To replicate the KNN results in this exercise, it is essential that you use $R$ version $4\mathrm{.}2\mathrm{.}1$ or later and the latest version of theExercise$\_12\mathrm{.}2$

relevant packages. For consistency, the exercise uses the random number generator $($RNG$)$ algorithm from $R$ version $3\mathrm{.}5\mathrm{.}3.$ To

replicate the results with newer versions of $R,$ execute the following line of code at the beginning of the $R$ session or your $R$ code:

suppressWarnings$($RNGversion$("3\mathrm{.}5\mathrm{.}3")).$

For $R,$ partition the data sets into $60\%$ training and $40\%$ validation and implement the $10-$fold cross$-$validation. Use the statement

set.seed$(1)$ to specify the random seed for data partitioning and cross$-$validation. When searching for the optimal value of $k,$ search

within possible $k$ values from $1$ to $10.$ If the predictor variable values are in the character format, then treat the predictor variable as a

categorical variable. Otherwise, treat the predictor variable as a numerical variable.

The accompanying data file contains $111$ observations with the binary target variable $y$ along with the predictor vales $x_1,x_2,x_3,$

and $x_4$

Click here for the Excel Data File

a$.$ Perform KNN analysis on the data set. What is the optimal value of $k?$ Enter the optimal $k$ in the box below:

Optimal $k$

b$-1.$ Report the accuracy, specificity, sensitivity$,$ and precision rates for the validation data set.

Note: Round your answers to $2$ decimal places.

b$-2.$ Which of the following statements is most accurate?

A$.$ The error rate of the $KNN$ model is $66\%.$

B$.$ The KNN model is able to correctly classify $64\%$ of the Class $1$ cases.

C$.$ The KNN model is able to correctly classify $64\%$ of the Class $0$ cases.

D$.$ Overall, the KNN model is able to correctly classify $73\%$ of the cases.

c$-1.$ What is the accuracy rate of the na$$ve rule $($classifying all cases into the predominant class$)$ for the test data set? $($In case of no

dominant class, choose class $1$ as the dominant class.$)$

Note: Report your answer in percentage. Round your answer to $2$ decimal places.

c$-2.$ Is the ROC curve of the KNN model closer to the optimum $($perfect$)$ model or the baseline model?

Optimum $($Perfect$)$ model

O Baseline model

y x$1$ x$2$ x$3$ x$4$

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$160600849534603$

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$044000659523583$

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$145200618319156$

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$144100809423415$

$038600568834566$

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