I would like to create a random dataset which allows me to conduct regression analyses as realistically as possible (e.g. for teaching, but also to test different models). The analyses I would like to conduct would be simple multivariable regression analyses, e.g.:
$ y = \beta_1 x_1 + \beta_2 x_2 \cdots $
The data should be 'random' enough to give realistic results, and ideally should not require a linear relationship (but for example splines).
What I am looking for is a method where I can specify the parameters (including error) of several regression models - and which then creates a dataset with $n$ samples which will give the precified results when using the same models.