$(22$ points$)$ In this next question, we'll use KNN to try to classify players' "preferred foot."

$($a$)(1$ point$)$ First, let's get a better sense of the balance of classes in our data $($eg$,$ how

many observations of each class we have$).$ Display the count of each value present in the

preferred foot column.

$($b$)(2$ points$)$ If we were to build a classifier which always guessed a player preferred their

right foot, what percentage of the time would we make a correct classification? In other

words, what percent of players actually do prefer their right foot?

$($c$)(1$ point$)$ Let's build a classifier using $10$ available dimensions: shooting, passing, drib$-$

bling, defending, attacking, skill, movement, power, mentality, and goalkeeping. Create

an $x$ dataframe with just these $10$ columns and display the first $5$ rows.

$($d$)(2$ points$)$ Now, rescale $($or normalize$)$ this $x$ data so that each IV has a mean of $0$ and

a standard deviation of $1.$ Display $($at least$)$ the first three rows of normalized data.

$($e$)(2$ points$)$ We'll want to be able to see how well our classifier performs out of sample,

so now create a validation$-$train split, setting $Y$ to be the "preferred foot" column of the

dataframe. Here, use $30\%$ of the data for validation and set the random state to $456.$

Display $($at least$)$ the first $3$ rows of $x$ training data.

$($f$)(4$ points$)$ Next, we'll want to determine the number of neighbors $k$ to consider for our

KNN classifier. For values of $k$ from $1-30($inclusive$),$ calculate either the error or the

accuracy of a KNN classifier. Display your results by creating a plot with considered

$k$ values along the horizontal axis and the corresponding error $($or accuracy$)$ displayed

along the vertical axis.

$($g$)(4$ points$)$ Based on your analysis, choose a reasonable value of k$.$ Fit a KNN classifier

that considers this number of neighbors and predict $Y$ values $($preferred foot$)$ for your

out of sample validation data. Display $($at least$)$ the first $3$ predictions for "preferred

foot."

$($h$)(2$ points$)$ Use actual and predicted Y values to calculate and display the confusion

matrix for your model. This will display without labels, but will show the classes in

alphabetical order $($Left$,$ Right; upper left corner is "Left$-$Left"$).$ As with the examples

in lecture, the rows will indicate the actual values and the columns will indicate the

predicted values. Approximately how many players who actually prefer their left foot

$("$True Lefts"$)$ were predicted to prefer their right foot?

$($i$)(2$ points$)$ Use the actual and predicted Y values to display the full classification report.

What does the recall for the classification "Left" suggest about our model?

$($j$)(2$ points$)$ Reflecting on the analysis above, do you feel like this model does a good job

or a bad job of predicting a player's preferred foot? Briefly explain your answer.