Polynomial Regression Polynomial regression can be used to fit a regression line to a curved set of points. Contrary to how it sounds, curvilinear regression uses a linear model to fit a curved line to data points. Curvilinear regression makes use of various transformations of variables to achieve its fit.
Nonlinear regression fits arbitrary nonlinear functions to the dependent variable.
Inspection of the y vs x plot reveals a degree of curvilinearity. From the above analysis, it appears that model 2 appears to be our best bet. A plot of y vs x with the predicted scores connect by a curved line is displayed above. You can also try this variation of the plot, connecting the points using a cubic spline. Here is another artifical example.