It is relatively straightforward when I want to know about the coefficients, fitted values, residuals and residual standard error of my (ordinary least squares) regression models, especially if you use R. However, when I use non-parametric bootstrap to estimate these statistics by resampling, for example, 5000 times, I then obtain 5000 estimates per coefficient, 5000 estimates per fitted value, 5000 per residual and 5000 residual standard error estimates. What is the best way for each statistic to summarize to a single estimate (resp. per coefficient, per fitted value, per residual and a single residual standard error)? The first things that comes to mind is using the mean or the median, but is it that straightforward?

Thanks a bunch!

P.s. I would like to ask the community to make a label for fitted values, since I am quite to this forum and thus unable to this myself. Thanks!

  • $\begingroup$ Could you give the reason(s) that you used bootstrap to get the estimate, instead of ordinary least square method? $\endgroup$ – user158565 Jul 10 '19 at 3:14
  • $\begingroup$ Sure! I am subsetting my dataset; where I, with my full dataset, get normality of my residuals, I quite often do not get that with my subsets. Together with other issues, like skewness, heavy-tailedness, outliers and heteroscedasticity. The ultimate aim is to forecast with the regression equations. I want, therefore, reliable estimates and decided to use non-parametric bootstrap in the cases as described above. $\endgroup$ – Derk Jul 10 '19 at 17:03

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