## 4 Results and Discussion
### Quantitative Analysis
\begin{table}
\begin{tabular}{c c c c} \hline  & \multicolumn{3}{c}{**Walmart Dataset**} \\ \hline
**Forecasting Models** & **Measures** & **Without Feature Engineering** & **With Feature Engineering** \\ \hline \multirow{8}{*}{Linear regression} & NRMSE & 5.64 & 3.96 \\  & ND & 5.20 & 3.75 \\  & RMSSE & 4.88 & 3.58 \\  & MAE & 4.52 & 3.42 \\  & MSE & 4.06 & 3.12 \\  & R2 & 0.76 & 0.83 \\ \hline \multirow{8}{*}{LSTM} & NRMSE & 3.96 & 2.88 \\  & ND & 3.68 & 2.90 \\ \cline{1-1}  & RMSSE & 3.52 & 2.72 \\ \cline{1-1}  & MAE & 3.46 & 2.50 \\ \cline{1-1}  & MSE & 3.32 & 2.42 \\ \cline{1-1}  & R2 & 0.80 & 0.88 \\ \hline \multirow{8}{*}{Bi-LSTM} & NRMSE & 2.90 & 2.15 \\ \cline{1-1}  & ND & 2.78 & 2.06 \\ \cline{1-1}  & RMSE & 2.53 & 2.02 \\ \cline{1-1}  & MAE & 2.46 & 1.88 \\ \cline{1-1}  & MSE & 2.06 & 1.48 \\ \cline{1-1}  & R2 & 0.82 & 0.90 \\ \hline \end{tabular}
\end{table} 
Table 3: Numerical analysis of different regression models on the Walmart dataset. Table 4 displays the numerical analysis of different models on the citadel POS dataset using NRMSE, ND, RMSSE, MAE, and MSE. The proposed Bi-GRU model uses less memory compared to other regression models. Table 4 clearly shows that Bi-GRU obtained a high R2 value of 0.96 and an NRMSE of 0.09, an ND of 0.08, an RMSSE of 0.08, and MAE of 0.07, and an MSE of 0.06. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Citadel POS Dataset**} \\ \hline
**Forecasting Models** & **Measures** & **Without Feature Engineering** & **With Feature Engineering** \\ \hline \multirow{6}{*}{ARIMA} & NRMSE & 6.58 & 3.52 \\  & ND & 4.73 & 3.41 \\  & RMSSE & 4.17 & 3.13 \\  & MAE & 3.28 & 2.64 \\  & MSE & 4.04 & 2.52 \\  & R2 & 0.73 & 0.83 \\ \hline \multirow{6}{*}{LSTM} & NRMSE & 5.29 & 2.96 \\  & ND & 4.91 & 2.92 \\  & RMSSE & 4.53 & 2.54 \\  & MAE & 4.01 & 2.58 \\  & MSE & 3.88 & 2.32 \\  & R2 & 0.76 & 0.84 \\ \hline \multirow{6}{*}{Bi-LSTM} & NRMSE & 3.94 & 3.67 \\  & ND & 3.18 & 3.02 \\  & RMSSE & 3.01 & 2.88 \\  & MAE & 2.77 & 2.61 \\  & MSE & 2.22 & 2.16 \\  & R2 & 0.77 & 0.92 \\ \hline \multirow{6}{*}{GRU} & NRMSE & 0.73 & 0.44 \\  & ND & 0.68 & 0.29 \\ \cline{1-1}  & RMSSE & 0.71 & 0.30 \\ \cline{1-1}  & MAE & 0.61 & 0.27 \\ \cline{1-1}  & MSE & 0.59 & 0.29 \\ \cline{1-1}  & R2 & 0.80 & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical analysis of different regression models on the Citadel POS dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Walmart Dataset**} \\ \hline
**Forecasting Models** & **Measures** & **Without Feature Engineering** & **With Feature Engineering** \\ \hline \multirow{6}{*}{GRU} & NRMSE & 0.95 & 0.41 \\  & ND & 0.64 & 0.32 \\  & RMSSE & 0.56 & 0.28 \\  & MAE & 0.67 & 0.18 \\  & MSE & 0.42 & 0.10 \\  & R2 & 0.88 & 0.93 \\ \hline \multirow{6}{*}{Bi-GRU} & NRMSE & 0.10 & 0.01 \\  & ND & 0.16 & 0.03 \\ \cline{1-1}  & RMSSE & 0.18 & 0.08 \\ \cline{1-1}  & MAE & 0.12 & 0.07 \\ \cline{1-1}  & MSE & 0.11 & 0.03 \\ \cline{1-1}  & R2 & 0.97 & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._In addition to the assessment of various classifiers, a statistical test was used to assess the performance of all the classifiers. For that reason, the Friedman test, also known as the nonparametric statistical test, was applied in this research. The Friedman test uses the data ranks rather than the data themselves and tests the null hypothesis in which the column properties are all identical. In some other way, all classifiers have a comparable impact on the classification process. In this statistical test, the probability of gaining the detected sample outcomes (\(p\)-value) is computed as a scalar value in the range of [0, 1]. Small values of \"\(p\)\" decline the null hypothesis. The Friedman test is calculated as \(p=0.0071\), which shows that the proposed Bi-GRU has a superior performance compared to other classifiers in a significant manner.