12  Classificiation

A classifier is an algorithm that takes an input and returns a label, or class.

This section utilizes NumPy and Pyplot:

import numpy as np 
import matplotlib.pyplot as plt

Exercises

1. Find the parameters of the linear regression of the model \(\hat{Y}=\beta_0+\beta_1 X\) on the following data:

   \(x\)	-4	-1	0	2	3	5	6	7	9
   \(y\)	22	19	15	16	15	19	19	20	22

   Given the linear model \(\hat{Y}=\beta_0+\beta_1 X\) for the above data, find:

   1. The residual errors \(e_i = y_i - \hat{y}_i\)
   2. The sum of squared errors \(\sum_{i=1}^{n} e_{i}^{2}\)
   3. The mean-squared error \(\frac{1}{n}\sum_{i=1}^{n} e_{i}^{2}\)

   Plot the data and the linear model.

2. Repeat the above for a quadratic model \(\hat{Y}=\beta_0+\beta_1 X + \beta_2 X^2\).