ECONOMETRICS (ECON 109) Summary of Lecture 2: Two-variable (Simple) Regression Model

Simple Linear Regression Model  A simple linear regression model is a regression model where there is ONLY ONE independent variable (X) affecting the dependent variable Y, and wherein the functional relationship between Y and X/Xs is linear, thus when expressed graphically will show a straight line. “LINEAR” – this pertains to linearity in parameters. That is, matter even if the independent variable X/Xs are not raised to the power of 1, but just as long as the parameters of the regression model (Betas – B1, B2… Bn) are raised to the power of 1 the relationship between Y and X/Xs will be linear. PRF: Yi   0  1 X i

   SRF: Yi   0  1 X i  Where: Yi is the estimator of actual Yi   0 is the estimator of actual  0 or the constant(intercept)  1 is the estimator of actual 1 or slope estimate   i is the estimator of actual residual term  i or the stochastic disturbance term
 The error term  i captures all relevant variables not included in the model because they are not observed in the data set

Classical Linear Regression Model (CLRM)   It is classical in a sense that it was first developed by Gauss in 1821 and since then has served as norm or standard against which regression models that do not satisfy the Gaussian Assumptions (listed below) may be compared with. The Gaussian, standard, or classical linear regression model (CLRM), which is the cornerstone of most econometric theory.

Ordinary Least Squares (OLS) Method  Attributed to Carl Friedrich Gauss 

  The method requires that we should choose  1 and  2 as estimates of  1 and  2 , respectively such that: n   Q   (Yi   1   2 X i ) 2 is a minimum i 1

where Q is also the SUM OF SQUARES of the (within-sample) prediction when we predict given Xi and the estimated regression