## 4 Experimental Results  
On a standalone machine, ten different models were implemented in \(R\) programming [36] using an Intel Core(r)(r)(r) processor at 2.80 GHz and 4.00 GB RAM, running on a 64-bit operating system. The steps can be divided into five main stages:  
* 10-fold cross-validation with feature selection;
* Prediction using seven machine-learning algorithms;
* Selection of the top four learners based on RMSE;
* Employment of stacking ensemble on these learners (using three at a time in combination) and selection of the best ensemble approach. The dataset contained no missing values. The values within the dataset were present on a mixed scale, in the form of ratios, percentage and average scores. The data was normalized using the min.max() normalization function in R. We used a realistic dataset so we did not have to consider outliers of the dataset and simulated our work using the original dataset [25]. To optimize the performance, the parameters of the models needed to be tuned. Table 4 shows the models used in the present study along with their tuning parameters and required packages. The work utilizes the rfe() and rfeControl() functions for feature selection with cross-validation. Table 5 lists the features selected for different years. The results from the various models and their ensembles were examined and compared with each other on the basis of several evaluation criteria. The following text gives the brief description of the evaluation parameters applied to the regression models. A correlation coefficient (r) is also called a linear correlation. It quantifies the strength of the relationship among dependent and independent variables. The linear correlation is also referred to as Pearson's correlation or product moment correlation. The estimation of \(r\) lies between \(-1\) and \(1\). If the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Method** & **Libraries** & **Tuning Parameters** \\ \hline Cubist & cubist() & cubist & neighbors = 30, \\  & & & Committees = 10 \\ \hline Decision tree & rpart() & rpart & minsplit = 20, \\  & & & minbucket =7, \\  & & & maxdepth = 30 \\ \hline Elasticnet & enet() & elasticnet & fraction, lambda = 0.05 \\ \hline Linear model & lm() & glm & None \\ \hline Neural network & nnet() & nnet & maxit = 100, \\  & & & \(\text{hlayers = 10}\), \\  & & & MaxNWts = 1000 \\ \hline Random forest & rf() & randomForest & mtry = 3, \\  & & & importance = TRUE \\ \hline Support vector machine & svm() & e1071 & nu = 10, \\  & & & epsilon = 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Models with tuning parameters. \begin{table}
\begin{tabular}{c l} \hline \hline
**Year** & **Selected Set of Features** \\ \hline
2014 & L1\(\approx\) f (H1, I1, J2, J3, E2, HE2) \\
2015 & L1\(\approx\) f (H2, J2, J3, CI2, HE1, HE2) \\
2016 & L1\(\approx\) f (H1, H3, J1, J2, J3, J4, C1, ED1, ED3, E1, E2, CI1, CI2, HE2, S1, W1) \\
2017 & L1\(\approx\) f (H3, J1, J2, J3, J4, C1, ED3, E1, E2, CI2, HE2) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Features selected for data of different years. value of \(r\) is in the negative range then it is a weak relationship. If it is in the positive range then it indicates a strong relationship. It is represented as in Equation (1):  
\[r=\frac{\sum\ xy-\frac{\sum\ x\sum y}{n}}{\sqrt{(\sum\ x^{2}-\frac{(\sum\ x)^{2} }{n})-(\sum\ y^{2}-\frac{(\sum\ y)^{2}}{n})}}. \tag{1}\]  
The coefficient of determination (R) is a statistical evaluation of how well the relapse line approximates the actual record points. The estimation of \(R\) extends between 0 and 1 and denotes the strength of linear association between \(x\) and \(y\). It is calculated as given in Equation (2):  
\[R=r^{2}. \tag{2}\]  
The root mean squared error (RMSE) proposes the complete match of the model to the data--how close the actual data values are to the predicted values. RMSE is a measure of how appropriately the model predicts the response. It is regularly utilized to calculate the dissimilarity of values estimated by a model and the actual value.