多元線性回歸模型估計(存儲版)
【正文】 bbbbbbb????????????????7 A “Partialling Out” Interpretation ? ?22011211122110???? r e g r e s s i o n e s t i m a t e d t h ef r o m r e s i d u a l s t h ea r e ? wh e r e,??? t h e n ,????i . e . ,2 wh e r ec a s e heC o n s i d e r txxrryrxxykiiii??bbbb?????????8 “ Partialling Out” continued Previous equation implies that regressing y on x1 and x2 gives same effect of x1 as regressing y on residuals from a regression of x1 on x2 This means only the part of xi1 that is uncorrelated with xi2 are being related to yi so we’re estimating the effect of x1 on y after x2 has been “partialled out” 9 Simple vs Multiple Reg Estimate s a m p l e i n t h e edu n c o r r e l a t a r e a n d OR ) ofe f f e c t p a r t i a l no ( i . e . 0?:u n l e s s ?~ Ge n e r a l l y ,???? r e g r e s s i o n m u l t i p l e wi t h t h e~~~ r e g r e s s i o n s i m p l e t h eC o m p a r e21221122110110xxxxxyxy???????bbbbbbbb10 GoodnessofFit ? ?? ?SSR SSE SSTT h e n ( S S R ) s q u a r e s of s u m r e s i d u a l t h 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 (c
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