municipality into residential, commercial, and industrial uses, and further divided each usage into situation-similar areas, and the price formation factors for each standard residential land are explained by major items such as street conditions The main factor is classified into a major factor and a minor minor factor, and the minor factor sub-item is the total value of each rating value obtained by empirical criteria for each condition, and the major factor is a percentage based on a separate rating criterion. A means to create a database by inputting the unit rating value together with the measured value into a computer,
The price formation factor is a means of adding 1 as the reference value to the total value of the rating value for each condition of the large item to (1 + total value), and taking a logarithm for each standard residential land price and condition,
In the multiple regression analysis with the logarithmic price as the objective variable and the price formation factor for each logarithmic condition as the explanatory variable, a means to standardize the variable and create a correlation matrix of the normal equation,
The off-diagonal element rij of the correlation matrix is changed to rij (1-RiRj) using the single correlation coefficient Ri, Rj for the price of the i, j factor to remove the apparent correlation part of the price medium. By reducing the correlation coefficient value of rij, the value of the partial regression coefficient bi is brought closer to the value of Ri that is expected from the evaluation experience, the “multicollinearity” is eliminated, and the specific gravity of the appropriate price formation factor Means for obtaining a partial regression coefficient bi and reducing the logarithm of the price as a target variable to obtain a regression price,
A device for evaluating a standard residential land, characterized by comprising means for creating a numerical price ascending order list of the set price, regression price and price formation factor based on the opening rate of the set price and the regression price and all the main factors .

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