An Introduction to Econometric Theory

1 Elementary Data Analysis

1.1 Variables and Observations

Where to begin? Data analysis is the business of summarizing a large volume of information into a smaller compass, in a form that a human investigator can appreciate, assess, and draw conclusions from. The idea is to smooth out incidental variations so as to bring the ‘big picture’ into focus, and the fundamental concept is averaging, extracting a representative value or central tendency from a collection of cases. The correct interpretation of these averages, and functions of them, on the basis of a model of the environment in which the observed data are generated, ¹ is the main concern of statistical theory. However, before tackling these often difficult questions, gaining familiarity with the methods of summarizing sample information and doing the associated calculations is an essential preliminary.

Information must be recorded in some numerical form. Data may consist of measured magnitudes, which in econometrics are typically monetary values, prices, indices, or rates of exchange. However, another important data type is the binary indicator of membership of some class or category, expressed numerically by ones and zeros. A thing or entity of which different instances are observed at different times or places is commonly called a variable. The instances themselves, of which collections are to be made and then analyzed, are the observations. The basic activity to be studied in this first part of the book is ...