The dataset $d$ are randomly partitioned into training dataset $d0$ and testing dataset $d1.$ The last

column is transform into a binary variable $y0$ and $y1$ and used as a target variable as follow:

top $10>30$ create target vary$0=1$ if top $10>30$;$y0=0$ otherwise

Question $5[20\%]$

ANN is applied to the dataset with ptime,phd$,$expend $($i$.$e$,$ columns $5,10,12)$ as input with size $=2$

and logistic is used. The following are the R commands and output:

factor $)$

col.nnann$\_$log $,$ size $=2,$ nt ry $=30$

summa ry$($ col.nn$net$0)$

$($a$)$ Write down exactly the system of equations of this ANN model.

$($b$)$ Suppose we have a record: $($i$1,$i$2,$i$3,$i$4)=($ptime$,$phd$,$expend$)=(331,72,5883).$ What is the probability

that top $10>30$ in this record?

$($c$)$ If we change the size from $2$ to $5$ and linear output, what is the number of parameters in this

new ANN model? What is the potential problem with this new ANN model? Be specific.

$($d$)$ Is it possible to use top$10$ as the target variable instead of using y$0$ in ANN? DO NOT write

any R codes, just explain your answer clearly.

Question $6[20\%]$

A binary variable expl is created from expend and a logistic regression is fitted using the

following $R$ commands:

expld$0$$expend

summary$($glm$($y$0$ pt ime$+$phd$+$exp$1,$ data$=$d$0,$ binomial