多元線性回歸模型估計-文庫吧資料
2025-05-23 01:36本頁面
【正文】 …… 5 A Fitted or Predicted Value For observation i, the fitted value is The residual for observation i is defined as in the simple regression case, The properties 1 2 3 The point ( ) is always on the OLS regression line: ikkiii xxxy bbbb ????? 22110 ????? ?iii yyu ?? ??kki xxxy bbbb ???? 22110 ????? ?yxxx k , 21 ?0? ?? iu0??0? ??? ?? iiki yuxu6 Interpreting Multiple Regression t i o ni n t e r p r e t a a h a s e a c h is t h a t ,?? t h a ti m p l i e s f i x e d , .. . , h o l d i n g so,?. ..???so ,?. ..????112221122110r i b u s c e t e r i s p axyxxxxxyxxxykkkkkbbbbbbbbb????????????????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
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