Regression models

What Is Regression Models?

Regression models are powerful statistical analysis tools used to examine the relationship between a dependent variable and one or more independent variables. Within the realm of quantitative analysis and financial modeling, these models help financial professionals understand how changes in certain factors might influence a particular outcome, making them indispensable for prediction and forecasting. Regression models are widely applied across various aspects of finance, from estimating asset returns to analyzing economic trends.

History and Origin

The concept of regression analysis originated from the work of Sir Francis Galton in the late 19th century. Galton, a cousin of Charles Darwin, first introduced the term "regression towards mediocrity" in his 1886 paper, where he observed that the heights of offspring tended to "regress" towards the average height of the population, rather than perfectly inheriting extreme characteristics from their parents.²⁷ This observation led to his quantification of this trend and the invention of linear regression analysis, laying the groundwork for much of modern statistical modeling. While Galton's initial interest was in genetics, his methods were soon formalized by others, such as Karl Pearson, for broader applications, ultimately evolving into the sophisticated regression models used today in diverse fields, including finance.²⁶

Key Takeaways

• Regression models quantify the relationship between a dependent variable and one or more independent variables.
• They are essential tools for prediction, forecasting, and understanding causal relationships (when carefully applied).
• The most common method for estimating linear regression models is Ordinary Least Squares¹, ², ³, ⁴⁵, ⁶⁷⁸, ⁹¹⁰, ¹¹, ¹²¹³, ¹⁴, ¹⁵¹⁶¹⁷, ¹⁸¹⁹, ²⁰²¹, ²², ²³²⁴, ²⁵