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Perceived quality of services and customer satisfaction is a concept that is increasingly important because of its impact on customer loyalty and other effects on the performance of a company. There is growing evidence that the links between quality of services, customer satisfaction and customer loyalty might be non-linear. However, there is no consensus about the actual functional form, since individual studies have discovered linear as well as concave, convex, S-shaped and inversed S-shaped relationships. Inconsistent results of previous studies suggest that different functional forms might be typical for different industries. The aim of this study was to examine the functional forms typical for the vehicle maintenance and repair industry, based on 34,421 computer-aided telephone interviews with customers of Slovenian automotive servicing companies performed between 2005 and 2011. For each of the connections between the constructs under consideration, we used linear and several non-linear regression models with the curve fit procedure in SPSS. The obtained results suggest that in describing the relationship between perceived quality of services and customer satisfaction, the non-linear functional model only slightly outperformed the linear one in terms of explained variance of data (R2). The relationship between customer satisfaction and customer loyalty on the other hand could clearly be best described using a non-linear model. Using the non-linear model that produced a concave functional form enabled us to achieve 41–47% better explanatory power compared to the linear model. On the basis of our research, we can make several recommendations to the management of automobile servicing companies; for example to concentrate the resources of their companies on improving the satisfaction of their least-satisfied customers, because by this approach, they can expect the highest yields in terms of improved customer loyalty
