/sci/ - Science & Math

Can someone elaborate on resampling methods for me?

I don't quite understand how you can avoid running the risk of sampling bias if you make an inference based off a small sample that you resampled from. If you resample values randomly but the data you start with happens to have a mean far from the population mean, isn't any inference based off the simulation at risk of bias?

Suppose I have a data set consisting of panel data, and I want to make a regression model.

When deciding whether or not to pool the time variable, is it appropriate to just create a scatter plot and see if there's an apparent trend across time? Or should I conduct an analysis of variance test with time as the independent variable and see if it comes out with a sufficiently small p-value? Or is there a better way?

pic unrelated

Is it a common practice to use calculus or real analysis techniques on regression equations?

Like if you had a really strong regression with a low sum of squares, strong t-stat for all coefficients, etc., would it be acceptable to make inferences about the system that regression describes using more deterministic math? Is that something people do?