多元線性回歸模型估計-展示頁
2025-05-27 01:36本頁面
【正文】 eis ?( S S E ) s q u a r e s of s u m e x p l a i n e d t h eis ?( S S T ) s q u a r e s of s u m t o t a l t h eis :f o l l o wi n g t h ed e f i n e t h e n W e??p a r t , du n e x p l a i n ea n a n d p a r t , e x p l a i n e da n of upm a d e b e i n g asn o b s e r v a t i oe a c h ofc a n t h i n k We222?????????iiiiiiuyyyyuyy11 GoodnessofFit (continued) How do we think about how well our sample regression line fits our sample data? Can pute the fraction of the total sum of squares (SST) that is explained by the model, call this the Rsquared of regression R2 = SSE/SST = 1 – SSR/SST 12 GoodnessofFit (continued) ? ?? ?? ?? ?? ? ? ?? ?????????22222????? v a l u e s t h ea n d a c t u a l t h eb e t we e nt c o e f f i c i e nn c o r r e l a t i o s q u a r e d t h e t oe q u a l b e i n g as of t h i n k a l s oc a n WeyyyyyyyyRyyRiiiiii13 More about Rsquared R2 can never decrease when another independent variable is added to a regression, and usually will increase Because R2 will usually increase with the number of independent variables, it is not a good way to pare models 14 Assumptions for Unbiasedness Population model is linear in parameters: y = b0 + b1x1 + b2x2 +…+ bkxk + u We can use a random sample of size n, {(xi1, xi2,…, xik, yi): i=1, 2, …, n}, from the population model, so that the sample model is yi = b0 + b1xi1 + b2xi2 +…+ bkxik + ui E(u|x1, x2,… xk) = 0, implying that all of the explanatory variables are exogenous None of the x’s is constant, and there are no exact linear relationships among them 15 Too Many or Too Few Variables What happens if we include variables in our specification that don’t belong? There is no effect on our parameter
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