A multivariate logistic regression model has been used to predict the status of generator products. The initial weights of the model are shown in the table below:

$\backslash$table$[[$Feature$,$Weight$],[$Intercept$,1],[$RPM$,1],[$Vibration$,1]]$

$($a$)$ Using this model to make predication for each of the following query instances:

$\backslash$table$[[$ID$,$RPM$,$Vibration,Status$],[1,568,585,1($Good$)],[2,586,565,1($Good$)],[3,609,536,1($Good$)],[4,562,309,($Faulty$)],[5,578,346,0($Faulty$)]]$

$($b$)$ Calculate the cross entropy loss for the set of predication generated in part $($a$)$

$($c$)$ Assuming a learning rate of $0\mathrm{.}001,$ calculate the weights at the next iteration of the gradient descent algorithm

$($d$)$ Calculate the cross entropy loss for the set of predictions generated using the new set of weights calculated in part $($c$)$