You should see that the shape of x is $(152,9)$ and the shape of y is $(152,).$ There are $152$ samples $($countries$),$ and $9$ features $($each of the key$\_$vars$)$ that we are using to make predictions.

Note that the numerical data columns in x represent different quantities and have different scales. A key step in machine learning is standardization: the transformation of features to be on the same scale $($with a mean of $0$ and a standard deviation of $1).$ Standardization can substantially increase model accuracy, performance and interpretability.

sklearn provides various utilities to perform standardization. We will use one here called StandardScaler, which will transform a data set so that each resulting column has zero mean and unit standard deviation.

Carrying out this scaling is a little complicated if we want to maintain the basic structure of our dataframe, so we have provided the relevant code in the next code cell below. $($The code examples describing StandardScaler in the sklearn documentation typically just extract out the numerical values in numpy arrays. For this exercise, we'd like to keep the labels together in a dataframe.$)$

Please perform the following steps in the below graded cell:

Import the StandardScaler object

Create and fit a StandardScaler object to our dataframe x

Create a new dataframe x$\_$scaled that contains the scaled $($transformed$)$ data, using the column and index labels from our unscaled dataframe x

Print out the mean and standard deviation of each column of x$\_$scaled

Peek at the head of the new dataframe x$\_$scaled

In examining the output, check that the means of each column have been scaled to nearly zero $($to within a very small tolerance$)$ and the standard deviations have been scaled to one. Some of the very small numbers might be printed out in scientific notation, where a number like $1\mathrm{.}928282$e$-16$ means $1\mathrm{.}928282*10**(-16).$