*2.3. Cross Validation and Model Development*

For comparison, three different types of models will be developed and tested:


To develop these models, the procedure shown in Figure 2 was employed here for both the linear and quadratic reduced models. The available data were initially separated into separate training and testing sets. Then, only data from the training set was used in cross validation with the LASSO approach and was used to identify a *λ* value which minimises the cross validation MSE (mean squared error). Utilizing the LASSO method with this *λ* reveals which of the parameters have been set to zero and the non-zero parameters were identified to generate reduced expressions. These reduced expressions were then fitted to the full training set data giving fitted values for the identified parameters. For the full linear model, there was no cross validation and all the parameters were obtained through regression using the training set. Finally, all the fitted models were validated to see if they were able to adequately predict the results of the testing data.

**Figure 2.** Procedure used to develop and validate reduced linear and quadratic models.
