Confidence interval for slope and intersect using bootstrapping

Hi!

I have 2 variables with some NaNs. I use bootstrapping to get the slope and intersect from a linear regression:

good = isnan(var1) + isnan(var2);  

p_bootstrp = bootstrp(1000, 'polyfit',var1(good == 0),var2(good == 0),1); 

med_slope = median(p_bootstrp(:,1));       % The slope
med_intersect = median(p_bootstrp(:,2));   % The intersect

But, I cannot figure out how to get the confidence intervals for this using bootci. I thought that I could use bootci the same way as when getting a confidence interval for the corelation coefficient but that doesn't work.

ci_slope = bootci(5000, @polyfit, var1(good == 0), var2(good == 0));

How do I calculate the confindence interval for linear regression using bootstrapping? Is there a Matlab function to do it?

Thanks,

Emma

[Aidan Starr]

Hi Emma,

Not sure if I'm missing something, but looks like you just need to include the order for polyfit to work.

ie:

ci_slope = bootci(5000, @polyfit, var1(good == 0), var2(good == 0),1);

Hope this helps, Aidan

Answer 1

[OCDER]

I believe it's just the percentile itself for bootstraps. If you get 1000 bootstrapped sample and results, then take the top 2.5% for the upper bound, bottom 2.5% for the lower bound, and you get your 95% CI.

 %  95% CI means 2.5% bottom and top
 LowerCI = prctile(p_bootstrp, 2.5,  1); Lower Slope, Lower Intersect
 UpperCI = prctile(p_bootstrp, 97.5, 1); Upper Slope, Lower Intersect

 To get an exact CI, you need to find the actual values and recompute the CI (just more details)

See Page 5

https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf