1. Write a python program that uses LOOCV to evaluate polynomials with orders from 1 to 8 based on data stored in below. Print the mean loss, the order and the coefficients of the polynomial that has the smallest LOOCV mean loss to IDLE shell. Plot the mean losses for all the polynomials as a curve against their orders. Your program should contain the following three functions:

   a) polynomial(n,f): fit a polynomial with an order of n to the data stored in f. (In this and the following two functions, f should a two columns matrix, i.e., each row is a pair of attribute and target values.) b) LOOCV(n,f): use LOOCV on data stored in f to generate the mean loss for polynomial with degree n.(Hint: convert the algorithm LOOCV to a python function.) c)plotit(n, f): plot the mean loss of each polynomial with an order of i, 1 i n, based on data stored in f.

DATA

-5.00 -565.00 -4.66 -360.20 -4.31 -160.97 -3.97 -253.33 -3.62 -216.29 -3.28 21.13 -2.93 -9.09 -2.59 -74.95 -2.24 -42.49 -1.90 -50.70 -1.55 111.38 -1.21 -31.25 -0.86 -1.61 -0.52 124.28 -0.17 109.41 0.17 101.76 0.52 18.32 0.86 -76.93 1.21 -64.01 1.55 9.07 1.90 185.28 2.24 59.63 2.59 -16.92 2.93 26.63 3.28 156.26 3.62 260.95 3.97 278.68 4.31 427.45 4.66 512.22 5.00 492.00