$(20$ points$)$ Now that we've gotten to know our data a little bit, we will use SciKit Learn

and a validation$/$train split to see how well our model $-$ using the same DV and IVs as Q$2-$

can predict a player's rank.

$($a$)(2$ points$).$ Based on the statsmodels output from Q$2,$ do you expect that these four

features $($passing$,$ attacking, defending, and skill$)$ will do a pretty good or pretty bad

job at predicting rank for out$-$of$-$sample data? Briefly explain why or why not.

$($b$)(2$ points$).$ Create an $x$ dataframe with just four features: passing, attacking, defending,

and skill. Create a Y dataframe $($or series$)$ with just the "rank" variable. Display the

first five rows of each.

$($c$)(2$ points$).$ Create a validation$/$train split where $25\%$ of the data is held out for

validation. Use a random seed of $123($i$.$e$.,$ set the random state to this value$).$ To show

your code has worked, display the first $5$ rows of the $x$ training data.

$($d$)(2$ points$)$ Use SKLearn to train a linear regression using only the training data. Display

the intercept and coefficients for your trained model $($coefficients do not need to be

labeled$).$

$($e$)(2$ points$)$ Compare the coefficients estimated by both regression models. How does the

coefficient for "attacking" change $($if at all$)$ when it is estimated in Q$2($using statsmodels

and the full dataset$)$ vs when it is estimated in Q$3($using SKLearn and just training data$)?$

$($f$)(2$ points$)$ Use your trained SKLearn regression model to predict rank values for the

hold$-$out set of $x$ validation data. Display at least the first three predicted values $($in a

format of your choice$).$

$($g$)(2$ points$)$ Display a scatterplot in which the horizontal axis shows the actual value of

the $Y$ validation data and the vertical axis displays the predicted $Y$ values for the $x$

validation data.

$($h$)(2$ points$)$ Calculate and display the Root Mean Squared Error $($RMSE$)$ for this model.

Provide a brief interpretation of what this means in terms of the "average error" of the

model.