Implement a regression analysis to understand the relationship between product sales and various influencing factors, then visualize these relationships using a scatter plot to identify trends.

Develop a classification model to categorize products based on their likelihood of going out of stock, and use a confusion matrix to visualize the model's accuracy in predicting stockouts.

Conduct a time series analysis to forecast future product sales based on historical data, and present the forecasted sales trends using a line chart for easy interpretation.

Apply optimization algorithms to calculate the optimal inventory levels for each product, taking into account factors such as demand variability, holding costs, and the risk of stockouts, to provide prescriptive recommendations for inventory management.