CHAPTER 2: TWO-VARIABLE REGRESSION ANALYSIS: SOME BASIC IDEAS

A Hypothetical Example
Conditional expected values of x – they depend on the given values of the variable X.
Population regression curve – the locus of the conditional means of the dependent variable for the fixed values of the explanatory variable (s).
The Concept of Population Regression Function (PRF)
Conditional Expectation Function (CEF) or Population Regression Function (PRF) or Population Regression (PR)
-          It states merely that the expected value of the distribution of Y given Xi is functionally related to Xi. In simple terms, it tells how the mean or average response of Y varies with X.
The Meaning of the Term Linear
Linearity in the Variables
The conditional expectation of Y is a linear function of Xi.
Linearity in the Parameters
From now on the term “linear” regression will always mean a regression that is linear in the parameters, the β’s. It may or may not be linear in the explanatory variables, the X’s.


The Significance of the Stochastic Disturbance Term
Why not introduce these variables into the model explicitly? Stated otherwise, why not develop a multiple regression model with as many variables as possible? The reasons are many.
1.      Vagueness of theory
2.      Unavailability of data
3.      Core variables versus peripheral variables
4.      Intrinsic randomness in human behavior
5.      Poor proxy variables
6.      Principle of parsimony
7.      Wrong functional form
The Sample Regression Function (SRF)
Estimator – a rule or formula or method that tells how to estimate the population parameter from the information provided by the sample at hand.
µi denotes the (sample) residual term.