## 5 Conclusions  
A Bi-GRU model was implemented in this study with effective feature engineering techniques for precise retail sales forecasting. In the initial phase, the unreliable samples in the Rossmann and Walmart datasets were eliminated by removing outliers, interpolating missing data, normalization, and de-normalization. Next, the feature engineering was performed using the APSO algorithm, RFE, and MRMR to select the active features from the pre-processed datasets, which were finally given to the Bi-GRU model for precise retail sales forecasting. The efficacy of the proposed regression model was analyzed using six evaluation measures: NRMSE, ND, RMSSE, MAE, MSE, and R2. The proposed Bi \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Models** & **R2** & **MAE** & **MSE** & **RMSSE** \\ \hline \multirow{6}{*}{Walmart} & XGBoost [39] & 0.98 & 0.12 & 0.06 & - \\  & Random forest [39] & 0.97 & 0.14 & 0.08 & - \\ \cline{1-1}  & OLS [39] & 0.72 & 0.67 & 1.11 & - \\ \cline{1-1}  & Bi-GRU & 0.99 & 0.07 & 0.03 & - \\ \cline{1-1}  & XGBoost [40] & - & - & - & 0.65 \\ \cline{1-1}  & Bi-GRU & - & - & - & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparative results between the existing regression model and the proposed Bi-GRU model by means of R2, MAE, MSE, and RMSSE. Figure 4: Graphical comparison between the proposed and existing regression models. GRU model with effective feature engineering achieved a superior performance in sales forecasting in relation to the traditional regression models: linear regression, LSTM, Bi-LSTM, and GRU. As mentioned in the numerical evaluation section, the proposed Bi-GRU model has minimum MAEs of 0.05 and 0.07 and MSEs of 0.04 and 0.03 on the Rossmann and Walmart datasets. In addition, the Bi-GRU model has a high R2 value of 0.98 and 0.99 on the Rossmann and Walmart datasets, which are better than the comparative regression models. On the other hand, the selection of active features decreases the processing time to 20.11 s and 30.12 s on the Rossmann and Walmart datasets. Still, the Bi-GRU model has issues like low-learning efficiency and a slow convergence rate. Furthermore, the results analysis of this sales forecasting is completely dependent on a specified dataset. In case of changes in the dataset region, the result also varies and cannot be compared with some other different datasets. Therefore, as a future extension, a novel hyperparameter-tuning technique will be integrated with the proposed regression model which will be suitable for improving the performance of retail sales forecasting under various datasets. Additionally, this research will be analyzed with real-time data for better visualization results. The paper investigation, resources, data curation, writing--original draft preparation, writing--review and editing, and visualization were performed by A.M.G. and H.D.P. The paper conceptualization and software were conducted by A.K. The validation and formal analysis, methodology, supervision, project administration, and funding acquisition of the version to be published were conducted by [PERSON]-[PERSON] and P.B.D. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The datasets generated during and/or analzsed during the current study are available in the [Rossmann dataset] and [Walmart dataset] repository: Rossmann dataset link = [[https://www.kaggle.com/competitions/rossmann-store-sales/data](https://www.kaggle.com/competitions/rossmann-store-sales/data)]([https://www.kaggle.com/competitions/rossmann-store-sales/data](https://www.kaggle.com/competitions/rossmann-store-sales/data)), and Walmart dataset link = [[https://www.kaggle.com/datasets/yasserh/walmart-dataset](https://www.kaggle.com/datasets/yasserh/walmart-dataset)]([https://www.kaggle.com/datasets/yasserh/walmart-dataset](https://www.kaggle.com/datasets/yasserh/walmart-dataset)). The authors declare no conflicts of interest.