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

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Andi 2022 年 8 月 14 日
コメント済み: Jeff Miller 2022 年 8 月 16 日
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);
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Jeff Miller 2022 年 8 月 15 日
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 2022 年 8 月 15 日
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.

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### 回答 (1 件)

Jeff Miller 2022 年 8 月 16 日

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
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Andi 2022 年 8 月 16 日
and how about the confidnecve interval.
Jeff Miller 2022 年 8 月 16 日
see edit

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