In this exercise, we consider the amounts that are borrowed for single family home purchases in Las Vegas, Nevada, during 2010. Use the data file vegas5_small for this exercise.

a. Compute summary statistics for AMOUNT, FICO, RATE, and TERM30. What is the sample average amount borrowed? What FICO score corresponds to the 90th percentile? What is the median interest rate paid, and what percent of the mortgages were for 30 -year terms?

b. Construct histograms for AMOUNT, \(\ln (A M O U N T), F I C O\), and RATE. Are the empirical distributions symmetrical? Do they have one peak (unimodal) or two peaks (bimodal)?

c. Estimate regressions for dependent variables \(A M O U N T\) and \(\ln (A M O U N T)\) against the independent variable \(F I C O\). For each regression, interpret the coefficient of \(F I C O\).

d. Estimate regressions for dependent variables \(A M O U N T\) and \(\ln (A M O U N T)\) against the independent variable RATE. For each regression, interpret the coefficient of RATE.

e. Estimate a regression with dependent variable AMOUNT and explanatory variable TERM3O. Obtain the summary statistics for AMOUNT for transactions with 30-year loans and for those transactions when the term was not 30 years. Explain the regression results in terms of the summary statistics you have calculated.