2.2 THIS CONCEPT OF POPULATION REGRRESION (Damodar N, Gujarati )

FUNCTION  ( PRF )

From the preceding discussion Figure.2.1 and 2.2, it is clear that each conditional  E ( Y | Xi ) is a  function Xi, where Xi is given value of value of X.

Symbolically,

E(Y|Xi) =f (Xi)                                                   (2.2.1 )

Where f (Xi) denotes some function of the explanatory variable X. In our example   E(Y|Xi) is  a linear function   Xi . Equation (2.2.1) is known as the conditional expectation function (CEF) or population regression function ( PRF ) or population regression  (PR) for short. It states merely that the expected value of the distribution   Y     given     Xi is functionally related to Xi. In simple term, it tells show the mean or average response   of   Y varies whit   X.

What from does the function   f (Xi)   assume?   This is an important question because in real situation we do not have the entire population available for examination. The function form of the  for examination. The functional from the PRF is therefore an empirical question, although in specific cases theory may have something to say.

For example, an economist might posit that consumption expenditure is linearly related to income. Therefore, as a first approximation or working hypothesis, we may assume that  PRF  E(Y|Xi)  is linear function  Xi say, of type