如何从 matlab 中的拟合 model 中获取因子的权重？

Question

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? In other words, get the weight for the term x or y? In my case x = I, Y = Ton, Z = Ah.

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


% 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',...
    [0.18995 0.07176 0.23217;0.19483 0.08339 0.26149;0.19956 0.09498 0.29024;0.20415 0.10652 0.31844;0.2086 0.11802 0.34607;0.21291 0.12947 0.37314;0.21708 0.14087 0.39964;0.22111 0.15223 0.42558;0.225 0.16354 0.45096;0.22875 0.17481 0.47578;0.23236 0.18603 0.50004;0.23582 0.1972 0.52373;0.23915 0.20833 0.54686;0.24234 0.21941 0.56942;0.24539 0.23044 0.59142;0.2483 0.24143 0.61286;0.25107 0.25237 0.63374;0.25369 0.26327 0.65406;0.25618 0.27412 0.67381;0.25853 0.28492 0.693;0.26074 0.29568 0.71162;0.2628 0.30639 0.72968;0.26473 0.31706 0.74718;0.26652 0.32768 0.76412;0.26816 0.33825 0.7805;0.26967 0.34878 0.79631;0.27103 0.35926 0.81156;0.27226 0.3697 0.82624;0.27334 0.38008 0.84037;0.27429 0.39043 0.85393;0.27509 0.40072 0.86692;0.27576 0.41097 0.87936;0.27628 0.42118 0.89123;0.27667 0.43134 0.90254;0.27691 0.44145 0.91328;0.27701 0.45152 0.92347;0.27698 0.46153 0.93309;0.2768 0.47151 0.94214;0.27648 0.48144 0.95064;0.27603 0.49132 0.95857;0.27543 0.50115 0.96594;0.27469 0.51094 0.97275;0.27381 0.52069 0.97899;0.27273 0.5304 0.98461;0.27106 0.54015 0.9893;0.26878 0.54995 0.99303;0.26592 0.55979 0.99583;0.26252 0.56967 0.99773;0.25862 0.57958 0.99876;0.25425 0.5895 0.99896;0.24946 0.59943 0.99835;0.24427 0.60937 0.99697;0.23874 0.61931 0.99485;0.23288 0.62923 0.99202;0.22676 0.63913 0.98851;0.22039 0.64901 0.98436;0.21382 0.65886 0.97959;0.20708 0.66866 0.97423;0.20021 0.67842 0.96833;0.19326 0.68812 0.9619;0.18625 0.69775 0.95498;0.17923 0.70732 0.94761;0.17223 0.7168 0.93981;0.16529 0.7262 0.93161;0.15844 0.73551 0.92305;0.15173 0.74472 0.91416;0.14519 0.75381 0.90496;0.13886 0.76279 0.8955;0.13278 0.77165 0.8858;0.12698 0.78037 0.8759;0.12151 0.78896 0.86581;0.11639 0.7974 0.85559;0.11167 0.80569 0.84525;0.10738 0.81381 0.83484;0.10357 0.82177 0.82437;0.10026 0.82955 0.81389;0.0975 0.83714 0.80342;0.09532 0.84455 0.79299;0.09377 0.85175 0.78264;0.09287 0.85875 0.7724;0.09267 0.86554 0.7623;0.0932 0.87211 0.75237;0.09451 0.87844 0.74265;0.09662 0.88454 0.73316;0.09958 0.8904 0.72393;0.10342 0.896 0.715;0.10815 0.90142 0.70599;0.11374 0.90673 0.69651;0.12014 0.91193 0.6866;0.12733 0.91701 0.67627;0.13526 0.92197 0.66556;0.14391 0.9268 0.65448;0.15323 0.93151 0.64308;0.16319 0.93609 0.63137;0.17377 0.94053 0.61938;0.18491 0.94484 0.60713;0.19659 0.94901 0.59466;0.20877 0.95304 0.58199;0.22142 0.95692 0.56914;0.23449 0.96065 0.55614;0.24797 0.96423 0.54303;0.2618 0.96765 0.52981;0.27597 0.97092 0.51653;0.29042 0.97403 0.50321;0.30513 0.97697 0.48987;0.32006 0.97974 0.47654;0.33517 0.98234 0.46325;0.35043 0.98477 0.45002;0.36581 0.98702 0.43688;0.38127 0.98909 0.42386;0.39678 0.99098 0.41098;0.41229 0.99268 0.39826;0.42778 0.99419 0.38575;0.44321 0.99551 0.37345;0.45854 0.99663 0.3614;0.47375 0.99755 0.34963;0.48879 0.99828 0.33816;0.50362 0.99879 0.32701;0.51822 0.9991 0.31622;0.53255 0.99919 0.30581;0.54658 0.99907 0.29581;0.56026 0.99873 0.28623;0.57357 0.99817 0.27712;0.58646 0.99739 0.26849;0.59891 0.99638 0.26038;0.61088 0.99514 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 0.05134;0.91024 0.29599 0.04814;0.90463 0.28696 0.04516;0.89888 0.27824 0.04243;0.89298 0.26981 0.03993;0.88691 0.26152 0.03753;0.88066 0.25334 0.03521;0.87422 0.24526 0.03297;0.8676 0.2373 0.03082;0.86079 0.22945 0.02875;0.8538 0.2217 0.02677;0.84662 0.21407 0.02487;0.83926 0.20654 0.02305;0.83172 0.19912 0.02131;0.82399 0.19182 0.01966;0.81608 0.18462 0.01809;0.80799 0.17753 0.0166;0.79971 0.17055 0.0152;0.79125 0.16368 0.01387;0.7826 0.15693 0.01264;0.77377 0.15028 0.01148;0.76476 0.14374 0.01041;0.75556 0.13731 0.00942;0.74617 0.13098 0.00851;0.73661 0.12477 0.00769;0.72686 0.11867 0.00695;0.71692 0.11268 0.00629;0.7068 0.1068 0.00571;0.6965 0.10102 0.00522;0.68602 0.09536 0.00481;0.67535 0.0898 0.00449;0.66449 0.08436 0.00424;0.65345 0.07902 0.00408;0.64223 0.0738 0.00401;0.63082 0.06868 0.00401;0.61923 0.06367 0.0041;0.60746 0.05878 0.00427;0.5955 0.05399 0.00453;0.58336 0.04931 0.00486;0.57103 0.04474 0.00529;0.55852 0.04028 0.00579;0.54583 0.03593 0.00638;0.53295 0.03169 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);

Data for fitting:

Ah = 15.0000 13.5000 16.7000 57.2000 57.8000 86.7000 42.8000 100.0000 64.0000
I =   1     1     1     3     3     3     5     5     5
Ton = 20    40    60    20    40    60    20    40    60