Mortgage Application Rates Part III: Utilizing Linear Regression Models

FYI: In my last post, we used A/B testing in Excel to test if an African American applicant has a smaller chance of having a loan approved than an applicant that is White Non Hispanic.

1. Do Other Biases Exist in Other Steps of the Loan Application Process?

FYI: Now that we know biases exist in the loan origination and denial steps in the process, digging deeper to see if there are more instances would be a good idea. Let's take a look at interest rates across different applicant races, given a loan originated.

Process: Because we want to highlight the impact an applicant's race has on an interest rate, a linear regression model would be a great way to represent this data. Let's first highlight the data set to represent X-values and the Interest Rate column to represent the Y-column. Doing this will show us the statistical significance of each x-variable and the impact it has on the interest rate.

Conclusion: From our regression model, we see that we are missing White applicants. Given our Adjusted R Square of roughly .61, let's see if we can make the model a little better so our information is more accurate. We'll accomplish this by creating a column for White applicants.

Process: Run regression model again with our new column.

Conclusion: Notice the Adjusted R Square? Our model improved from .61 to .65. Also, by looking at the p-value column, we notice that loan amounts and an applicant being female do not have statistical significance in impacting the interest rate. Knowing this, let's see if we can improve the model again by excluding these two variables.

Process: Delete Mortgage Amount and Female Column.

Conclusion. After running this third model, all of our x-values now have statistical significance on our model (after excluding mortgage amount and female applicant). Because our model only slightly improved from .648 to .649, we can stick with this model to analyze.

2. Analysis of Regression Model

FYI: Now that we have our model, we can take a look at the impact each Race has on an applicant's interest rate

Process: Analyze the Coefficients Column to see the impact of each variable on the mortgage interest rate.

Conclusion: From our model we can see that, much like our pivot table analysis, there are large differences in the impact an Applicant's Race has on their interest rate. The difference in interest rates between African American and White applicants is approximately 1.9%.

SUMMARY: Both loan origination/denial rates and interest rates have evidence of bias, which is based on an applicant's race.