What is a regression curve?

Regression curve is a study taught in advanced statistic courses.

The simplest form of regression is fitting a line to data. Suppose I
want to predict a tiger's height from its age. I can find the
equation of the "best" line that relates height to age, and I can then use that line to make predictions about what a "normal" height should be
at any given age for a tiger.

Regression methods go beyond fitting lines to data and explore fitting
curves, using more than one variable to make predictions, and how to
tell if the model you choose fits the data well.

A good book to start with is "Introduction to Linear Regression
Analysis" by Montgomery and Peck, published by John Wiley and Sons.

Okay?