How can I fit curve to results of fit, including confidence interval

I use "fit" on several sets of data and obtain the coefficients and confidence intervals for each set. For example

data = repmat((1:100)',1,100) + rand(100); % each column of "data" is a data set, which will be fitted to a straight line

coeffs = zeros(100,2); % to store the slope and intercept of each straight line
intervals = zeros(200,2); % to store the confidence intervals of the slopes and intercepts

for n = 1:100
    linfit = fit((1:100)',data(:,n),'poly1'); % fit each column to a straight line
    coeffs(n,:) = coeffvalues(linfit);
    intervals(2*(n-1)+1:2*n,:) = confint(linfit);
end

Now, I want to fit the coefficients to a curve of choice, but the fit should account for the fact that the coefficients lie in the ranges given by "interval", rather than being the values stored in "coeffs". In other words, the above code gives 100 points, each with its own error bar. I want to fit a curve to these points including their error bars.

Any help appreciated. Thanks.