leastsquaresregression-資料下載頁
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【正文】 103 3 .8 8 2 2 4 .1 0 3 9 4 7 .5 4 9 6 2 .1 .8 6 8,6 2 .1sl o p e .8 6 8 2 .2 3 6 3 52 4 .1 0 3in te r c e p t 9 4 7 .5 4 9 ( 2 .2 3 6 ) 3 3 .8 8 2 1 0 2 3 .3 0 9?l e a st sq u a r e s p r e d ic tio n l in e 1 0 2 3 .3 0 9 2 .2 36xyyxx s y s rsb r b y b xsbbyx? ? ? ? ? ?? ? ?? ? ? ?? ? ? ???SAT scores: result SA T M e a n p e r Sta te v s % Se n i o r s T a k i n g T e s ty = 2 . 2 3 7 5 x + 1 0 2 3 . 4R2 = 0 . 7 5 4 28208709209701020107011200 10 20 30 40 50 60 70 80% o f S e n i o r s T a k i n g T e s tMean SAT Scorer2 = ()2 = .7534 If 57% of NC seniors take the SAT, the predicted mean score is ? 1 0 2 3 . 3 0 9 2 . 2 3 6 3 5 ( 5 7) 8 9 5 . 8 4y ? ? ?Avoid GIGO! Evaluating the least squares line 1. Create scatterplot. Approximately linear? 2. Calculate r2, the square of the correlation coefficient 3. Examine residual plot Residuals ? residual =observed y predicted y = y y ? Properties of residuals 1. The residuals always sum to 0 (therefore the mean of the residuals is 0) 2. The least squares line always goes through the point (x, y) Graphically residual = y y y yi yi ei=yi yi X xi Residual Plot ? Residuals help us determine if fitting a least squares line to the data makes sense ? When a least squares line is appropriate, it should model the underlying relationship。 nothing interesting should be left behind ? We make a scatterplot of the residuals in the hope of finding… NOTHING! Car Wt/ Fuel Consump: Residuals ? CAR WT. FUEL CONSUMP. Pred FUEL CONSUMP. Residuals ? .290501931 ? ? ? ? ? ? 2 ? ? ? Example: Car wt/fuel consump. residual plot page 13 R E S I D U A LS v s W T( X ) 0 . 6 0 . 4 0 . 200 . 20 . 41 . 5 2 2 . 5 3 3 . 5 4 4 . 5W T ( X )RESIDUALSR E S I D U A LSAT Residuals % T A K E R e s i d u a l P l o t 1 0 0 5 00501000 20 40 60 80% T A K EResidualsLinear Relationship? L i n e a r ( ? )01020304050604 2 0 2 4 6 8XYGarbage In Garbage Out G I G Oy = 4 x + 1 101020304050604 2 0 2 4 6 8XYResidual Plot – Clue to GIGO R e s i d u a l P l o t 2 0 1 0010204 2 0 2 4 6 8X V a r i a b l eResiduals G I G Oy = 4 x + 1 101020304050604 2 0 2 4 6 8XYR e s i d u a l P l o t 2 0 1 0010204 2 0 2 4 6 8X V a r i a b l eResidual
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