Use the data $($a sample of $20$ banks$)$ given below to answer the following question$($s$).$

$\backslash$table$[[,$financial,TotCap$/$Asset$,$TotExp$/$Asset$,$TotLnsLses$/$Asset$],[$Obs$,$condition,s$,0\mathrm{.}65,],[1,1,9\mathrm{.}7,0\mathrm{.}12,0\mathrm{.}62],[2,1,1,0\mathrm{.}11,1\mathrm{.}02],[3,1,6\mathrm{.}9,0\mathrm{.}09,0\mathrm{.}67],[4,1,5\mathrm{.}8,0\mathrm{.}1,0\mathrm{.}69],[5,1,4\mathrm{.}3,0\mathrm{.}11,0\mathrm{.}74],[6,1,9\mathrm{.}1,0\mathrm{.}13,0\mathrm{.}79],[7,1,11\mathrm{.}9,0\mathrm{.}1,0\mathrm{.}63],[8,0,8\mathrm{.}1,0\mathrm{.}13,0\mathrm{.}72],[9,0,9\mathrm{.}3,0\mathrm{.}16,0\mathrm{.}57],[10,0,1\mathrm{.}1,0\mathrm{.}16,0\mathrm{.}43],[11,0,11\mathrm{.}1,0\mathrm{.}08,0\mathrm{.}8],[12,0,20\mathrm{.}5,0\mathrm{.}12,0\mathrm{.}69],[13,0,9\mathrm{.}8,0\mathrm{.}07,0\mathrm{.}53],[14,0,7\mathrm{.}9,0\mathrm{.}08,0\mathrm{.}73],[15,0,9\mathrm{.}6,0\mathrm{.}09,0\mathrm{.}3],[16,0,12\mathrm{.}5,0\mathrm{.}09,0\mathrm{.}49],[17,0,18\mathrm{.}3,0\mathrm{.}08,0\mathrm{.}55],[18,0,7\mathrm{.}2,0\mathrm{.}11,0\mathrm{.}44],[19,0,14,0\mathrm{.}08,0\mathrm{.}51],[20,0,8\mathrm{.}3,0\mathrm{.}08,]]$

The "Financial Condition" column records the judgment of an expert on the financial condition of each bank. This dependent variable takes one of two possible values$--$weak or stron according to the financial condition of the bank. The predictors are two ratios used in the financial analysis of banks: TotLns&Lses$/$Assets is the ratio of total loans and leases to total a and TotExp$/$Assets is the ratio of total expenses to total assets. The target is to use the two ratios for classifying the financial condition of a new bank.

Run a logistic regression $($on the entire dataset$)$ that models the status of a bank as a function of the two financial measures provided. Specify the success class as weak $($this is similar to creating a dummy that is $1$ for financially weak banks and $0$ otherwise$),$ and use the default cutoff value of $0\mathrm{.}5.$

a$)$ Write the estimated equation that associates the financial condition of a bank with its two predictors in three formats:

i$.$ logit as a function of the predictors:

ii$.$ odds as a function of the predictors:

iii. probability as a function of the predictors:

b$)$ Consider a new bank whose total loans and leases$/$assets ratio $=0\mathrm{.}9$ and total expenses$/$assets ratio $=0\mathrm{.}05.$ From your logistic regression model, estimate the following four quantities fo this bank: the logit the odds the probability of being financially weak