Assumptions of the classical Linear Model (Clm) e So far, we know that given the Gauss Markov assumptions, OLS IS BLUE e In order to do classical hypothesis testing we need to add another assumption(beyond the Gauss-Markov assumptions) Assume that u is independent of x,x2…,xk and u is normally distributed with zero mean and variance 0: u- Normal(0, 02) Economics 20- Prof anderson

一、简单线性回归模型的设定 二、简单线性回归模型的基本假定 三、简单线性回归模型参数的估计方法 四、参数估计量的统计性质 五、拟合优度的度量 六、回归系数的区间估计和假设检验 七、回归模型预测 八、EViews应用

Redefining variables Changing the scale of the y variable will lead to a corresponding change in the scale of the coefficients and standard errors. so no change in the significance or interpretation Changing the scale of one x variable will lead to a change in the scale of that coefficient and standard error, so no change in the significance or interpretation Economics 20- Prof anderson

Consistency e Under the Gauss-Markov assumptionS OLS IS BLUE, but in other cases it wont always be possible to find unbiased estimators o In those cases, we may settle for estimators that are consistent, meaning as n→>∞,the distribution of the estimator collapses to the parameter value Economics 20- Prof anderson

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

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

Single equation regression models: -The dependent variable, Y, is expressed as a linear function of one or more explanatory variables, the Xs. Assumption the cause-and-effect relationship, if any, between Y and the Xs is unidirectional: explanatory variables are the cause; the dependent variable is the effect

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

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:

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