Question $1(50)$

This data set of size $n=15($Yield data$)$ contains

measurements of yield from an experiment

done at different temperature levels. The

variables are $y=$ yield and $x=$ temperature in

degrees Fahrenheit. The table below gives the

data used for this analysis

Use data points $\{1,4,7,10,13\}$ as the validation

and remaining as the training set

a$.$ Use the given Python code to find different polynomial regression functions for degrees

$M=\{1,3,5,10,15\}$ for the training set dataset.

import numpy as np

$m=1$ # degree of the polynomial regression function

mymodel $=n$ p$.$polyld$($np$.$polyfit $(x,y,1)$

b$.$ Plot each function with the following code

plt$.$scatter$($x$,$ y$)$

myline $=$ np$.$linspace $(40,110,100)$

plt$.$plot $($myline$,$ mymodel $($myline$))$

plt$.$show $()$

c$.$ Get coefficient of the models with this function

print $($mymodel$.$coefficients$)$

d$.$ Calculate the cost for training dataset and also for the validation set with learned regression

models. Use the cost equation that we learned in the class.

e$.$ Decide which model is better to select and explain your answers.