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?

$162$

$79$

$11$

$23$