Analysis of Financial Data

Chapter 4. An introduction to simple regression

Regression is an important tool financial researchers use to understand the relationship among two or more variables. Even when, as done in later chapters, we move beyond regression and use slightly more complicated methods, the intuition provided by regression is of great use. This motivates why we devote this chapter (and the next three) to regression. It is important for the reader to develop the basic tools of regression before proceeding on to more sophisticated methods.

In finance, most empirical work involves time series data. However, as we shall see in the second half of this book, working with time series data requires some specialized tools. Hence, with some exceptions,^[18] for the next few chapters you will not see too many examples involving financial time series data. The examples in this chapter will mostly involve cross-sectional data. The reader interested in more traditional applications involving financial time series can be reassured that they will reappear starting in Chapter 8. However, before we get to time series methods, a good understanding of basic regression is required.

Regression is particularly useful for the common case where there are many variables and the interactions between them are complex. All of the examples considered in Chapter 3 really should have involved many variables. For instance, market capitalization likely depends on many characteristics of the firm, such as sales, assets, income, etc. ...