The data sets used for this end$-$of$-$chapter exercise will need to be normalized in order to create a neural network that can produce reliable predictions. This will be accomplished using the scale$()$ function in R$,$ which has not been covered in the text. The modifications to ensure that nnet$()$ produces usable results will therefore be prescribed in the following steps. Complete each step and then answer the exercise questions below.

Step $1.$ Import the training and scoring data sets for this exercise into data frames in RStudio. Ensure that the training data frame$$s name is ch$11$Train and the scoring data frame$$s name is ch$11$Score.

Step $2.$ Load the R library required to create a neural network model.

Step $3.$ Use the following two commands to create data frames containing the normalized independent variable values for the training and scoring data sets.

ch$11$TrainNorm $<-$ data.frame$($scale$($ch$11$Train$[2$:$8]))$

ch$11$ScoreNorm $<-$ data.frame$($scale$($ch$11$Score$[2$:$8]))$

Step $4.$ The independent variable values that were normalized using the scale$()$ function in step $3$ will be used to train the neural network model. Issue the command:

attach$($ch$11$TrainNorm$)$

Step $5.$ Set the seed value to $43.$

Step $6.$ You will train a neural network model to predict the Credit$\_$Risk dependent variable in the ch$11$Train data frame, using the independent variables in the normalized ch$11$TrainNorm data frame. The hidden layer$$s size attribute is set to $7,$ which uses the generally accepted formula:

$((7$ independent variables $+5$ dependent variable levels$)/2)+1$; which is $(12/2)+1=7$

Issue the command:

ch$11$NNModel $<-$ nnet$($as$.$factor$($ch$11$Train$Credit$\_$Risk$)$ ~ Credit$\_$Score$+$Late$\_$Payments$+$Months$\_$In$\_$Job$+$Debt$\_$Income$\_$Ratio$+$Loan$\_$Amt$+$Liquid$\_$Assets$+$Num$\_$Credit$\_$Lines, data$=$ch$11$TrainNorm, size$=7,$ maxit$=1000)$

Step $7.$ Use the predict$()$ function to apply your neural network model $($ch$11$NNModel$)$ to the normalized scoring data frame $($ch$11$ScoreNorm$)$ to predict Credit$\_$Risk classes for each observation. Store these predictions in a data frame with a relevant name.

Step $8.$ Use the predict$()$ function to apply your neural network model $($ch$11$NNModel$)$ to the normalized scoring data frame $($ch$11$ScoreNorm$)$ to predict Credit$\_$Risk confidence percentages $($post$-$probabilities$)$ for each observation. Store these predictions in a data frame with a relevant name.

Step $9.$ Create a data frame with a relevant name that contains the step $7$ class predictions, the step $8$ confidence percentages, and the unnormalized scoring data $($ch$11$Score$).$ View this data frame in RStudio, then answer the following questions.

Using the neural network$$s predictions as generated using the steps outlined in this exercise, how many loan applicants will have their loans denied? $23$

$162$

$79$

$11$

$23$

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Using the neural network$$s predictions as generated using the steps outlined in this exercise, and assuming that loan officers can automatically approve all loans predicted to be low or very low risk, how many loans will be automatically approved by loan officers? $142$

$142$

$16$

$114$

$126$

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The bank has a policy that a manager can approve a loan for an applicant who is predicted to be high risk, but only if that applicant$$s moderate risk prediction is greater than $30\%.$ Using this model$$s predictions, how many high$-$risk applicants can have their loans approved by a manager?

$12$

$2$

$0$

$3$

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Normalizing the data has resulted in most confidence percentages being $100\%$ in this exercise$$s predictions. However, not all predictions have $100\%$ confidence. How many predictions of high credit risk in this neural network$$s results are not $100\%?$

$77$

$12$

$2$

$79$

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Based on the predictions generated by this model for this scoring data, what is the lowest credit score a person could have and still achieve a classification of Low?

$710$

$700$

$662$

$650$

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