Use the templates repository for boilerplate code.

Linear regression

1. Write a function that, given a pandas data frame X, and column names x and y, will fit a polynomial of a given degree to X[x], X[y].
2. Write a function that, given a \(N \times p\) feature matrix X and a traget vector y, returns a list of booleans indicating which columns of X should receive a relevant regression coefficient.
3. Choose a regression data set (e.g. the white wine quality set) and compare the MSE for ridge regression, lasso, and elastic net over a similar range of values for \(\lambda\). What do you observe? When do lasso and elastic net start setting regression parameters to zero?

Scipy

1. Write a function curve_predict(f, X_train, y_train, X_test), which given training data X_train, y_train and a function f performs a least-squares fit using scipy and predicts the values for X_test.