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Polynomial Regression on Simulation Data

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Polynomial Regression on Simulation Data

• Function: y = 5 − [url removed, login to view] + [url removed, login to view]

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.

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