leastsquaresregression(參考版)
2025-07-20 15:26本頁面
【正文】 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 eResiduals。 。 。 s )Expenditure ($1,00039。 s )Expenditure ($1,00039。 s )Expenditure ($1,00039。 s )Expenditure ($1,00039。 . 84 ( 6 . 3 2 5 ) ( 1 . 5 8 1 )xyx y ssr? ? ? ? ? ? ?? ? ? ? ?Calculations 1011 .5 8 1.8 .2 。 8 。 s )Expenditure ($1,00039。i s t he ob ser v e d v a l ue o f whe n .i i iiy b b x yb b x x xy y x x??? ? ??Observed y, Predicted y 234567 2 3 4 FUEL CONSUMPTION CAR WEIGHT FUEL CONSUMPTION vs CAR WEIGHT (, ) = observed y predicted y when x= yhat = a + bx = a + b* Scatterplot: Fuel Consumption vs Car Weight F u e l C o n s u m p ti o n v s C a r W e i g h t2345671 2 3 4 5C a r W e i gh t ( 1 0 0 0 l bs )Fuel consumption (gal/100 miles)Fu e l c o n s u m p t i o n“Best” line? Scatterplot with least squares prediction line F U E L C O N S U M P T I O N v s C A R W E I G H Ty = 1 . 6 3 9 x 0 . 3 6 3 1r2 = 0 . 9 5 3 82345671 . 5 2 . 5 3 . 5 4 . 5W E I G H T ( 1 0 0 0 l b s )FUEL CONSUMP. (gal/100 miles)How do we draw the line? Residuals 01 ? ()thththiiiiiii
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