You want to fit an exponential model of the form, y ≈ yb = dX j =0 βje−ju=d; where the input u and output y are scalars. You are given python functions:

model = LinearRegression()
model. fit(X, y) # Fits a linear model for a data matrix X
yhat = model. predict(X) # Predicts values

Using these functions, write python code that, given vectors u and y:

• Splits the data into training and test using half the samples for each.
• Fits models of order dtest = [1,2,...,10] on the training data.
• Selects the model with the lowest mean squared error