Use the regression equation to describe the relationship between the response and the terms in the model. The regression equation is an algebraic representation of the regression line. Enter the value of each predictor into the equation to calculate the mean response value. Unlike linear regression, a nonlinear regression equation can take many forms.
For nonlinear equations, determining the effect that each predictor has on the response can be less intuitive than it is for linear equations. Unlike the parameter estimates in linear models, there is no consistent interpretation for the parameter estimates in nonlinear models. The correct interpretation for each parameter depends on the expectation function and the parameter's place in it. If your nonlinear model contains only one predictor, assess the fitted line plot to see the relationship between the predictor and response.
Convergence on a solution does not necessarily guarantee that the model fit is optimal or that the sum of squared errors (SSE) are minimized. Convergence on incorrect parameter values can occur due to a local SSE minimum or an incorrect expectation function. Therefore, it is crucial to examine the parameter values, fitted line plot, and residual plots, to determine if the model fit and parameter values are reasonable.
In these results, there is one predictor and seven parameter estimates. The response variable is Expansion and the predictor variable is temperature on the Kelvin scale. The lengthy equation describes the relationship between the response and the predictors. The effect that a 1 degree Kelvin increase has on copper expansion highly depends on the starting temperature. The effect of changing temperatures on copper expansion cannot be easily summarized. Assess the fitted line plot to see the relationship between the predictor and response.
If you enter a value for temperature in Kelvin into the equation, the result is the fitted value for copper expansion.
Expansion = (1.07764 - 0.122693 * Kelvin + 0.00408638 * Kelvin ** 2 -
1.42627e-006 * Kelvin ** 3) / (1 - 0.00576099 * Kelvin + 0.000240537 *
Kelvin ** 2 - 1.23144e-007 * Kelvin ** 3)