The accompanying data file shows information about $103$ home loan applications. Variables on each application include $(1)$ whether the application is conventional or subsidized by the federal housing administration $($LoanType$),(2)$ whether the property is a single$-$family or multifamily home $($PropertyType$),$ and $(3)$ whether the application is for a first$-$time purchase or refinancing $($Purpose$).$

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a$.$ Using the first five applications, compute the matching coefficients for all pairwise observations based on LoanType, PropertyType, and Purpose.

Note: Round your answers to $2$ decimal places.

b$-1.$ Which of the following loan applications is the most similar pair?

multiple choice $1$

Loan applications $1$ and $2$

Loan applications $1$ and $3$

Loan applications $1$ and $4$

Loan applications $1$ and $5$

b$-2.$ Which of the following statements best describes the most similar pair of the loan applications in part b$-1?$

multiple choice $2$

They both are conventional single$-$family purchases

They both are conventional multi$-$family purchases

They both are federal$-$housing single$-$family refinances

They both are federal$-$housing multi$-$family refinances

b$-3.$ Which of the following loan applications is the least similar pair?

multiple choice $3$

Loan applications $1$ and $3$

Loan applications $2$ and $3$

Loan applications $1$ and $4$

Loan applications $2$ and $4$

b$-4.$ Which of the following statements best describes the least similar pair of the loan applications in part b$-3?$

multiple choice $4$

One application is a conventional single$-$family refinance, while the other is a federal$-$housing multi$-$family purchase

One application is a federal$-$housing single$-$family refinance, while the other is a conventional multi$-$family purchase

One application is a conventional multi$-$family refinance, while the other is a federal$-$housing single$-$family purchase

One application is a federal$-$housing multi$-$family refinance, while the other is a conventional single$-$family purchase