Problem: A few observations on the OLS formula

Problem

1. Prove that if \(y_i=c\) for all \(i\) ( \(y\) is constant) then \(b_2=0\) and \(b_1=c\) .
2. Prove that if \(x_i=c\) for all \(i\) ( \(x\) is constant) then \(b_2\) cannot be calculated.
3. Prove that the point \(\left( \bar{x},\bar{y} \right)\) lies on the OLS trendline.