One of the CLRM assumptions is: there is no perfect multicollinearity-no exact linear relationships among explanatory variables, Xs, in a multiple regression. In practice, one rarely encounters perfect multicollinearity, but cases of near or very high multicollinearity where explanatory variables are approximately linearly related frequently arise in many applications

Dummy variables (also indicator variables; binary variables categorical variables; dichotomous variables.) Qualitative variables in regression model For example: sex, race, color, religion, nationalit y, marital status, etc

The models we discussed are models that are linear in parameters; variables Y and Xs do not necessarily have to be linear The price elasticity of demand~the log-linear models The rate of growth~semilog model Functional forms of regression models which are linear in parameters, but not necessarily linear in variables:

Multiple Regression Model: A regression model with more than one explanatory variable, multiple because multiple nfluences (i.e., variables)affect the dependent variable

The Object of Hypothesis Testing To answer- How \good\ is the estimated regression line. How can we be sure that the estimated regression function (i.e., the SRF) is in fact a good estimator of the true PRF?

5.1 The Meaning of Regression Analysis 1.Regression analysisthe study of the relationship between one variable Y (the explained, or dependent variable) and one or more other variables X/Xs (explanatory, or independent variables)

Statistical inference draws conclusions about a population [i.e., probability density function(DF)] from random sample that has supposedly been drawn from that population

The Normal Distribution: the distribution of a continuous r.v. whose value depends on a number of factors, yet no single factor dominates the other. 1. Properties of the normal distribution: 1)The normal distribution curve is symmetrical around its mean valueu. 2)The PDF of the distribution is the highest at its mean value but tails off at its extremities

2.1 SOME NOTATION 1. The Summation Notation X, =X1++...+n can be abbreviated as:Σx,orΣx 2. Properties of the Summation Operator

Definition (1) Econometrics: economic measurement. (2) Econometrics: the social science in which the tools of economic theory, mathematics, and statistical inference are applied to the analysis of economic phenomena. (3) Econometrics: the result of a certain outlook on the role of economics, consists of the application of mathematical statistics to economic data to lend