I want to compare few methods of variable selection. I want to do it using simulations. I'm aware of the fact that it won't be an ultimate answer to question 'Which method is the best one?', but I'm looking just form some hint. To do such simulations I need a method to draw a 'random linear model'. Is there any well accepted algorithm of drawing 'random linear model'? By well accepted I mean method that was used for example in some scientific paper.
I was thinking about following simple approach:
1) Choose $n$ and $k$, which denotes number of observations and number of variables.
2) Generate random matrix $X$ by drawing each element using uniform distribution $(0,1)$.
3) Generate parameters using uniform distribution $(0,1)$.
4) Generate residuals using Normal Distribution $(0,\sigma^2)$ for some fixed and arbitrary chosen $\sigma^2$
5) Calculate $Y=X\beta + \epsilon$