14.1 Restricted Least Squares (RLS) 1. OLS and RLS ()Unrestricted least squares(ULS) When using the ordinary least square method(OLS) to estimate the parameters, we do not put any prior constraint() or restriction(s) on the parameters. So we can estimate the parameters without any restrictions. This is ULS

One CLRM assumption is: The model used in empirical analysis is \correctly specified\

12.1 The Nature of Autocorrelation 1. Definition (1) CLRM assumption: No autocorrelation exist in dishurbances ui; E(iμi)=0 Autocorrelation means: E(μiμ)≠0 (2) Autocorrelation is usually associated with time series data, but it can also occur in cross-sectional data, which is called spatial correlation

11.1 The Nature of Heteroscedasticity Homoscedasticity: equal variance. Heteroscedasticity: unequal variance. Heteroscedasticity is usually found in cross-sectional data

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)