2.3.4. Data Variable Transforms

As discussed above, each of the 56 'basic models' justifies the predictive relation and power between a certain pair of variables and the relevant statistical descriptions for the SLR model. However, the models are established based on the assumption that no variable is transformed, i.e., both variables on the RHS and LHS in the model use their data values in the *source domain*.

In this study, we transform the values of the independent variable on the RHS of each of the 56 models in nine ways in prior and build nine models by re-estimating the parameters of the SLR model that fit the independent variable in the *transform domain*. For comparison purpose, the models also include the initial case of 'no transform' (i.e., the base model), and are written as:


With all these transforms performed prior to establishing the model, the model can be simplified as Equation (5) uniformly, and the linearity for all other SLR models derived from a basic model also holds:

$$
\Upsilon = \mathfrak{a} + \beta X'\tag{5}
$$

For a model with (*X*, *Y*) as the RHS and LHS variables, the 56 cases already included their counterpart, i.e., (*Y*, *X*) as the RHS and LHS variables, respectively (see Section 2.3.3), meaning that all cases would be considered. As such, since there are nine models derived from each 'basic model' totally, there would actually be 56 × 9 = 504 SLR models in this work using the same set of data.

2.3.5. Indicators Used to Justify the SLR Modelling Results

Other than P-Co-Co and Cos-Sim which are in themselves 'indicators' for paired data variables, in this study, the following measures are used to tell the quality of an established SLR model. These include:


To visualise the summarised and tabularised computational results, they are also plotted as heat maps to provide a clear view. A heat map is a visualisation tool that is frequently used in the field of data-driven decision-making (DDDM) since Toussaint Loua provided its first application in 1873.

#### **3. Results**
