I have to solve the following issue:
- I run my linear regression model many times (let's say 1000 times) with two variables: y - continuous dependent variable, x - continuous independent variable (mean of several consequent measurements).
- The independent variable in each model was randomly drawn using its mean and standard deviation
- I have the regression coefficient and standard error for this independent variable in each of the models.
Somehow I have to combine these results into one regression result. As far as I know the regression coefficients of 1000 models can be just averaged. However, this is not really clear to me how can I estimate the total variance of 1000 models.