Defining a new parameter for regression models with aggregated data in aquatic science

In aquatic ecosystem analysis, it is common to create regression models of aggregated data. There are several published papers on regression models that produce high values for the coefficient of determination (r-super-2) and low p‐values but that have nevertheless failed to predict responses in individual lakes. There appears, therefore, to be a need for a descriptive parameter that can be used to determine the certainty in aggregated regression models. To explore the applicability of a new parameter, the aim of this study was to develop a new parameter to detect the reliability of aggregated data in regression analysis. This parameter was tested using three different examples of empirical data from Himmerfjärden bay (Sweden) and one example of 111 Swedish lakes. The results showed that even for a high r-super-2 and a low p‐value, it is possible that the aggregated data are too highly variable to make correct conclusions about causality. To investigate this, the new parameter should be used to indicate if r-super-2 can demonstrate a causality relationship. However, if the parameter rejects r-super-2 as valid, it does not mean that there is no causality; it indicates that the uncertainty in the aggregated data is too high to draw conclusions regarding causality. In such cases, more effort needs to be made to decrease uncertainty in the variables. Copyright © 2014 John Wiley & Sons, Ltd.