4 - Computing the OLS Regression Line
from PART 1 - DESCRIPTION
Published online by Cambridge University Press: 05 June 2012
Summary
Of all the principles which can be proposed for that purpose, I think there is none more general, more exact, and more easy of application, that of which we made use in the preceding researches, and which consists of rendering the sum of squares of the errors a minimum.
Adrien-Marie LegendreIntroduction
Chapters 4 and 5 introduce the concept of regression, the fundamental analytical tool of econometrics. The regression line summarizes the relationship between two variables. Chapter 4 covers the mechanics of regression. We discuss the theory behind fitting a line, present an algebraic exposition of the ordinary least squares (OLS) regression coefficients, and show several ways to have Excel report regression results. We note that OLS is not the only way to fit a regression line. Chapter 5 focuses on interpreting what OLS regression does and the results it produces. Of course, these two chapters are only an introduction to regression analysis. The remainder of this book is dedicated to ever more powerful and sophisticated applications of the method of regression.
Fitting the Ordinary Least Squares Regression Line
Workbook: Reg.xls
In this section, we use an artificial data set to demonstrate how the OLS (also abbreviated LS) regression line summarizes a bivariate scatter plot. We will describe the optimization problem behind the OLS regression procedure and show that OLS is only one of many varieties of regression analysis.
We emphasize throughout the book that there are many possible ways to summarize the relationship between variables.
- Type
- Chapter
- Information
- Introductory EconometricsUsing Monte Carlo Simulation with Microsoft Excel, pp. 72 - 94Publisher: Cambridge University PressPrint publication year: 2005