UDL Chapter 6 Problems

Problem 6.1

Show that the derivates of the least squares loss function in equation 6.5 are given by the equations in 6.7.

Each loss component:

$${\ell }_i=({\varphi }_0+{\varphi }_1{x}_i-y_i{)}^2$$

Derivatives:

$$\frac{\partial {\ell }_i}{\partial {\varphi }_0}=2({\varphi }_0+{\varphi }_1{x}_i-y_i)$$ $$\frac{\partial {\ell }_i}{\partial {\varphi }_1}=2({\varphi }_0+{\varphi }_1{x}_i-y_i)(x_i)$$

Problem 6.2

Problem 6.3

Problem 6.4

Problem 6.5

Problem 6.6

Problem 6.7

Problem 6.8

Problem 6.9

Problem 6.10

Problem 6.11