LinearFitErrorAnalysis - y= y = 1 N N i =1 Variance = 2 =...

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Unformatted text preview: y= y = 1 N N i =1 Variance = 2 = yi2 yi yi 1 N N 1 i =1 ( yi y) 2 2 = Variance Adev = 1 N N i =1 yi y 2 N i=i y yi 2 i y = y ( x|p1 , p2 ,..., pM ) 2 2 ~N M 2 red = 2 2 red NM ~1 2 red y yi 0= y( xi |{..., pk ,...}) pk 2 i y = a + bx 2 a + bxi N ( a , b) = i =1 0= 0= 2 a 2 b N =2 i =1 N =2 a + bxi yi 2 i xi ( a + bxi ( = 2 aS + bSx Sy yi ) 2 i N i =1 Sxx = 2 i i =1 S= yi N i =1 1 2 i xi2 2 i Sx = Sxy = N2 4 x2 x 2 aS + bSx = Sy ( = 2 aSx + bSxx Sxy N xi i =1 N xi y i 2 i i =1 f ( x) = Sy = 2 i a= = ) 1 N N yi i =1 = SSxx SxxSy SxSxy N i =1 f ( xi ) aSx + bSxx = Sxy ) 2 i (Sx )2 b= SSxy SxSy 2 2 pj = 2 i 2 pj yi a Sxx Sx xi = 2 yi i 2 a = rab = Sxx and Sx SSxx b Sxi Sx = 2 yi i 2 b = S N ( a + bxi i =1 = 2 2 y ,i + b2 yi ) 2 2 x ,i 2 y ,i + b2 2 x ,i = 1 wi N 2 a =0=2 N i =1 wi ( a + bxi yi ) a= i =1 wi ( y i bxi ) N i =1 wi 2 2 1 ( b2 b1 ) 2 ( b2 b1 ) 2 bmin = b2 2 (b2 ) 2 (b3 ) 2 (b2 ) 2 (b3 ) (b2 (b2 b3 ) b3 ) 2 2 2 2 (b2 ) (b2 ) 2 (b1 ) (b1 ) ...
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