IN PYTHON ONLY

For this case, you need to apply the decision rules and cutoff probability of $0\mathrm{.}5$ from Section $4\mathrm{.}3$

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to classify the two loans in Table $10$ of the article$$Should This Loan be Approved or Denied?$$: A Large Dataset with Class Assignment Guidelines

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as $$higher risk$$ or $$lower risk$$ for loan approval by writing Python code to reproduce results $($not format$)$ in Tables $7($a$),8,9$ of this article using the SBA case data SBAcase$\mathrm{.}11\mathrm{.}13\mathrm{.}17.$csv$.$ The variable $$Selected$$ indicates which observations are the $$training$$ data and which are the $$testing$$ data $(1=$ training data to be used to build the model, $0=$ testing data to validate the model$).$ Partition the data using this variable.

$($a$)$ Review Python documentation: statsmodels

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$$and example code from the class.$$Fit a logistic regression model to reproduce results $($not format$)$ in Tables $7($a$),8,9$ of this article using the SBA case data SBAcase$\mathrm{.}11\mathrm{.}13\mathrm{.}17.$csv by using STATMODELS sm$.$glm or smf$.$glm$.$

The logit model produces an estimated probability of being a $1.$ Classify as $1$ if this estimated probability $>$ cutoff, e$.$g$.,0\mathrm{.}5.$The following code from Table $10\mathrm{.}3$ in the example code may be helpful to perform this classification:

logit $=$ sm$.$GLM$($train$\_$y$,$ train$\_$X$,$ family$=$sm$.$families.Binomial$())$

result$=$ logit$.$fit$()$

predictions $=$ result.predict$($valid$\_$X$)$

predictions$\_$nominal $=[0$ if x $<0\mathrm{.}5$ else $1$ for x in predictions$]$

logit$\_$result $=$ pd$.$DataFrame$(\{\text{'}$actual$\text{'}$: valid$\_$y$,$

$\text{'}$p$(0)\text{'}$: $1-$ predictions,

$\text{'}$p$(1)\text{'}$: predictions,

$\text{'}$predicted$\text{'}$: predictions$\_$nominal $\})$

$$

$($b$)$ Refer to Table $8$ of the article. Write the estimated equation that associates the outcome variable $($i$.$e$.,$ default or not$)$ with predictors RealEstate, Portion, and Recession, in three formats:

$($i$)$ The logit as a function of the predictors $($see $(10\mathrm{.}6)$ of DMBA Chapter $10\mathrm{.}2)$

$($ii$)$ The odds as a function of the predictors $($see $(10\mathrm{.}5)$ of DMBA Chapter $10\mathrm{.}2)$

$($iii$)$ The probability as a function of the predictors $($see $(10\mathrm{.}2)$ of DMBA Chapter $10\mathrm{.}2)$

$($c$)$ Explain why risk indicators in Table $8$ were selected using p$-$values in Table $7($a$).$

$($d$)$ Interpret parameter $($coefficient$)$ estimates of the model in Table $8$ with a focus on the odds of default. Answer the following questions by interpreting parameter estimates of the model in Table $8$ and specifying odds and probabilities of default for these risk indicators.

$($i$)$ Is a loan backed by real estate more likely or less likely to default $($by how much$)?$ Explain using parameter estimates.

$($ii$)$ Is a loan active during recession more likely or less likely to default $($by how much$)?$ Explain using parameter estimates.

$($iii$)$ How much does the portion of a loan guaranteed by SBA increase or decrease the likelihood of default? Explain using parameter estimates.