LRM: Interpretation of the OLS estimator

Problem

In the LRM,

  1. Explain why we must view the OLS estimator \(b_2\) as a random variable before we observe the sample.
  2. Explain why we must view the OLS estimator \(b_2\) as a constant after we observe the sample.

Solution

  1. Before the experiment, my data is unknown and must be viewed as random variables. Therefore, \(b_2\) must be viewed as a function of random variables making it a random variable.
  2. After the experiment, the data is known and \(b_2\) can be calculated. The actual value that we find for \(b_2\) is viewed as a drawing from the random variable described in part a.