I agree with you that "regressor" is too obscure and should be changed.

I disagree about the "y = mx + c". Haven't we already discussed this? That form is used in linear algebra, but not used in statistics. Quoting from Yale:

"A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0)."

http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm

This function is being used for statistics, not linear algebra. The users of the module are not people doing linear algebra, and most users of statistics will be familiar with the Y = a + bX form (or possibly reversed order bX + a).

The TI-84 offers two linear regression functions, ax+b and a+bx. So does the Casio Classpad. The Nspire calls them a+bx and mx+b.

https://www.statology.org/linear-regression-ti-84-calculator/

I've seen:

a + bx
ax + b
bx + a
mx + c
mx + b

among others. I don't think that there is any justification for claiming that a majority of users will be most familiar with mx+b.