A fitted regression line on a graph represents of the mathematical regression equation for your data. Use fitted regression lines to illustrate the relationship between a predictor variable (x-scale) and a response variable (y-scale) and to evaluate whether the model fits your data.
A regression fit line can be drawn to fit a linear, quadratic, or cubic model.
You are studying the relationship between a particular machine setting and the amount of energy consumed. You suspect that this relationship has curvature, but you need to confirm and document the curvature. You produce the following plots:
Fitted regression lines can be added to graphs such as scatterplots and matrix plots.