# How to get the weigths of factor from fit model

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Alex Milns on 16 Aug 2022
Edited: Alex Milns on 16 Aug 2022
Hi! Dear community members, I have a specific question related to fitting experimental data.
For example I get the surf fit model
[sf,gof] = fit([I, Ton],Ah,'poly22','Normalize', 'on', ...
'Robust', 'Bisquare')
% Get data into fitted surface for create result graph
hPlot = plot(sf);
X = get(hPlot,'XData');
Y = get(hPlot,'YData');
Z = get(hPlot,'ZData');
set(gcf,'visible','off')
%Create figure for fitted polynomial model
createfigure1(X,Y,Z,I,Ton,Ah)
Linear model Poly22:
sf(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2
where x is normalized by mean 3 and std 1.732
and where y is normalized by mean 40 and std 17.32
Coefficients (with 95% confidence bounds):
p00 = 73.63 (16.64, 130.6)
p10 = 23.25 (-3.79, 50.28)
p01 = 7.638 (-19.4, 34.67)
p20 = -19.04 (-59.59, 21.52)
p11 = 3.776 (-24.9, 32.45)
p02 = -7.146 (-47.7, 33.41)
gof =
struct with fields:
sse: 1.7321e+03
rsquare: 0.7800
dfe: 3
rmse: 24.0283
My question is: how can one get an estimate of which term (x or y) has the most influence on the final fitting function... And how can one analytically obtain the function for a biharmonic v4 fitting?
Code of fucntion createfigure1() and initial data attach below:
function createfigure1(xdata1, ydata1, zdata1, XData2, YData2, ZData2)
%CREATEFIGURE1(xdata1, ydata1, zdata1, XData2, YData2, ZData2)
% XDATA1: surface xdata
% YDATA1: surface ydata
% ZDATA1: surface zdata
% XDATA2: line xdata
% YDATA2: line ydata
% ZDATA2: line zdata
% Auto-generated by MATLAB on 02-Jun-2022 21:55:49
% Create figure
figure1 = figure;
colormap(gray);
% Create axes
axes1 = axes('Parent',figure1);
hold(axes1,'on');
% Create surf
surf(xdata1,ydata1,zdata1,'DisplayName','Fit Result','PickableParts','none',...
'Tag','curvefit.gui.FunctionSurface',...
'Parent',axes1,...
'EdgeLighting','flat',...
'SpecularExponent',5,...
'AlignVertexCenters','on',...
'LineWidth',1,...
'FaceAlpha',0.75,...
'FaceColor',[1 1 1],...
'EdgeAlpha',0.5,...
'EdgeColor','interp',...
% Create line
line(XData2,YData2,ZData2,'DisplayName','Experimental','Parent',axes1,...
'MarkerFaceColor',[1 0 0],...
'MarkerEdgeColor',[1 1 1],...
'MarkerSize',8,...
'Marker','o',...
'LineStyle','none',...
'Color',[0.466666666666667 0.674509803921569 0.188235294117647]);
% Create zlabel
zlabel('\$A_{l}\$','FontSize',14,'Interpreter','latex','Rotation',0);
% Create ylabel
ylabel('\$T_{p}\$','FontSize',14,'FontName','Times New Roman',...
'Interpreter','latex');
% Create xlabel
xlabel('I.','FontSize',14,'FontName','Times New Roman',...
'Rotation',28);
% Create title
title('\$ A_{l} = f(I, T_{p}) \$','FontSize',14,'FontName','Times New Roman',...
'Interpreter','latex');
view(axes1,[-57.561079176767 23.2221402047369]);
grid(axes1,'on');
hold(axes1,'off');
% Set the remaining axes properties
set(axes1,'Colormap',...
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0.2528;0.62233 0.99366 0.24579;0.63323 0.99195 0.23937;0.64362 0.98999 0.23356;0.65394 0.98775 0.22835;0.66428 0.98524 0.2237;0.67462 0.98246 0.2196;0.68494 0.97941 0.21602;0.69525 0.9761 0.21294;0.70553 0.97255 0.21032;0.71577 0.96875 0.20815;0.72596 0.9647 0.2064;0.7361 0.96043 0.20504;0.74617 0.95593 0.20406;0.75617 0.95121 0.20343;0.76608 0.94627 0.20311;0.77591 0.94113 0.2031;0.78563 0.93579 0.20336;0.79524 0.93025 0.20386;0.80473 0.92452 0.20459;0.8141 0.91861 0.20552;0.82333 0.91253 0.20663;0.83241 0.90627 0.20788;0.84133 0.89986 0.20926;0.8501 0.89328 0.21074;0.85868 0.88655 0.2123;0.86709 0.87968 0.21391;0.8753 0.87267 0.21555;0.88331 0.86553 0.21719;0.89112 0.85826 0.2188;0.8987 0.85087 0.22038;0.90605 0.84337 0.22188;0.91317 0.83576 0.22328;0.92004 0.82806 0.22456;0.92666 0.82025 0.2257;0.93301 0.81236 0.22667;0.93909 0.80439 0.22744;0.94489 0.79634 0.228;0.95039 0.78823 0.22831;0.9556 0.78005 0.22836;0.96049 0.77181 0.22811;0.96507 0.76352 0.22754;0.96931 0.75519 0.22663;0.97323 0.74682 0.22536;0.97679 0.73842 0.22369;0.98 0.73 0.22161;0.98289 0.7214 0.21918;0.98549 0.7125 0.2165;0.98781 0.7033 0.21358;0.98986 0.69382 0.21043;0.99163 0.68408 0.20706;0.99314 0.67408 0.20348;0.99438 0.66386 0.19971;0.99535 0.65341 0.19577;0.99607 0.64277 0.19165;0.99654 0.63193 0.18738;0.99675 0.62093 0.18297;0.99672 0.60977 0.17842;0.99644 0.59846 0.17376;0.99593 0.58703 0.16899;0.99517 0.57549 0.16412;0.99419 0.56386 0.15918;0.99297 0.55214 0.15417;0.99153 0.54036 0.1491;0.98987 0.52854 0.14398;0.98799 0.51667 0.13883;0.9859 0.50479 0.13367;0.9836 0.49291 0.12849;0.98108 0.48104 0.12332;0.97837 0.4692 0.11817;0.97545 0.4574 0.11305;0.97234 0.44565 0.10797;0.96904 0.43399 0.10294;0.96555 0.42241 0.09798;0.96187 0.41093 0.0931;0.95801 0.39958 0.08831;0.95398 0.38836 0.08362;0.94977 0.37729 0.07905;0.94538 0.36638 0.07461;0.94084 0.35566 0.07031;0.93612 0.34513 0.06616;0.93125 0.33482 0.06218;0.92623 0.32473 0.05837;0.92105 0.31489 0.05475;0.91572 0.3053 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0.00705;0.51989 0.02756 0.0078;0.50664 0.02354 0.00863;0.49321 0.01963 0.00955;0.4796 0.01583 0.01055],...
'GridAlpha',0.5,'GridColor',...
[0.501960784313725 0.501960784313725 0.501960784313725],'MinorGridAlpha',...
0.35,'MinorGridColor',...
[0.501960784313725 0.501960784313725 0.501960784313725],...
'TickLabelInterpreter','latex','XColor',...
[0 0.447058823529412 0.741176470588235],'XMinorGrid','on','XMinorTick','on',...
'YColor',[1 0.411764705882353 0.16078431372549],'YMinorGrid','on',...
'YMinorTick','on','ZColor',[0 0.549019607843137 0.137254901960784],...
'ZMinorGrid','on','ZMinorTick','on');
% Create colorbar
colorbar(axes1);

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