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The application of regression analysis for estimating the market value of commercial real estate

Banaś Marek, Czaja Józef, Dąbrowski Janusz

Geomatics and Environmental Engineering

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2022

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Vol. 16, no. 1

17--35

EN

The transaction price of a land property with commercial buildings depends on both its quantitative and qualitative attributes. Quantitative attributes include surface areas of plots of land and usable floor spaces of premises and buildings with various intended purposes, as well as values of rents. Qualitative attributes are represented by the global attributes of these properties. In the analysis of the land property market with commercial buildings, all pairs that relate a transaction price to individual attributes are considered. The market value prediction is based on multiple regression analysis for a two-dimensional random variable, represented by the price and the predetermined attribute. The final market value of the property being valued is calculated as the weighted average of the market values predicted for each attribute. This research paper presents the procedure for determining the market value of land with commercial buildings, which falls within the method of statistical analysis of the market. The derived formulas and substantively justified algorithms may be the basis for market analysis and estimation of the market value of such land. This procedure has been thoroughly verified using two practical numerical examples.

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Gauss-Markov model with random parameters to adjust results of surveys of geodetic control networks

Banaś Marek, Czaja Józef, Dąbrowski Janusz

Reports on Geodesy and Geoinformatics

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2021

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Vol. 111

1--6

EN

Alignment of an engineering object project in the field is always conducted at the points of the geodetic control network, the coordinates of which are determined on the basis of the results of its elements survey and with connection to the national spatial reference system. The points of the national spatial reference system determined on the basis of previous surveys have specified coordinates with adequate accuracy, which is included in their covariance matrix. The coordinates of the geodetic control network points are determined more accurately than the points of the national spatial reference system and this means that the results of surveys of the geodetic control network have to be adequately incorporated into the coordinates of the reference points. In order to perform this incorporation, it may be assumed that the coordinates of the reference points are random, that is, they have acovariance matrix, which should be used in the process of adjusting the results of the geodetic control network observation. This research paper presents the principles for the estimation of the Gauss-Markov model parameters applied in case of those geodetic control networks in which the coordinates of the reference points have random character. On the basis of the observation equations δ+AX=L for the geodetic control network and using the weighting matrix Pand the matrix of conditional covariances [wzór] for the observation vector L, the parameter vector X is estimated in the form of the derived formula [wzór]. The verification of these estimation principles has been illustrated by the example of a fragment of a levelling geodetic control network consisting of three geodetic control points and two reference points of the national spatial reference system. The novel feature of the proposed solution is the application of covariance matrices of the reference point coordinates to adjust the results of the survey of geodetic control networks and to determine limit standard deviations for the estimated coordinates ofgeodetic control network points.

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Application of Advanced Statistical Procedures for Adjustment of Results in Measurements of Displacements

Czaja Józef, Dąbrowski Janusz Andrzej

Geomatics and Environmental Engineering

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2019

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Vol. 13, no. 1

5--15

EN

In this paper, the authors verified the formulated principles of the estimation of Gauss–Markov models in which estimated parameters X were random. For this purpose, methods for the prior definition of covariance matrix CX for the estimated parameters were provided, which were used to determine the conditional covariance matrix of observation vector L and then estimate the most probable values of parameters Xˆ. Covariance matrix Cov(Xˆ) obtained as a result of this estimation was used to define the limit values of the variance of these parameters. Practical application of the proposed method for the Gauss–Markov model estimation for random parameters was illustrated on a fragment of a leveling network of points to determine the vertical displacements of a landslide surface.

PL

W artykule autorzy poddali weryfikacji sformułowane zasady estymacji modeli Gaussa–Markowa [10], w których szacowane parametry X miały charakter losowy. W tym celu zostały podane sposoby określania a priori macierzy kowariancji CX dla estymowanych parametrów, które zostały wykorzystane do wyznaczenia macierzy kowariancji warunkowych wektora obserwacji L, a następnie do estymacji najbardziej prawdopodobnych wartości parametrów Xˆ. Uzyskana w wyniku tej estymacji macierz kowariancji Cov(Xˆ) została wykorzystana do ustalenia granicznych wartości wariancji tych parametrów. Zastosowanie proponowanego sposobu estymacji modelu Gaussa–Markova do parametrów losowych zostało zilustrowane na przykładzie fragmentu niwelacyjnej sieci punktów przeznaczonej do wyznaczania pionowych przemieszczeń powierzchni osuwiska.