How to get the weigths of factor from fit model
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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
adjrsquare: 0.4133
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',...
'AlphaDataMapping','direct',...
'SpecularExponent',5,...
'AlignVertexCenters','on',...
'LineWidth',1,...
'FaceAlpha',0.75,...
'FaceColor',[1 1 1],...
'EdgeAlpha',0.5,...
'EdgeColor','interp',...
'AlphaData',0.5);
% 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');
axis(axes1,'padded');
hold(axes1,'off');
% Set the remaining axes properties
set(axes1,'Colormap',...
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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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