LinearFitErrorAnalysis

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ) ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online