# statistical modeling

#### harnessing the power of multivariate analysis

The power of statistical models comes from the ability to consider the impacts of many moving parts at the same time. Charts and graphs can only show two to four different dimensions at a time, depending on the skill of the analyst. By contrast, statistical analysis can include as many data points and variables as is supported by the data and solid statistical principles. By incorporating multiple variables into a statistical model, we gain a more comprehensive understanding of the complex relationships and dynamics at play in a given phenomenon. These models allow us to examine how different variables interact with each other, providing insights into how the presence of one variable may modify the effect of another. This consideration of interactions can uncover nuanced patterns and uncover hidden insights that may not be apparent when analyzing variables in isolation.

Statistical models can be usefully divided into two groups: predictive, and inferential. The main difference between inferential statistical modeling and predictive statistical modeling lies in their primary objectives and the types of insights they generate.

- Inferential statistical modeling focuses on understanding the relationships and patterns within a sample data set and then generalizing those findings to a larger population. It aims to draw conclusions and make inferences about the population based on the analysis of a representative sample. Examples include:
- Marketing mix modeling, where the goal is to estimate the incremental change in sales that would result from adjusting, say, the TV ad budget up or down.
- Program assessment, where the goal is to estimate the impact of a program, tactic, or initiative, including where the program is more effective or less effective

- Predictive statistical modeling aims to forecast or predict future outcomes based on historical data. It involves developing models that can be used to estimate or forecast unknown or future values based on the patterns and relationships observed in the data. While inferential modeling aims to understand the underlying mechanisms and provide insights into the broader population, predictive modeling focuses on generating accurate predictions or forecasts for specific events or outcomes. Examples include:
- Demand forecasting, where the goal is to estimate how much demand there will be at a particular time. This can be useful for setting staffing levels for a call center, or setting the necessary power supply levels to accommodate electricity demand.
- Stock movement forecasting, where the goal is to predict what is about to happen in the stock market so that appropriate actions can be taken now.

Both types of statistical models are very powerful when wielded correctly by an experienced modeler, and can be utilized to improve decision-making at all levels of an organization. Where there’s data and a needed decision, there’s the opportunity for a statistical model to play a part.