The Consumer Financial Protection Bureau (CFPB) used an algorithm developed for healthcare research by Marc Elliott, a statistician at the Rand Corp., in its cases alleging racial discrimination against auto lending companies. Most notably, that formula was the underpinning of its prosecution of Ally Financial, the former General Motors lending arm, which paid $80 million to settle with the regulator in 2013.

Mr. Elliott’s algorithm, which is a tool that estimates the probability that someone is white, black, Asian or Hispanic based only on their address and last name, has been relied upon by the CFPB to accuse some of the country's largest auto lenders of discrimination, including the financing arms of Toyota and Honda.

Car dealerships routinely include an additional bit of interest, called a markup, on top of the rate charged by a lender, as payment to the dealership for its work arranging the loan. The CFPB used Mr. Elliott's system to look at tens of thousands of loans, and arrived at the conclusion that car dealers charge larger markups to minority borrowers.

Both the GOP and the auto lending industry have issues with the regulator’s use of that tool.

The CFPB’s use of that algorithm is viewed by Republicans—who have sought to limit the powers of that agency created in the aftermath of the financial crisis—as a clear example of how the CFPB has overstepped its bounds by using a novel statistical method to indirectly regulate car dealers, which is a class of businesses outside of its jurisdiction.

The auto lending industry views it as a tool used to imply that it allows racist practices, a claim it feels should be validated with more than a math equation.

"You're using an imperfect tool to result in some pretty serious headlines," said Scott Pearson, an attorney who represents lending firms. "That's why they don't like it. They think it's unfair."