I am doing a simulation study on a simple linear regression model to see how well OLS estimator performs. I am planning to use coverage probability to assess the estimation of slope parameter using 1000 replications with sample size of 100
Suppose the model is simple as $y_i=0.5+2*x_i+\epsilon_i$
I am not sure which of the following two options to choose in simulation.
- simulate all 100 $x_i$ values, say from a normal distribution. Then in each of the 1000 replications, use the same 100 $x_i$ values for generation of $y_i$.
- In each of 1000 replications, first simulate 100 $x_i$ values, and based on these covariate values, generate $y_i$.
Any help is appreciated.