Symbols in the LRM

Problem

In the LRM \(y_i=β_1+β_2x_i+ε_i\) we have 5 different symbols, \(y_i,x_i,ε_i,β_1,β_2\)

  1. What are the names of these 5 symbols?
  2. Which of them are observed by the econometrician and which are not?
  3. Which of them are modelled as random variables and which are not?

Solution

  1. Dependent variable, explanatory variable, error term, beta parameter 1, beta parameter 2
  2. Observed: \(y_i,x_i\) . Not observed: \(ε_i,β_1,β_2\)
  3. Random variables (before experiment): \(y_i,x_i,ε_i\) . Parameters: \(β_1,β_2\)