How to compute the slop of bootstrap population with its confidence interval?

Hi everyone,

I read through all the documentions and avaible function of Bootsrap in matlab most of them compute the mean or correlation of each iteration. However, i need to compute the slop of bootstrap population. For example:

My data set consist of around 50 observations, i like to randomly pick 100 observations with replacmenet for 2000 bootstrap iterations. For each iteration, i require to compute the slop and eventually, i will get 2000 slop observations. Then i need to compute the 95% confidence interval of these observations.

May someone suggets me how i can do this:

Here is a simpel start:

A = [0.045494, 0.065669, 0.073061, 0.104542, 0.296978, 0.498353, 0.503342... 
    0.515458, 0.660300, 0.663664, 0.677255, 0.724817, 0.805800, 0.899355... 
    0.987775, 2.121619, 2.165055, 2.196833, 3.265653, 3.479858, 8.702472 ...
    10.070092, 10.720080, 12.896169, 12.912647, 14.24436,1 14.287428, 17.337397, 18.903783, 20.940314, 21.404639, 22.234169]
% A is the data
m = bootstrp(100,@mean,A);

[Jeff Miller]

I think we need a bit more information about what you are trying to do.

First, what do you mean by slope (e.g., how would you compute the slope just for the single sample A that you show)? To compute a slope requires (X,Y) pairs, but you only seem to be using a single variable (values of A).

Second, your values of A are sorted from largest to smallest. Is that important for your analysis? If you take random bootstrap samples from A, the sample values will be in random order.

[Andi]

For slope, we use number of observations as X and Y is the bootstrap population. For example, if we set bootstrap population 30 then the x is 1, 2, 3... 30,

Regarding the second, point, I think it be good for me to test both approaches, and see how it effect my analysis.

Answer 1

[Jeff Miller]

It sounds like this is what you are after, although I'm not sure why you want to do it:

m = bootstrp(100,@mySlope,A);
LowerCI = prctile(m,2.5);  % lower / upper bounds for 95% conf interval
UpperCI = prctile(m,97.5);

function slope = mySlope(Yvals)
    Xvals = 1:numel(Yvals);
    P = polyfit(Xvals,Yvals,1);
    slope = P(1);
end

[Andi]

and how about the confidnecve interval.

[Jeff Miller]

see edit