Re: linear regression with errors in both variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg96324] Re: linear regression with errors in both variables*From*: dh <dh at metrohm.com>*Date*: Wed, 11 Feb 2009 05:24:15 -0500 (EST)*References*: <gmrmga$a1k$1@smc.vnet.net>

Hi Joerg, this is an addendum to my former message for the case where the x and y axis have different scales. The following example assumes that the error in the y axis is 100 times that of the x axis. sx and sy denote the standard deviations. a anb be define again the line: y==a+b x. res denotes the weighted sum of squares of distances. The metric is taken as: {{1/sx^2,0},{0,1/sy^2}} d = Table[{RandomReal[], 100 RandomReal[]}, {4}]; sx = 1; sy = 100; res[a_, b_] = Module[{perp, met = {{1/sx^2, 0}, {0, 1/sy^2}}}, perp = {b sx^2, -sy^2}; perp = perp/Sqrt[perp.met.perp]; Plus @@ (perp.met.(# + {a/b, 0}) & /@ d)^2]; sol = Minimize[res[a, b], {a, b}] fun[x_] = a + b x /. sol[[2]] Plot[fun[x], {x, 0, 1}, Epilog -> {Red, Point[d]}, PlotRange -> ({0.95 Min @@ #, 1.05 Max @@ #} & /@ Transpose[d])] hope this helps, Daniel Joerg wrote: > Hi, > > I want to test the hypothesis that my data > follows a known simple linear relationship, > y = a + bx. However, I have (known) measurements > errors in both the y and the x values. > > I suppose just a simple linear regression > does not do here. > > Any suggestions how do test this correctly? > > Thanks, > > joerg >