Estimating the concession fee for the use of a football stadium

the concession

Estimating the concession fee for the use of a football stadium

BACKGROUND
Concessions should be placed within the exercise of public power when this exercise is understood as the function performed by a Public Administration (PA) in the interest of the community (Giannini, 1977).With a concession, in fact, the PA entrusts a private company with the management of an asset, a public service or the performance of works instrumental to the provision of the latter, with the aim of obtaining a concrete advantage for the public interest.This choice is based on the idea that through the greater availability of private resources and its more efficient distribution capacity, the PA can achieve better management of the public good and/or service.In recent decades, the transfer of the right of use of real estate assets has been widely used as an effective approach to improve the provision of public services through private investment.At the same time, this practice has become a crucial tool for the management and valorisation of public real estate assets (Manganelli & Tajani, 2014).
The use of this option in the management of public assets, when it is aimed at providing a public service, constitutes precisely a service concession.The service concession, in turn, entails the full transfer, from the granting administration to the successful bidder, of the operational risk related to the economic management of the asset.
The concession for the use of real estate intended to provide public services is the tool often used by the public administration to obtain, with the recourse to private investment, the valorisation of the asset and a more efficient management of the service.A typical case is that of football stadiums, the management of which is normally entrusted in concession to companies that assume the burden of guaranteeing the safety and functionality of the facility to provide a satisfactory experience for the spectator.When the management of the asset entails profit margins for the concessionary company, the public service concession must provide for the payment of a fee as consideration for the use of the asset.This work deals with the issue of estimating the concession fee for football stadiums granted to clubs with teams playing in professional leagues.The issue is addressed through the implementation of a direct probabilistic and multi-parametric approach, which attempts to overcome the limitations of the procedures normally used in these cases, based on cost value or income analysis, resulting from the subjective nature that often characterises the choice of fundamental parameters.Specifically, a multiple regression analysis is developed on the basis of information and data from the examination of existing concession contracts for similar properties.The results show that the variance of the fees is explained by the level of the football league in which the concessionaire's team plays, the capacity of the stadium, the year of construction of the stadium, and the year of the last major renovation on the building structure.Abstract public asset or using the same, or to construct the public work and manage it.In the latter case, one speaks of a mixed concession, as in the case of the airport concession (Engel et al., 2018;Gillen and Mantin, 2014), which allows for the use of a state asset (airport grounds), the construction of the airport and the management of services and other airport activities.The object under discussion is therefore a public good.Public assets that are potentially the subject of concessions are distinguished between state property (natural or artificial) and non-disposable heritage assets.State property is intended, by its nature or by the characteristics conferred on it by law, to serve overriding interests of the community.In view of this special purpose, these assets are non-marketable (inalienable).On the other hand, non-disposable heritage assets are used for institutional purposes and for the satisfaction of public interests, which are not included in the category of state property.The granting of temporary use of state property and/or non-disposable heritage assets to parties other than the administration that owns them only takes place by means of public law measures, such as, primarily, the administrative concession.With it, the administration retains a series of prerogatives aimed at regulating, in a form compatible with the public interest, the temporary use of the property by the concessionaire and establishing essential guarantees for the eventual restoration of the public purposes for which the property is intended.On the other hand, the assets of the available heritage, i.e. those not intended for institutional purposes (buildings for residential and non-residential use, agricultural land, etc.), therefore owned by the PA under private law, are instead granted for use by means of contracts in the form and with the contents of the negotiations envisaged by lease, rental or commodatum contracts.When the object of the concession is a natural state property (e.g.natural resources), the objective is a more efficient economic exploitation of the resource.For example, in Indonesia, which has the third largest forest area in the world, the central government has issued logging concessions to corporations and cooperatives, assigning them the management of the area and in return receiving revenue from logging concession rights (Kato, 2005).Ribeiro et al. (2020) show how the forest concession is the dominant governance instrument for access to natural resources in public forests in Brazil.Téllez Ramíreza and Azamar Alonso (2021) discuss the privatization of Mexican mining and metallurgical companies, which were previously exclusively under state jurisdiction.
In the case of concessions to third parties of an artificial state property and/or a non-disposable heritage asset, the objectives are different and involve micro-or macroeconomic aspects.Ferrari et al. (2019) highlighted the strategic role of terminal concession agreements, in the context of Underlying a concession, therefore, must be a careful assessment of the financial sustainability of the operation for the concessionaire.Among the fundamental items of financial equilibrium is also the concession fee.The aim of this research is to outline the specificities of estimating the concession fee for the use of a football stadium.This objective is pursued through the elicitation and application of a direct probabilistic and multi-parametric approach (market approach), which attempts to overcome the limitations of the procedures normally used in estimating special assets such as stadiums, based on reproduction cost value and/or income analysis.The implementation of these approaches is generally affected by the subjective nature that often characterizes the choice of parameters contributing to the valuation.The work is organised as follows.In the first paragraph, the concessionary instrument is defined and the context in which it is normally used is outlined.In the second paragraph, the difference between a public good concession and a public service concession is highlighted, which is of relevance in determining the appropriate amount of the concession fee.In the third paragraph, the focus is on the case of concession agreements for sports facilities, particularly football stadiums.The fourth paragraph addresses the specificities of sports facilities and provides an overview of the different approaches used to estimate the concession fee.The fifth paragraph develops the estimation of the concession fee in a case study involving a football stadium located in the city of Avellino, using the implementation of a multiple linear regression analysis.Finally, the conclusions summarize and discuss the results of applying the regression model, highlighting the advantages compared to commonly used valuation approaches.

THE CONCESSION AS AN INSTRUMENT FOR THE EXERCISE OF THE PUBLIC FUNCTION
From the point of view of legal theory, the term concession is defined as the act whereby the PA allows the private party the use of resources and/or the exercise of activities reserved to the public authorities.The concession therefore entails the establishment between the private party and the PA of a complex relationship in which public and private components are closely connected (Altieri, 2020 In other cases, in the absence of public resources, the concession is a useful tool in the management and enhancement of PA-owned real estate assets (Manganelli et al., 2022;Forte et al., 2021).By entrusting the economic management of the asset to the private sector, administrations pursue the objective of maintaining and/or improving many public properties by guaranteeing their suitability for the purposes for which they are intended (Del Giudice et al., 2020).

THE CONCESSION FEE
A fundamental distinction in terms of the rules applicable to the measurement of the fee is that between a public good concession and a public service concession.
The concession of public property confers rights of use of the property as in the case of maritime or water property (Mišura et al. 2020).Mezak et al. (2019) highlight the critical issues that arise in determining the real value of a concession fee about the maritime property, and propose procedures and measures that may enable more accurate concession fee values to be set.The authors show that any concession contract longer than five years should be revised in the event of significant changes in economic indicators.Tsimoshynska et al. (2021) propose an innovative methodological approach for estimating the concession fee for road concession projects in Ukraine.The concession fee is estimated by considering several factors, including vehicle travel distance, gross vehicle weight, road surface wear and tear and deformation, road capacity, and road load factor.Engel et al. (2018) determine the optimal duration of a concession contract for an airport, showing that it is inversely proportional to passenger flow.On the other hand, the qualifying and distinguishing element of the concession of a public service as opposed to the concession of a public good is the transfer to the concessionaire company of the operational risk, understood as the risk of exposure to market fluctuations.«The prevailing case law identifies the discriminating criterion in the underlying objectives pursued by the granting administration, which, if they go beyond the mere ordinary use of the asset, placing themselves in a broader perspective, necessarily qualify the relationship in terms of services».(Council of State Section V, 16 June 2022, no.4949).
A service concession takes shape when, therefore, because of the full transfer of the economic management of the asset from the grantor administration to the successful bidder, the remuneration of the concessionaire derives from the compensation for assuming the operating risk.Economic management does not mean the mere exploitation of the property, but the realisation of investments on the property or burdens to be borne in order to make it suitable for the functions instrumental to the business activity.Market fluctuations entail the risk for the concessionaire of not being able to recover the expenses.
At the basis of a concession, therefore, there must be a proper evaluation of a sustainable fee for the concessionaire, derived from the development of an economic and financial plan capable of ensuring the financial feasibility of the operation in the medium and long term.
In this regard, the National Anti-Corruption Authority (ANAC) noted, in its Opinion of 15 February 2013 with reference to maritime state concessions, that «administrative concessions having as their object stateproperty or non-disposable heritage assets may be instrumental to the provision of a service to the community, and therefore constitute a service concession, when the use of the property takes the form of the exercise of a public service, since such concessions are complex cases, in which not only the making available of the public property, in return for payment of a fee, is relevant, but also the contractual aspects relating to the management activity and the duration depending on the economic-financial balance of the investment» and in particular «the concession of assets conceals a service concession when the public asset, having a natural vocation to be used in favour of the community for activities of general interest and having a structure and destination suitable for generating cash flow, is entrusted for management to the concessionaire on which the operating risk is transferred, inasmuch as it derives its remuneration from such management, in return for the payment of a fee to be paid to the grantor established on the basis of the forecast of the consolidation of earnings over the reference time period".

THE CASE OF SPORTS FACILITIES
In Italy, the concession has become the ordinary instrument for the management of sports facilities, such as a football stadium.The possibility of having safe facilities, adequate to the times, functional to the provision of the sporting service that is carried out in it, and suitable for providing the spectator with a satisfactory experience, given the PA's inability and limitations in guaranteeing such services, entails the necessary transfer of the economic management of the facility to a private subject.The sports facility falls within the PA's property assets, intended for a public service and therefore subject to the regime of non-disposable heritage assets.The fact that these categories of property belong to the nonjournal valori e valutazioni No. 34 -2023 disposable heritage assets does not qualify the concession of them in terms of a 'concession of assets'.In cases of coexistence between the public nature of the asset and the public function of the service, it is necessary to verify whether the public nature of the asset is founded precisely in its instrumentality to the performance of a public service.Administrative justice has repeatedly affirmed that: «In the case of the management of municipal sports facilities we are dealing with a local public service.... whereby the use of the asset merges with the promotion of sport and, together with the socialising and aggregative effect, takes on the role of an instrument for improving the quality of life to the benefit not only of the health of citizens, but also of the social vitality of the community (cultural, tourist, image of the territory, etc.)» (Cons.Stato, V, 28 January 2021, no.858; 18 August 2021 no.5915).Thus, the functional constraint that defines their natural vocation to be used for the benefit of the community makes sports facilities instrumental goods for the performance of a public service.In concession contracts for such facilities, this is normally the prevailing component with respect to the 'concession of a public good'.Given the aforementioned condition, whereby in the context of service concessions the operational risk of economic management is fully transferred to the concessionaire, the concession fee must necessarily be linked to a balanced financial plan.Within the category 'sports facilities', a distinction must therefore be made between those with economic significance and those without economic significance.For the purposes of qualifying a local public service in terms of economic importance, it is necessary to verify in concrete terms whether or not the activity to be performed presents the connotation of 'profitability', even if only potentially.When the management is placed outside a logic of business profit, i.e. the concession cannot therefore be a source of remuneration because the market is not able or not interested in providing the services that are the subject of it, the facilities are devoid of economic importance and the service granted is in this case qualified as «non-economic».This is the case, for example, of facilities whose management, in relation to their structural characteristics, the sports disciplines that can be practised in them and the lack or marginality of the services of economic relevance that can be used in them, does not allow for the generation of sufficient revenues to cover the overall costs.In these cases, the concession contract does not provide for the payment of a fee by the concessionaire (the concession is free of charge), or even, when the management is unable to sustain itself, financial support from the administration to the concessionaires may be necessary.
The investigation into stadium concessions has highlighted that for some facilities, in exchange for the  2016), the granting municipality has committed to making an annual financial contribution (significantly higher than the fee or revenue percentage itself).This was due to the non-economic relevance of the facility, its public use and its recognised social value, and therefore to cover the management costs in support of the achievement of the economic-financial balance of the facility's management.Therefore, facilities are of 'economic importance' when the remuneration of the factors of production and capital invested by the concessionaire comes from the activity connected with their operation, without public financial support.The notion of services of economic importance therefore includes those facilities that «present, due to the way they are carried out, a significant economic component, aimed at ensuring not only the simple coverage of expenses incurred but also a potential business profit» (Council of State, no.5072/20).
In the light of the above and, in particular, of the necessary analysis of the potential profitability of a facility (to be measured over the hypothesised management period), in order to qualify it as economically significant or not, the following are important: the type of sports facility and its functional characteristics; the presence of complementary facilities for welcoming the public (e.g.stands with controllable access); the existence of accessory facilities (e.g.bars, relaxation rooms, etc.); the location of the facility in a multifunctional context, such as to favour the use of other value-added services.

The estimation of the concession fee for a stadium in the observed experiences
An important issue, and one of interest in this research, is therefore the estimation of the amount of the concession fee for a sports facility of economic importance.This fee must evidently be sustainable, i.e. guarantee the financial viability of the operation for the concessionaire and at the same time represent the fair compensation for the use of the asset.The procedure, normally used in professional practice to estimate stadium concession fees, is the cost approach.In this regard, a brief critical note on this approach is provided.Motivating the choice with the absence of a congruous number of comparables and relative market data, the PAs, in the evaluations already developed directly or on their behalf by specialised agencies, have estimated the fee by means of a prior estimate of the market value of the facility, obtained with the depreciated replacement cost method (Manganelli, 2011;RICS, 2022), and applying to this amount a coefficient capable of expressing the rent.The rationale for this approach starts from the assumption that if the capitalisation procedure journal valori e valutazioni No. 34 -2023 makes it possible to obtain, by discounting at an appropriate rate the expected future income from the rental of a property, its market value, inversely the income could be deducted if the market value were known.Therefore, the coefficient to be applied to the value of the property should correspond to the inverse of the capitalisation rate.The first issue is the search for the market value of the real estate.For these types of real estate, however, since they belong to the category of so-called special real estate, i.e. real estate with a non-ordinary use, it is unlikely to find useful comparables for a direct estimate.The depreciated reproduction cost method is therefore used.
The depreciated reproduction cost is based on the substitution principle, whereby no ordinary investor is willing to pay, for a property that has no market value, a sum greater than the amount corresponding to the market value of the land and the hypothetical production cost of another property, similar in character, location and functional utility to the property to be valued, but considered in the latter's condition of use and maintenance.
In practice, the depreciated reproduction cost should be estimated by adding to the amounts needed to acquire the land to be considered vacant, the cost of reconstructing the buildings, technological systems and special works that make it up to new, and finally subtracting from the latter the depreciation resulting from economic and functional obsolescence, and the physical deterioration that the buildings and systems in their current condition present compared to the hypothetical new ones.The list of estimation steps is extensive, and some of them pose serious problems, the solutions to which are not simple.Among these, the issue of estimating the value of land and the choice of the capitalization rate should be mentioned.Both should be addressed, as the estimation logic requires, through either a direct or indirect approach.
The direct approach is implementable when the market can provide indications of similar empirical evidence, such as prices of areas with similar uses or yields of similar investments.
Choosing an indirect approach, on the other hand, involves assumptions that have little objective evidence.For example, the estimate of the area value should in this circumstance be developed by applying the transformation value, which means starting from the market value of the finished product; but the latter is precisely the value we are looking for.There is also little objectivity in the choice of the rate of return, since this is an investment that, due to specific characteristics of the property, has no analogy.Moreover, as already pointed out, the reference for the choice of this parameter cannot be the market.
On the one hand, therefore, the approximation of the estimation of the market value, on the other hand, the strong sensitivity of the result (the fee) to the variation of the rate, the choice of which can be conditioned by subjective factors, give awareness of the possibilities of error of this approach and of the uncertainty that would characterise the result.
Alternatively to the depreciated cost value, the estimation could be conducted through the income approach.
Practically, this involves developing a Discounted Cash Flow Analysis, assuming the sustainable fee as the unknown factor in the financial equilibrium, taking into account the revenues and costs of management (RICS, 2022).However, this approach discounts the inherent uncertainty associated with estimating certain valuation parameters.In particular, on one hand, the current economic and geopolitical situation makes it uncertain to forecast inflation rates and market trend changes.On the other hand, the unavailability of information on similar cases prevents a proper choice of the discount rate, which should account for the expected profit considering the operational risk assumed by private investors based on the ordinary potential use of the asset.Therefore, an alternative approach is proposed for estimating the concession fee of a stadium, based on objective market data (market approach -direct comparison), aiming to overcome the limitations of the approaches described above.Given the possibility of obtaining an adequate comparison sample for the specific case, the direct approach employed consists of a multiple regression analysis.This procedure allows for (i) determining the marginal prices (weights) of the factors contributing to the formation of the concession fee in an endogenous manner and (ii) explicitly expressing the functional relationship between the explanatory characteristics and the dependent variable (fee) to be estimated.Regarding (ii), if statistical analysis confirms its reliability, a linear function is preferred over more complex non-linear expressions, ensuring the simplicity of market phenomena interpretation even for less experienced individuals.

THE PROPOSED ESTIMATION PROCEDURE
In the market approach it is necessary to develop a market survey aimed at searching for existing concessions for similar (comparable) properties, from which data useful for the estimative comparison with the facility under valuation can then be drawn.The reference market for the search for comparables, spatially speaking, cannot have city boundaries, and equally limited would be regional ones.The perimeter within which it is therefore logical to extend the market investigation is the national territory.
The market analysis allowed the collection of valid or very recent concession contracts for the use of football stadiums by sports clubs, in sufficient number to develop a statistical procedure, based on regression analysis, capable of objectively justifying the variability of the journal valori e valutazioni No. 34 -2023 recorded data.In the search for concessions, account was taken of the similarity between the 'blazon' of the concessionary football club, the size of the cities (the average population is around 115,000, with a standard deviation of just over 55,000) and the way the concessions were granted.
With reference to this last aspect, only those cases were considered in which the concessionaire is entrusted with ordinary maintenance, while extraordinary maintenance remains the responsibility of the grantor, and which envisage as compensation only the payment of an annual fee, also in the form of an obligation to carry out works for a pre-set cost.Therefore, the cases of fee supplements with a percentage of receipts, or of retrocessions to the concessionaire of economic contributions were excluded.
The regression analysis envisaged the construction of a functional relationship between the response variable, which in this case is the concession fee, and a series of explanatory variables, plus an error term corresponding to a random variable, expressing an uncontrollable and unpredictable variation in the response variable.In the present case, a multiple linear regression was developed.
The method of «least squares» (OLS) was employed to determine the parameters of the function that best fit the estimated values to the observed ones.
The statistical method implemented is the least squares (OLS) method, which allowed the determination of the function parameters that best fit the estimated values to the observed ones (Schwager and Margolin, 1982;Zimmerman, 1994;Greene, 2011).

The data
In Tabella 1 Table 1 shows the summary list of the twentythree observations from existing concessions used as the basis for the analysis, indicating the region and municipality where the property is located, the name of journal valori e valutazioni No. 34 -2023 64 the stadium, the concessionary football club, and the date and/or duration of the concession.Some considerations should be made regarding the sample constructed for the implementation of the regression analysis.Although small in comparison to other applications in research found in the reference scientific literature, which refer to the 'rule of thumb' (Green, 1991) -according to which the inequalities N 50+8m for multiple correlation and N 104+m for partial correlation, where N is the number of individuals in the sample and m is the number of explanatory variables -, the number of data found in the present case is sufficient when referring to the Italian real estate market (which is structurally opaque, especially when contextualised to special goods) and to national sector studies, where the sample size used is comparable to that contemplated in the present work (Simonotti, 1991;Del Giudice, 1992;Curto 1994;Morano, 2002).
It is evident that the sample size affects the number of independent variables that can be included in the regression model.However, while this condition may result in a lower explanatory capacity of the model, it also leads to a higher estimation performance of the results.Indeed, some research has shown that calibrating regression models with a high number of explanatory variables contributes to reducing the reliability of the corresponding estimated coefficients (Cassel and Mendelsohn, 1985).
Table 2 provides the following additional information: the current league (A, B or C) in which the concessionaire football club is active (League); the number of seasons the club has been in the various leagues -from A to C -since its foundation (Leagues Years); the year the stadium was inaugurated (Construction Year); the year of the last major maintenance work (Renovation Year); the stadium's capacity (Capacity); and finally the annual fee (Fee).The latter is differentiated for those contracts with a longer term and possible change of category.
Per For the calculations, some of the variables took the following numerical measures: • Construction year = difference between estimate date (2022) and year; of construction; • Renovation year: = difference between estimate date (2022) and year of last major renovation.The regression model allows the estimation of the value of the response variable (Fee -Y in Equation ( 1)) by substituting in the functional relationship with the independent (explanatory -X in Equation ( 1)) variables the measurements that characterize the object under evaluation.The final output of the analysis, in addition to journal valori e valutazioni No. 34 -2023 65  3 and 4 show the descriptive statistics of the variables and the correlation matrix between variables, respectively.
The fees show a significant correlation with the league the club currently plays in and the years the club has played in the top division.There is also a significant correlation between current stadium capacity and years in the top league.Also consistent with expectations are the significant correlations between the year of construction and the years played in A League as well as the correlation between the years in B League and those in the top division.

The results
Il The regression model chosen excluded those variables that the verification tests recorded as not significant in explaining the dependent variable.The years of the championships played by the football team in the different categories (League Years A, B, C) were excluded.None of the 3 variables (individually or as a whole), when included in the regression, significantly improved the predictive ability of the model, and when the R-square showed positive changes, these changes were not matched by increases in the adjusted R-square.Guidance on the selection of the most accurate model is also derived from the results of the Akaike test (AIC) and the calculation of PRESS (Predicted Residual Error Sum of Squares).The Akaike test represents an approach aimed at the assessment and comparison of statistical models, allowing quantification of how precisely a statistical model is estimated, considering both the adequacy of the fit to the data and its complexity.The calculation of PRESS is a widely used cross-validation method in the field of regression analysis.The assumptions underlying the model are fulfilled.There is an absence of multicollinearity between the variables: the value of the Variance Inflation Factor (VIF) is below the alert threshold (Morano and Tajani, 2014); the residuals are independent (uncorrelated) and have homogeneous variance (homoscedasticity), the linearity hypothesis is also not violated (see the scatter plot of the residuals in Figure 1).The residuals are also normally distributed (see QQ-plot in Figure 2, in which the standardised residuals are 'plotted' against the corresponding percentiles of a standardised normal distribution).
The regression coefficients have signs consistent with the empirical interpretation of the phenomenon.As the category decreases (i.e. from 1 to 4, i.e. league A to D), the concession fee decreases.As the capacity increases, the fee increases, while it decreases as the number of years since the last renovation increases.Older stadiums (by year of construction) have higher fee values: this latter result should be interpreted by considering the variable ' Construction Year' as a proxy for the 'blazon' of the football club.

CONCLUSIONS
The estimation of the concession fee of a football stadium represents an estimation issue that has so far been resolved either using empirical approaches (based on mutual agreement of the parties involved) or by basing it on the cost value of the facility.
A football stadium belongs to the category of special properties in terms of type and specialised design, which are part of the non-disposable heritage assets, i.e. intended for the fulfilment of a public interest.PAs, owners of stadiums, in relation to the high cost of managing such properties, often entrust the latter, through concession contracts, to sports clubs.Since this is a service concession, the fee must account for the journal valori e valutazioni No. 34 -2023 67  operational risk of management and therefore this parameter becomes an essential item of the financial balance.The latter will have to be constructed in relation to the organisational solution chosen by the PA to satisfy the interests of the community, the specific management methods, the related maintenance costs and charges, the fee structure (free or imposed) for users, the discipline of social dues, the practicability of ancillary activities, etc.When the concessionaire is a football club, whose team plays in professional leagues, the public service concession can be of economic importance, i.e. the activity can generate 'profitability' also for the owner.This profitability, however, is not related to the value of the property, but to the management activity.This work has constructed a model for direct estimating the concession fee on the basis of objective data relating to existing contracts for the use of stadiums by football clubs (not among those considered 'best') that play or have played in the top leagues of the Italian championship.The variables considered in the regression model implemented to explain the variance of the recorded fees are essentially related to the income capacity connected to the management of the property.In particular, these are variables that effectively affect the definition of the financial equilibrium of the operation for the private investor.
The variables used that correlate with the concession company's revenues are: the league in which the soccer team plays, the stadium's capacity, and the club's coat of arms, while the year of the last major renovation performed on the property is evidently to be placed in relation to operating costs.The implementation of multiple linear regression analysis on the collected sample has provided a statistically reliable function, and it allows overcoming, through the endogenous estimation of the marginal contributions of the independent variables, the inherent randomness in the approaches typically used for evaluating stadium concession fees.Furthermore, the obtained model facilitates an easy interpretation of the correlations between the considered explanatory factors and the concession fee, and it is valid for predictive purposes regarding potential changes in the concession fee's value due to variations in the independent variables.
journal valori e valutazioni La stima del canone di concessione d'uso di uno stadio di calcio

Table 1 -
List of concessions

Table 4 -
Correlation matrix Correlations in bold have a 5% significance level (two-tailed))

Table 5 -
Results of regression analysis

Table 5
shows the results of the analysis.The equation resulting from the model is as follows: Fee = 33,186.*YearRenovationThe R-square of the regression model is 0.75618, i.e. approximately 76% of the variance of the concession fees is explained by the variables considered.The standard error of the regression is € 21.805,42.The F-Fisher statistic, which analyses the combined influence of the explanatory variables, indicates the good predictive ability of the regression model; the p-value, less than 0.05, confirms that the relationships in the model are real, i.e. the null hypothesis is rejected.The Student t-test, and the associated p-value, performed on the individual explanatory variables also indicates that the regression coefficients (β0) are significantly different from zero.
No. 34 -2023   Maritime  Economics & Logistics, Vol.21, No. 1, 2019, pp.99-110.FORTE F., DEL GIUDICE V., DE PAOLA P., DEL GIUDICE F.P., Cultural Heritage and Seismic Disasters: Assessment Methods and Damage Types, Green Energy and Technology, 2021, pp.Comparative Analysis of the Concessioning Model of Maritime Domains in the Territory of Both the European Union and the Republic of Croatia with a Focus on the Seaports , Scientific Journal of Maritime Research,VOL.34, 2020, pp.146-155.