Question

When is a nonlinear regression used? How do you know that the data are non-linear?

Answer 1

The dataset is plotted on a scatterplot and we see if the data follows an approximate linear pattern. However we can only plot when we have one independent variable. If we have more than one IV, we should use a residual plot to check if it follows a random pattern or not. If we can see a linear pattern in the scatterplot or a random pattern in residuals, we choose linear regression to obtain the desired regression equation, otherwise a non linear regression model should be used. If we can't obtain an adequate fit using the linear regression model, we use the non linear regression to obtain the desired fit because a linear pattern is not successful in fitting the curve. Non linear regression can fit more type of curves, i.e logarithm, polynomial etc.

For example: In the following dataset, the curve does not follow a linear trend and hence a non linear regression should be used.