Use the templates repository for boilerplate code.

Pandas

1. Write a function to read a .csv file into a pandas data frame, returning it. Give it an optional argument determining the delimiter.
2. Write a function that modifies a data frame, adding the squared values of a given column. That column's name should be passed as argument to the function, along with the data frame. Remember that python passes arguments by reference, so you can modify it in the function.
3. Advanced: Write another function adding a column computed from other columns via a given function to that data frame. The function, the name of the new column, and the names of the columns to be used as the function's arguments should be passed to your function.

K-Nearest Neighbors

1. Write a function that, given known values \(y_i\) and computed values \(\hat y_i\) calculates the mean squared error

\[MSE(y, \hat y) = \sum_{i = 1}^n \frac 1 n (y_i - \hat y_i)^2\]

2. Write a function that, given training data \(\tilde X, \tilde y\), test data \(X, y\) and a number \(k\) generates a \(k\)-Nearest-Neighbor model \(\hat f_{\tilde X, \tilde y, k}\) and computes the \(MSE(y, \hat y)\) for the \(k\)-Nearest-Neighbor prediction \(\hat y = \hat f_{\tilde X, \tilde y, k}(X)\) and \(y\), given the test data.
3. Advanced: Head back to the list of datasets and find one with continuous variables that interests you. Select a number of variables as your input set \(X\) and the quantity \(y\) that you're interested in predicting. Split the data in training and test set and plot the mean standard error of a k-nearest neighbors prediction in dependence of \(k\). How does this change if you include more input variables into \(X\)?