However, we can compare the standard error of the regression (S) for the two models. R-squared does not appear because it is invalid for nonlinear regression. The residual plot displays the randomness that we want to see for an unbiased model. In the fitted line plot, the nonlinear relationship follows the data almost exactly. The equation for the nonlinear regression analysis is too long for the fitted line plot:Įlectron Mobility = (1288.14 + 1491.08 * Density Ln + 583.238 * Density Ln^2 + 75.4167 * Density Ln^3) / (1 + 0.966295 * Density Ln + 0.397973 * Density Ln^2 + 0.0497273 * Density Ln^3) Comparing the Regression Models and Making a Choice A rational function is the ratio of two polynomial functions. Instead, I’ll jump to the solution and not show all the work to get there, much like a cooking show! I want you to see how the following nonlinear model compares to the linear model based on the best solution.įor our data, a rational function provides the best nonlinear fit. Because this blog post focuses on the basics of choosing between linear and nonlinear models, I’m not going to cover how the researchers chose the optimal functional form of the nonlinear model. So, it’s no surprise that the linear model was insufficient. Our example dataset is one that the NIST uses to illustrate a hard-to-fit nonlinear relationship. It’s for these reasons that I always recommend fitting linear models first. For instance, some starting values can cause the algorithm to fail to converge on a solution or to converge on an incorrect solution. Some datasets can require substantial effort to find acceptable starting values. Unlike linear regression, you also need to supply starting values for the nonlinear algorithm. The downside is that it can take considerable effort to choose the nonlinear function that creates the best fit for the particular shape of the curve. The main positive is that nonlinear regression provides the most flexible curve-fitting functionality. The fact that you can fit nonlinear models with virtually an infinite number of functional forms is both its strength and downside. As I mentioned earlier, nonlinear regression can be harder to perform.

Now, let’s fit the same data but using nonlinear regression. Related posts: Linear Regression and Seven Classical Assumptions of OLS Linear Regression Example of a nonlinear regression model

Consequently, it’s time to try nonlinear regression. There’s nothing more we can do with linear regression.

Our linear regression model can’t adequately fit the curve in the data.

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