This question is on linear regression. (i) Give the formula for a multivariate linear regressor with a 3rd degree polynomial and 2 variables, assuming that there are no relations between the two variables [2 marks].

(ii) See the data in the table below of paired values x1 and x2. The goal is predicting x2 from x1. Name the type of linear regressor that should be used here, and give its general formula (you dont need to find the actual values of any intrinsic parameters) [2 marks].

x1 x2

0 4

5 29

10 214

15 469

20 824

25 1279

30 1834

(iii) Give the formula for the generalised linear basis function [2 marks].

(iv)Explain why one would want to introduce non-linear basis functions in linear classifiers [2 marks]?

x1 x2 0 4 5 59 10 214 15 469 20 824 25 1279 30 1834