LinearModelFit vs. Fit with low precision/accuracy data

*To*: mathgroup at smc.vnet.net*Subject*: [mg99438] LinearModelFit vs. Fit with low precision/accuracy data*From*: andreas.kohlmajer at gmx.de*Date*: Tue, 5 May 2009 06:03:41 -0400 (EDT)

Hi all! I have some difficulties to understand the difference between LinearModelFit and Fit with my low precision/accuracy data. I have 3 different flow curves {flow [m=B3/h], back pressure [mbar]}: data = { {{33.1, 0.19}, {37.5, 0.15}, {255.9, 4.79}, {390.8, 9.88}, {439.4, 11.93}, {481, 13.77}, {558, 17.39}, {574.2, 18.15}, {601.3, 19.5}, {665.4, 22.74}, {711.3, 25.26}, {726, 26.06}, {745, 27.08}, {789.2, 29.39}, {798.4, 30.11}, {811.9, 30.7}, {825.8, 31.74}, {847.6, 33.12}, {851.3, 33.34}}, {{12.5, 0.06}, {37.5, 0.5}, {82, 1.18}, {100.8, 1.47}, {172.3, 2.91}, {247.2, 5.11}, {257.8, 5.43}, {279.6, 6.13}, {353, 8.73}, {433.5, 11.82}, {443.6, 11.82}, {545, 16.41}, {636.8, 20.72}, {710.2, 24.03}, {814.6, 30.82}, {853.3, 32.95}, {924.6, 38.44}}, {{12.5, 0.05}, {17.7, 0.06}, {65, 1.08}, {115.9, 1.03}, {127.5, 2.49}, {266.7, 4.85}, {282.1, 5.51}, {309.1, 6.2}, {369.2, 8.52}, {373.8, 8.71}, {395.4, 9.49}, {418.1, 10.28}, {445.6, 11.37}, {489.7, 13.15}, {494.9, 13.34}, {522, 14.25}, {539.4, 15.25}, {606.5, 17.88}, {615.1, 18.65}, {677.5, 21.52}, {689, 21.52}, {768.8, 26.41}, {838.1, 30.56}, {877.1, 33.07}, {943.7, 37.58}} }; The data is quite inaccurate, so I specified two different accuracies for flow (whole digit) and back pressure (1 decimal): data[[All, All, 1]] = SetAccuracy[data[[All, All, 1]], 1]; data[[All, All, 2]] = SetAccuracy[data[[All, All, 2]], 2]; The model is a simple parabola: model = {x, x^2}; The linear model fit is: lm = LinearModelFit[#, model, x] & /@ data The regular fit is: ft = Fit[#, model, x] & /@ data The linear model fit returns a low precision/accuracy constant, whereas the regular fit returns a parabola fit with no valid digit for any of the coefficients. Of course, the data is too inaccurate to calculate a sufficient fit, but why do I see this difference between LinearModelFit and Fit?

**Follow-Ups**:**Re: LinearModelFit vs. Fit with low precision/accuracy***From:*Darren Glosemeyer <darreng@wolfram.com>