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. The quadratic model appears to fit the data better than a linear model.
Fitted regression lines can be added to graphs such as scatterplots and matrix plots.