Problem: Derivative of RSS
Problem
Do this problem without checking any notes.
\[RSS=f\left( b_1,b_2 \right)=\sum_{i=1}^{n}{ {\left( y_i-b_1-b_2x_i \right)}^2 }\]
Find
\[ \frac{∂f}{∂b_1}\]
and
\[ \frac{∂f}{∂b_2}\]
Solution
\[ \frac{∂f}{∂b_1}=\sum_{i=1}^{n}{ -2\left( y_i-b_1-b_2x_i \right) }\]
\[ \frac{∂f}{∂b_2}=\sum_{i=1}^{n}{ -2x_i\left( y_i-b_1-b_2x_i \right) }\]