Polynomial Regression on Simulation Data

Function : y=5-0.1x+0.004x^{2}-3 * 10^{-5}x^{3} + \epsilon 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. 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.