When testing your code, I get the same CI when using plot(mdl) and when using predict.
x=rand(100,1);
y=rand(100,1);
mdl=fitlm(x,y,'VarNames',{'X','Y'});
figure ;
plot(mdl) ;
[ypred,yci]=predict(mdl,x);
hold on;
plot(x,yci,"ko","DisplayName","Predicted CI")
hold off;
But you can reproduce the same type of plot by an alternative way:
figure ;
plot(x,mdl.Fitted,"r-","LineWidth",2,"DisplayName","Fit") ;
[ypred,yci_curve]=predict(mdl,x,"Prediction","curve");
[~,yci_obs]=predict(mdl,x,"Prediction","observation");
hold on ;
plot(x,yci_curve,"r.","DisplayName","Confidence bounds") ;
plot(x,yci_obs,"ro","DisplayName","Prediction bounds") ;
hold off ;
legend ;
Here, I represented both confidence and prediction intervals, which have not the same values.
