steepest and shallowest linear fits of error-affected y data

steepest and shallowest linear fits of error-affected y data

The title pretty much says what Id like to do. I belief theres no built-in method in matlab to do so. Actually this is really easy to do by hand but I couldnt figure out an algorithm to mimic this. My compromise solution is the following: x1;2;3;4;5;6;7;8;9;10; y10;9;8.5;7.8;7.5;7;6.6;6.0;5;5.0; err0.5;1.0;0.8;0.6;1.0;0.8;1.2;0.9;0.5;0.5; errorbarx,y,err,.; hold on; maxgrady; maxgradx; maxgrade; mingrady; mingradx; mingrade; m0; nlengthy; if remn,20 mn2; else mn-12; end for k1:m maxgradykykerrk; maxgradxkxk; maxgradekerrk; mingradykyk-errk; mingradxkxk; mingradekerrk; end r0; for kn-m1:n if remn,20 rk; else rk-1; end maxgradyryk-errk; maxgradxrxk; maxgradererrk; mingradyrykerrk; mingradxrxk; mingradererrk; end ft fittype axb, independent, x, dependent, y ; opts fitoptions Method, NonlinearLeastSquares ; wtmaxerr-err; opts.Weights wt; opts.StartPointx1 y1; fitmed, gof fit x, y, ft, opts; hmed plotfitmed,-k; max opts.Weightsmaxgrade; opts.StartPointmaxgradx1 maxgrady1; fitmaxfitmaxgradx,maxgrady,ft,opts; hmaxplotfitmax; Min opts.Weightsmingrade; opts.StartPointmingradx1 mingrady1; fitminfitmingradx,mingrady,ft,opts; hminplotfitmin; Im not happy with that. I couldve done better manually. BTW, Ive searched the web and to my surprise I couldnt find an algorithm to do this even though this is a very common erorr-analysis method. Any ideas EDIT: My 2nd attempt x1;2;3;4;5;6;7;8;9;10; y9.8;9;8.5;7.8;7.5;7;6.6;6.0;5.5;5.0; err0.8;1.0;0.8;0.6;1.0;0.8;1.2;0.9;0.5;0.5;; w1.err; f0fitlmx,y,linear,weight,w; y0f0.Coefficients.Estimate1; s0f0.Coefficients.Estimate2; cicoefCIf0; y0_maxci1,1 s_maxci2,1 y0_minci1,2; s_minci2,2; yfity0xs0; yfitmaxy0_maxxs_max; yfitminy0_minxs_min; errherrorbarx,y,err,o; hold on; plotx,yfit,-k; plotx,yfitmax,-r; plotx,yfitmin,-b; Dont like it...I can see with my bare eyes that theres a steeper possible fit... With this example-data I could just use the 1st and last data-points...but notice that this is not always possible