reject = beta_0 + beta_1 loanprc + beta_2 atotinc + beta_3 atotinc^2 + beta_4 ob
ID: 1199251 • Letter: R
Question
reject = beta_0 + beta_1 loanprc + beta_2 atotinc + beta_3 atotinc^2 + beta_4 obrat + beta_5 pubrect + u in which: reject: = 1 if loan is rejected, and 0 if not. obrat: other obligations, % of total income pubrec: = 1 if filed for bankruptcy atotinc: Total monthly income loanprc: loan amount /purchase price atotinc^2 = atotinc* atotinc From the model above, what sign do you expect from each partial slope coefficient in the model above? Justify your answers. From the estimation of model above, one can obtain the following: Interpret the coefficients of pubrec and of loanprc. How do you explain the signs of atotinc and atotinc^2 ?Explanation / Answer
Answer:
Part a), Loanprc is loan amountpurchase price. Hence as the loan amount increases the probability of a loan rejection increases keeping all the other things constant. Hence we expect a positive sign for the coefficient of loanprc.
As the monthly income increases, the probability of the loan rejection decreases. Hence the sign of coefficient of atotinc will be negative.
As the monthly income increases, its square will increase at a much faster pace than the original income. Thus the probability of rejection will increase as the chances of a person reporting incorrect income are high. Hence we expect coefficient of atotinc^2 to be positive.
As the other obligations increase, the probability of rejection of a loan increases. Hence its coefficient sign will be positive.
If the person has been filed for bankruptcy, his loan will be rejected. Hence its coefficient will be positive.
Part b) If a person has been filed for bankruptcy, his probability of defaulting on a loan are high and hence the probability of rejecting a loan will be high. Thus keeping all the other things constant, if pubrec =1, the probability of rejecting a loan are higher by 1.323 (or 32%) than a person with pubrec=0. 1.323=exp(0.28), this is done because above model is a logit model.
Keeoing all the other things constant, if a person applies for a higher loan amount the probablity of rejection are higher by 1.2 or 20% (=exp(0.189)).
Part c) As the monthly income increases, the probability of loan rejection decreases. Hence negative relation between monthly income and rejection of loan. Thus the coefficient is negative.
However as the increase in monthly income square is at a much higher pace than the increase in original income. Hence the chances of loan rejection increases as the chances of a person reporting wrong income are high. Thus the coefficient is positive.
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