計量經濟學英ppt課件-免費閱讀
【正文】 1 Multiple Regression Analysis y = b0 + b1x1 + b2x2 + . . . bkxk + u 2. Inference 2 Assumptions of the Classical Linear Model (CLM) So far, we know that given the GaussMarkov assumptions, OLS is BLUE, In order to do classical hypothesis testing, we need to add another assumption (beyond the GaussMarkov assumptions) Assume that u is independent of x1, x2,…, xk and u is normally distributed with zero mean and variance s2: u ~ Normal(0,s2) 3 CLM Assumptions (cont) Under CLM, OLS is not only BLUE, but is the minimum variance unbiased estimator We can summarize the population assumptions of CLM as follows y|x ~ Normal(b0 + b1x1 +…+ bkxk, s2) While for now we just assume normality, clear that sometimes not the case Large samples will let us drop normality 4 . . x1 x2 The homoskedastic normal distribution with a single explanatory variable E(y|x) = b0 + b1x y f(y|x) Normal distributions 5 Normal Sampling Distributions ? ?? ?? ?? ?? ?e r r o r s t h eofn c o m b i n a t i ol i n e a r a isit b e c a u s en o r m a l l y dd i s t r i b u t e is ?0 , 1N o r m a l ~ ?? t h a tso ,?,N o r m a l ~?st v a r i a b l ei n d e p e n d e n t h eof v a l u e ss a m p l e t h eon lc o n d i t i o n a s,a s s u m p t i o n C L M U n d e r t h ejbbbbbbbjjjjjjsdV a r?6 The t Test ? ?? ?1:f r e e d o m of d e g r e e s t h eN o t e?b y e s t i m a t e t oh a v e w eb e c a u s en o r m a l ) ( v so n d i s t r i b u t i a is t h i sN o t e ~ ??sa s s u m p t i o n C L M U n d e r t h e221j?????knttseknjjssbbb7 The t Test (cont) Knowing the sampling distribution for the standardized estimator allows us to carry out hypothesis tests Start with a null hypothesis For example, H0: bj=0 If accept null, then accept that xj has no effect on y, controlling for other x’s 8 The t Test (cont) ? ?0?jH ,h y p o t h e s i s n u l l a c c e p t t h eo w h e t h e r td e t e r m i n e t or u l er e j e c t i o n a w i t ha l o n g s t a t i s t i
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