1 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
• 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.