Before we proceed to a formal analysis of regression theory,let us dwell briefly on the matter of terminology and notation. In the literature the terms briefly on the matter of terminology and notation . In the literature the terms dependent variable and explanatory variable are described variously. A representative list is:
Althought it is matter of personal taste and tradition, in this text we will uses the dependent variable/explanatory variable or the more neutral, regressand and the regressor terminology.
If We are studying the dependence of variable on only a single explanatory variable, such as that of consumption expenditure on real income,such a study is know as simple, or two-variable, regression analysis. However, if we are studying the dependence of one variable on more than on explanatory variable, as in the crop-yield , rainfall, temperature, sunshine, and fertilizer example, it is known as multiple-regression analysis. In the other word, in two-variable regression there is more than one explanatory variable.
The term random is a synonym for the term stochastic. As noted earlier, a random or stochastic variable is a variable that can take on any set of values, positive or negative, with a given probability.9
Unless stated otherwise, the later Y will denote the dependent variable and X's ( X1, X2,...,Xk ) will denote the explanatory variables, Xk being the kth explanatory variable. The subscript i or t will denote the ith or the tth observation or value. Xki (or Xkt ) wiil denote the ith ( or tth ) observation on variable Xk. N( or T ) will denote the total number of observation or values in population, and n( or t ) the total number of observations in a sample.
As a matter of convention, the observation subscript i will be used for cross- sectional data (i.e., data collected at one point time ) and the subscript t will used for time series data ( i.e.,data collected over a period of time).
The nature of cross-sectional and time series data, was well as the important topic of the nature and sources data for empirical analysis, is discussed in following section.
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9See App.A for formal definition an further detail.
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