Considering the following senario:

We want to user linear regression to find the relationship between two variables x and y. Since we can't access the population, we need to use some sampling method to sample some data and make the regression. Let's say the true slope of the linear relationship between x and y is 5.

Now consider we have two sampling methods, one is good and the other is bad. Using the good sampling method, the slopes computed with different group of samples are all around 5 so the standard error of coefficient is low. Using the bad sampling method, the sploes are way from 5, and their deviation is high so the standard error of coefficient is high. In this senario, a lower standard error stands for a better sampling method and a reliable coefficient.

What if we have a third (bad) sampling method? With this method, the sploes are way from 5 too but their deviation is small. Let's say the slopes are all around -5. In this case, the standard deviation of the coefficient is also small, but the corresponding method is not good and the coefficient is not reliable. So my question is will this situation affect our interpretation of the standard error of coefficient? Why and why not?

  • $\begingroup$ This situation appears to be implausible or even impossible. How do you know the third method is bad? And if you know that, why do you need to ask whether that knowledge will affect your interpretation? $\endgroup$ – whuber Dec 7 '19 at 18:34

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