## 5 Modelling the Communication Solutions
### Model Performance  
The model [34] is built with the statistical package R [35] using the data taken from simulation. Multiple linear regression is used to build each facet of the model. Linear regression modelling is used for two reasons. The figures presented in Section 7 show visually how the data produced from the experiments fit a linear trend for each of the evaluation metrics with regard to the changing physical feature. This observation is more acute however for some solutions, ETX and ETX-NH, than for others, ETT. In all figures for reliability and stability, ETX and ETX-NH show a linear trend with a comparatively low standard error while ETT shows wider value dispersion and higher standard error over the range. In general the ETT solution shows wider dispersion of values for many of the physical features and shows wider standard error from a linear trend for the reliability, stability and efficiency evaluation metrics, though the data does show a general linear trend throughout. Liner regression modelling represents a simple modelling technique which is well suited to demonstrate the purpose of solution modelling within the framework. For each solution, least squares linear regression is used to model how each evaluation metric responds over the set of physical features. The set of physical features are used as the predictor variables for each of the models, with each of the evaluation metrics acting as the response variables. For example, reliability is used as a response variable with predictor variables network size, density, scale, link conditions, size (standard deviation) and scale (standard deviation). Each communications solution will have separate model built for each response variable resulting in twelve individual models for the dataset. A separate model is required for each evaluation metric as the it is important at this stage to give an individual result for each of the metrics. Applying a single score for a network solution would assume that all applications value each of the metrics equally. A method to combine the evaluation metrics into an overall score is discussed in Section 6.1. Separating the modelling and the scoring process in this manner allows the pre-built models to be exported for any application without re-building. As the physical features drive the predicted result for each of the models, it is interesting to note which physical features have the largest impact on each result. A T-test is performed determining the features that constitute a significant role in shaping the response for each metric (response variable). Table 2 highlights these significant features. The table shows how each communications solutions response is shaped using different features. The table returns some expected results, such as the importance of scale, size and the communication channel in determining the response for nearly all cases, but also offers other insights into the dynamics of the evaluation metrics with respect to the features. Scale (standard deviation) has a large impact on ETT response while having less effect on ETX and ETX-NH. While scale is generally important in determining the response for all the evaluation metrics it has less of an impact in determining the stability of a communications solution. These individual models are used to determine whether the proposed approach can reliably determine the correct solution to use in a network given a set of requirements. In order to achieve this the problem is broken down into a set of smaller problems, asking whether an ordered list can be determined of performance capabilities per metric for each solution, i.e., for any given set of physical features the model determines the order of the solution performance from best to worst for each evaluation metric. A model is built for each solution and evaluation metric from training data. A test data set is then used to examine the accuracy of the models.