Hello, I would appreciate any help with this question!

Problem One. Consider the following situation. You are hired by a bank to design a statistical model for their small business underwriting team. Over the years the bank has collected data on the performance of small business loans. Their dataset is structured as follows. Each observation is for a small business 1' that received a one-time loan from the bank. The variable Default; is a dummy variable that equals one if small business If defaulted on the loan at any point and zero otherwise. The variable Score; measures the business credit bureau Experian's credit score of the small business i when the loan was made. The final variable is Unemploymentf which measures the unemployment rate at the time and location ofthe small business 1' when the loan was made. a) Suppose prior to your hiring, existing analysts at the bank ran the following linear probability regression: Default; = 30 + 315mm; + zUnempioymentf And they find estimates 5'0: 0.1 31 = 0. 002 33: 1. 5 when the run the regression on their data. Using this model what is the predicted value for the default of business 1 when their Experian credit score is 80 and the unemployment rate is 0.05? What is the traditional interpretation of this fractional predicted value? b} Now find the predicted value for a business i where their Experian credit score is 100, a very good score, and the ...._ unemployment rate is only 0.01. What is the predicted value Default; then for this small business? How is this a challenge to the interpretation you made in part a] above? c] Now suppose under your guidance the team runs a probit model. The probit model has P(Defauitf = 1 Scorthnempioymentf) = (13030 + Blscoref + gUnemponmentf) where the part appearing inside the '13 term I e g + IScoref + zUnempioyment- is called the 'Index'. Suppose the estimation you run results In the estimates of 80 2, ,8] = 0. 002, 82 20. What Is the value of the index with these estimates for a small business iwith an Experian credit score of 80 and an unemployment rate of 0.05? What Is the value of the index with these estimates for a small business i with an Experian credit score of 100 and an unemployment rate of 0.01? cl] Go to a standard normal lCDF calculator [such as httpswwwdanielsopercomfstatcalcfcalculatoraspx?id=55, my apologies for the spam] and plug in the values for each of the two indexes you found above and calculate the resulting probabilities. According to your estimated probit model, what are the estimated default probabilities for each of these two small businesses? e] Imagine economic conditions had been worse for both ofthese businesses when the loans were made. For the first business imagine the unemployment rate had been 0.06 instead of 0.05. Forthe second business imagine it the unemployment rate had been 0.02 instead of 0.01. What is the change in each of their default probabilities? Does an increase in the unemployment rate by 0.01 have equal or heterogeneous marginal eects for these two businesses