def standardize(df, dont_standardize=None):
    """
    Parameters
    ----------
    df : pandas DataFrame
        Contains independent variables
    dont_standardize : List
        Names of variables to not standardize

    Returns
    -------
    Tuple of DataFrames: standardized_df, stats_df
        standardized_df is the standardized version of df
        stats_df contains the mean and std of the variables
    """
    dont_standardize = [] if dont_standardize is None else dont_standardize

    ## Get the mean and std and then the standardized dataframe
    mu = df.mean()
    sigma = df.std()

    standardized_df = (df - mu) / sigma

    ## If necessary, don't change some columns
    for name in dont_standardize:
        standardized_df[name] = df[name]

    return standardized_df