Linear Regression Analysis
Using the sample data provided our consulting firm has come up with a number of
statistics to back up our findings on the proper credit rating in which to make loans to
borrowers. The first method we used to find a good minimum credit score was to take the
amount of days delinquent of payment used for previous loans given and match them
against the credit scores of the borrowers who had taken those loans out. We used what is
referred to as a “simple linear regression”, which is a method of analysis where the X and
Y variables are compared on a graph and a trend line that represents the average of the
points that fall on the graph. That line best represents what would typically fall on the Y-
axis, or dependent variable part of the graph if you input the independent variable on the
X-axis. The independent variable is one that is taken from the outside and influences the
dependent variable.
The amount that the dependent variable is changed based on the independent
variable is based on the R^2 value which is also known as the Coefficient of
Determination. We determined that the dependent variable in this regression is “Days
Delinquent” and the independent variable is “Credit Score”. With the dependent and
independent variables identified, and using the Coefficient of Determination, we can tell
what percentage of the dependent’s variable is influenced by the dependent variable. In
our regression we discovered that the R^2 value was .926 (See Appendix A) which
means that any change in “Days Delinquent” is 92.6 percent because of a change in
“Credit Score”. We had plotted all of the sample data into a graph and obtained the
formula for the linear regression that was present in the graph. With that data we had
calculated out the formula of a line and applied credit score as the X value, and days
delinquent as the Y value. (See Appendix A) Using the formula, for every one point of
credit score a loan applicant goes up, the average borrower will be .255 less days
delinquent.
Our next task was to use this information to figure out which credit score would
be expected to yield an average delinquency of 90 days. So this time we had plugged in
90 days into the Y value of the formula we obtained from the regression. When we
worked the formula out we determined that a borrower with a credit score of 446 would
likely average a delinquency of 90 days (See Appendix B)
Using the result of the average delinquency of 90 days, which yielded a credit
score of 446, we calculated that 50% or half of the loans to borrowers would be
delinquent if Mary decided to use that credit score as a minimum for extending the
subprime loans. We came to this conclusion by using the normal distribution assumption
of regression, which is used to approximate the real-valued random variables that cluster
around a single mean. The real-valued random variables in our case are the days delayed
and the single mean value is 90 days delayed. The graph of a normal distribution has a
“bell” shaped curve also known as a bell curve. The bell curve has a symmetric
distribution at the mean. What this means statistically is that 50% of borrower with a
credit score of 446 will be 90 or more days delinquent and towards the top end of the
graph, while 50% of borrower with a credit score of 446 will be 90 or less days
delinquent and towards the bottom of the graph (toward the X-axis). [See appendix C]
With the acceptance of Citywide State bank for Mary to enter the Subprime market, we
recommended using a minimum credit score for Mary to accept. We have created along
with the minimum credit score a buffer zone in which to decide whether or not to accept
a loan. We determined this buffer zone to reside between a credit score of 485 and 524.
These scores yield a delinquency of 80 to 70 days, which should allow Mary to utilize
many loans at the lower end of the spectrum while at the same time, creating a safe zone
where these loans will have a lower chance of defaulting. However, in a perfect world we
would have information on other banks; if we make the credit score requirement too low,
we will have more borrowers but we will also have more risk due to the fact that
applicants will have lower scores. On the other hand, a higher score requirement would
minimize risks, but would decrease the quantity of loans. Furthermore, we would stress
that any loans to potential borrowers residing within this credit score zone be looked at in
greater detail to determine whether or not to accept. This will allow a case-by-case basis
to occur allowing Mary to get the greatest number of loans, with the least amount of
default.
Appendix
A.
Y-Axis = Days Delinquent
X-Axis = Credit Score
B.
90 = -.255(Credit Score) + 203.65
-113.65 = -.255(Credit Score)
445.69 = Credit Score
C.