BT on SRF

A brief review of the meaning of the sample regression function (SRF). A few key ideas from Gujarati here:

• As with univariate inferences, we expect sampling fluctuation/variation. In theory, there is one population regression function (PRF) but several sample regression functions (SRF). It is important to see: we assume an unknowable population; we take a sample to learn something about the popluation. As samples vary, so do sample statistics. How to characterize the inevitable variation ("fluctuation" in Gujarati's term)? We can use a distribution to describe (characterize) unavoidable variation in the sample statistic.
• Note the correspondence: the PRF contains population parameters (slope, intercept) while the SRF contains estimators.
• What is linear in linear regression? We require linearity in the parameters (slope, intercept) but we do not require linearity in the variable(s); i.e., X^2 is okay!