In the beginning, we have two variables, X and Y.  Economists are interested

in the relationship between X and Y.  We could graph them or we could

calculate the correlation between them, but we run regressions instead.  Our

first goal is to understand why regressions have such an appeal for

economists.

Regression Model.  X and Y are data.  ε is an error term (unobservable data). 

Data and errors have a subscript that identifies the observation number. 

The parameters (generally Greek letters) are scalars (numbers) that are the

same for all observations.

The summations are all from 1 to n, where n is the number of observations. 

The subscripts on the variables are omitted for clarity.  The intercepts are

omitted because we are using the “small x” notation. 

Now, we have an estimation formula we can work with.

The simplest regression is ... 

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William R. Parke

What is a regression?