Plotting confidence band based on a subset result from fitlm

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kg wong 2020-1-14

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https://ww2.mathworks.cn/matlabcentral/answers/500307-plotting-confidence-band-based-on-a-subset-result-from-fitlm

编辑： kg wong 2020-1-14

Here there,

I was using regress to perform regress on given data but I am looking for a way to plot the confidence level band as well. I search the forum, someone recommend me to use fitlm and predict function. The model I am dealing with include a cross term. I search the MATLAB example and found something similar

load carsmall
X = [Acceleration,Weight];
T = [0 0 0;1 0 0;0 1 0;1 1 0;0 2 0];
mdl = fitlm(X,MPG,T);
% model : Y = a0 + a1*acceleration + a2*weight + a3*acceleration*weight + a4*weight^2
a0 = mdl.Coefficients.Estimate(1);
a1 = mdl.Coefficients.Estimate(2);
a2 = mdl.Coefficients.Estimate(3);
a3 = mdl.Coefficients.Estimate(4);
a4 = mdl.Coefficients.Estimate(5);
N = 200;
newAcc = linspace(min(Acceleration), max(Acceleration),N).';
newW = linspace(min(Weight), max(Weight),N).';
Xn = [newAcc, newW];
Y = a0 + a1*newAcc + a2*newW + a3*newAcc.*newW + a4*newW.^2;

In some threads, someone suggests to use predict to return the confidence level like

% Xn here is the new X input to find the fitted Y
[Yn, cil] = predict(mdl, Xn);

In the page https://www.mathworks.com/help/stats/linearmodel.predict.html, cil is called predict CIs band, is it the same as confidence levels band? I am sure sure if I remember it correctly but I read somewhere predict CIs is different from CIs?

Anyway, here predict estimates the CIs band for model between Y and X but that is not what I am looking for. In my case, I only care the cross term and the corresponding coefficient such that I need to plot the linear relation F = a3*acceleration (ignore weight). That is to say, I use the Y,X model to estimate all coefficients and find the linear relation about acceleration on the cross term. I wonder in this case, how should I compute and plot the CI band on F. Thanks.