Polynomial Regression on Simulation Data

Polynomial Regression on Simulation Data • Function: y = 5 − 0.1x + 0.004x 2 − 3 × 10−5x 3 + . • Generate 50 training data points: (x,y). • Generate 10000 testing data points: (xtest, ytest). • Use function lm(y ∼ poly(x,i)) to train your model, here i is the flexibility from 1 to 20. Hint: you can use for loop for this step. And repeat this whole process 30 times. • Calculate the Training MSE for each flexibility, in total you should have 20×30 MSE. • Calculate the Testing MSE for each flexibility, in total you should have 20 ×30 MSE. • Calculate the Average MSE for the 20 Training MSE. 1 • Calculate the Average MSE for the 20 Testing MSE. • Use plot() function to draw average Training MSE. • Use lines() function to draw all your Training MSE and Testing MSE in one figure. You can use for loop to draw all lines. • Please point out the first MSE for both Training and Testing by using points() function. • Please point out the lowest MSE for Testing and the corresponding Training MSE by using points() function. • Please point out the last MSE for both Training and Testing by using points() function.