Figure 3.1: Regression of EARNINGS residuals on S residuals 2.3.3.2 Properties of the Multiple Regression Coefficients Concerning simple regression analysis, the regression coefficients should bethought of as different categories of random variables whose random components are related to the existence of the disturbance term in the model. Each regression coefficient is calculated as a function of the values of Y and the explanatory variables in the sample. Y, in turn, is determined by the explanatory variables and the disturbance term. It follows that the regression coefficients are indeed determined by the values of the explanatory variables and the disturbance term, in which their properties depend on critically upon the properties of the disturbance term. In continuation of the assumption that the Gauss–Markov conditions are satisfied, which are (i) that the expected value of uin any observation is 0 (ii) that the population variance of its distribution is the same for all observations (iii) that the population covariance of its values in any two observations is 0, and (iv) that it is distributed independently of any explanatory variable. The first three conditions are the same as for simple regression analysis but (iv) is a generalization of (i) to (iii). Furthermore, there are two practical requirements to be met.
