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In the paper we present some guidelines for the application of nonparametric statistical tests and post-hoc procedures devised to perform multiple comparisons of machine learning algorithms. We emphasize that it is necessary to distinguish between pairwise and multiple comparison tests. We show that the pairwise Wilcoxon test, when employed to multiple comparisons, will lead to overoptimistic conclusions. We carry out intensive normality examination employing ten different tests showing that the output of machine learning algorithms for regression problems does not satisfy normality requirements. We conduct experiments on nonparametric statistical tests and post-hoc procedures designed for multiple 1 × N and N × N comparisons with six different neural regression algorithms over 29 benchmark regression data sets. Our investigation proves the usefulness and strength of multiple comparison statistical procedures to analyse and select machine learning algorithms.

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Ecosystems provide services that contribute to the well-being of people living within a city’s borders and on the urban–rural fringe. While benefits from green areas in urban settings are well investigated, peri-urban areas are significantly less addressed by researchers than cities. This study aims to evaluate the importance of environmental amenities in peri-urban areas using the hedonic pricing method to assess people’s willingness to pay for environmental goods and services. A local regression model (geographically weighted regression) and two global regression models (generalized spatial two-stage least squares and ordinary least square) are used to identify the spatial patterns and level of influence of protected areas, forests, rivers, trees, and landscape diversity. This paper includes the Central European case study example of a peri-urban area of the city of Wroclaw, Poland. The results from the three models show that out of all of the environmental amenities included in this study, proximity to protected areas—such as Natura 2000 sites and landscape parks—and the diversity of land-use patches within the 500-m radius around the sites exert the strongest influence on plot prices. The overall impact of environmental amenities on vacant plot prices in peri-urban areas is low or, as in the case of river and streams, not significant. The results of the analysis reveal the preferences of the new peri-urban inhabitants concerning green spaces that have an effect on the real estate market in Poland.