how to find the error of a 2 column data set using repeated simpsons rule in matlab

main.m
% First, load your data set into 2 arrays, x and y
x = [1 2 3 4 5]; % example x array
y = [2 4 1 3 5]; % example y array

% Next, set up the initial parameters for the repeated Simpson's rule
a = x(1); % lower bound of integration
b = x(end); % upper bound of integration
n = length(x) - 1; % number of sub-intervals
h = (b - a) / (2 * n); % step size

% Repeat Simpson's rule to calculate the approximate integral value
approx = y(1) + y(end); % initialize approximate value
for i = 1:n
    approx = approx + 4 * y(2*i - 1) + 2 * y(2*i); % add odd and even terms
end
approx = approx * h / 3;

% Finally, calculate the error using the composite Simpson's rule error formula
error = ((b - a) / 180) * h^4 * max(abs(diff(y))) % using the first derivative of y for max value
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main.m
error = (b - a) / 180 * h^4 * max|f''(x)|,
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