Properties of the OLS estimator

Problem

Setup: a linear regression model with a random sample

\[y_i=β_1+β_2x_{i,2}+β_3x_{i,3}+ \ldots +β_kx_{i,k}+ε_i\]

1. Find an expression for RSS as a function of \(b_1,b_2,b_3\) .
2. Find the derivative of RSS with respect to \(b_1\)
3. Show that \(∑e_i=0\)
4. Find the derivative of RSS with respect to \(b_2\)
5. Show that \(∑e_ix_{i,2}=0\)