Imagine you are a data analyst working for a retail company, and your team is tasked with using regression analysis to address a specific business problem. For example, you could be examining the relationship between advertising spending and sales revenue to optimize the company's marketing budget allocation.

What are the key steps involved in conducting a regression analysis for this business problem? Discuss how you would approach data collection, data preprocessing, model selection, and model evaluation in this context.

In the real world, data can be messy, and assumptions of regression models might not always hold true. What are some potential challenges you might encounter when applying regression analysis to this business problem? How would you address these challenges to ensure the accuracy and reliability of your findings?

What other variables or factors, beyond advertising spending, might influence sales revenue in a retail setting? How would you determine which additional variables to include in your regression model to provide a comprehensive analysis?

How would you interpret the results of the regression analysis to provide actionable insights to the retail company's decision$-$makers? What metrics or indicators would you use to communicate the impact of advertising spending on sales revenue effectively?

Reflecting on the potential outcomes of your regression analysis, what business recommendations or strategies would you propose based on your findings? How might these insights be leveraged to optimize the company's marketing efforts and drive revenue growth?