How to determine if new data lies outside old prediction intervals

I have made a prediction model (using fit and predint) based on data in my table T. I know how to test if the existing data is outside the prediction interval, but I am unsure how to test new datapoints. I do not want to use the new data to make a new fit, I want to use the existing fit model and prediction intervals from the original data.

I am not sure how to generate a continuous function for the upper and lower interval.

Thanks.

load example_table.mat

T=sortrows(T,"Xdata");

x=T.Xdata;
y=T.Ydata;

fitresult = fit(x,y,'exp1');

pred = predint(fitresult,x,0.95);

plot(fitresult,x,y)
hold on
plot(x,pred,'m--')

legend({'Data','Fitted curve', 'Prediction intervals'},...
       'FontSize',8,'Location','northwest')

%% See which rows fall outside of interval
outside = (y < pred(:, 1)) | (y > pred(:, 2));
rows_outside_interval = T(outside, :)

rows_outside_interval = 2x4 table
            When            Data1    Xdata    Ydata 
    ____________________    _____    _____    ______

    29-Feb-2024 07:07:54    -1.5     367.5    30.803
    26-Feb-2024 21:05:07      18     389.4    9.4924

% Now I add a new row (that would fall outside), and want to test this against the existing
% prediction interval. Stuck here. 

ht=height(T);
T(ht+1,:)=T(1,:);
T(ht+1,"Xdata")={300};
T(ht+1,"Ydata")={25};
T(ht+1,:)

ans = 1x4 table
            When            Data1    Xdata    Ydata
    ____________________    _____    _____    _____

    03-May-2024 14:19:42     27       300      25  

[Tony]

One idea is to find the pair of x points in the prediction interval series where the new data x lies in-between, assume the prediction is interpolated linearly in that interval, find the y value of the prediction intervals via linear interpolation for the data x, and then compare with your data y

[Marcus Glover]

Thanks, that is a good idea. I'll look at that and I could even fit the prediction line series itself and see which is faster as I may have a lot of new data at times.