$1)$ Estimate an OLS model of loss given default prediction using the first $1000$ observations $($shaded in light blue$)$ in the $$Data Assignment $4$ file. The file contains information about defaulted personal loans. The variables included in the dataset are: Recovery rate, Loan to Value ratio, Purpose $($of the loan$),$ Characteristic $($of the borrower$)$ #$1,$ and Characteristic $($of the borrower$)$ #$2.$ Do the variables included in the data help predict losses given default? Notice that, unlike the corporate loss given default data we went over in class, there are no multiple debt instruments in this case. As a result, there will be no clustering and no need to use robust standard errors.

$2)$ Repeat the analysis in $1$ above but using Beta transformed losses given default as the basis of the analysis.

$3)$ Use the remaining observations in that dataset $($shaded in yellow$)$ to backtest both models. To do this you will need to use the forecasting equations estimated in $1$ and $2$ above $($using only the first $1000$ observations$)$ to make forecasts for the loss given default of the remaining observations. Which model seems more accurate in this case?