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Line of best fit issues

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CAM
CAM 2016-5-12
评论： CAM 2016-5-12
I'm trying to do a line of best fit for an inverse power law, but all that's happening is I get various straight lines, no matter how I modify the initial conditions. What am I doing wrong here?
The data set is:
xdata1 = [0.04693787, 0.04950828, 0.055079095, 0.05966484, 0.06726917, 0.07483848,...
0.08550887, 0.09262812, 0.10443364, 0.11312852, 0.12925825, 0.14189875,...
0.15786561, 0.17330371, 0.19025153, 0.21165918, 0.23235789, 0.2654872,...
0.2993237, 0.34658992, 0.39076304, 0.423297, 0.4524684, 0.4967165, ...
0.5380719, 0.5675377, 0.6398708, 0.69314486, 0.7508544, 0.79197264, ...
0.8810876, 0.9802301, 1.1350182, 1.229517, 1.2968477, 1.4817507, ...
1.693017, 1.9087932, 2.123576, 2.426353, 2.628365, 2.847196, 3.1256309, ...
3.3410332, 3.8686156, 4.1907067, 4.5396147, 4.9175715, 5.3984737, 5.7705083,...
6.2509465,6.593261, 7.335153, 7.6344023, 8.38099, 8.958565, 9.834646, 10.796403, ...
11.387635, 12.501262, 13.542086, 14.669565, 15.268034, 16.320227, 17.444931, ...
18.156626, 19.932209, 19.932209, 22.175037, 23.079704, 24.670237, 27.082804, ...
29.731304, 32.206657, 33.520576, 34.888103, 35.830643, 39.334614, 42.045353,...
45.54594];
ydata1 = [469.75888,399.54205,358.66376,289.0264,220.6734,177.82794,143.30125,...
109.411385,93.057205,74.98942,67.31704,48.69675,46.138397,37.180267,29.961428,...
22.875732,19.4564,14.855081,12.634629,9.139817,7.77365,6.61169,5.327979,4.7828584,...
3.854229,3.4598916,2.7881267,2.2467902,1.9109529,1.5399265,1.3097472,0.9474635,...
0.80584216,0.64938164,0.55231583,0.4216965,0.33982083,0.24582441,0.17782794,...
0.14330126,0.103663296,0.08816831,0.07104974,0.048696753,0.0392419,0.026895989,...
0.022875732,0.015678788,0.011970851,0.008659643,0.005048066,0.003854229,0.002788127,...
0.00224679,0.001382372,9.47E-04,7.23E-04,4.70E-04,3.22E-04,2.21E-04,1.88E-04,...
1.51E-04,1.09E-04,8.35E-05,6.04E-05,5.14E-05,3.92E-05,3.52E-05,2.84E-05,...
2.17E-05,1.33E-05,9.65E-06,6.98E-06,5.33E-06,4.29E-06,3.85E-06,2.50E-06,...
1.91E-06,1.63E-06,1.18E-06];
And the main code is: clc clear all %All three below simply call the data files which we are to use. ElectronData; % here we define the function f1 = @(b,x) 1./(b(1).*(x).^b(2)+b(3).*(x).^b(4)+b(5).*(x).^b(6));
xdc1 = linspace(min(xdata1), max(xdata1), 150);% Continuous ‘xdata’ for each
b0 = [1; 1; 1; 1; 1; 1];%initial estimate vectors
B1 = nlinfit(xdata1, ydata1, f1, b0);%non-linear regression
%below, we're simply graphing the thing
figure(1)
loglog(xdata1, ydata1, 'bp') %ElectronData
hold on
loglog(xdc1, f1(B1,xdc1))%Best fit for Electrons
hold off
grid
%and now for the titles and lables
title('Low and High Energy Cosmic Ray Spectra')
xlabel('KE')
ylabel('Flux')
legend('Helium Data', 'Electron Data', 'Proton Data', 'Location','Southwest')
  1 个评论
CAM
CAM 2016-5-12
I should also note that loglog is necessary to properly view the data. If you do a normal plot, given the range of the data, it doesn't display correctly!

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