figure the true regression line (bluesolidand the upper and lower prediction curves (reddashedand confidence curves (dotted nonlinear regression models so far we have been mostly dealing with linear regression modelsin which the prediction function is of the form ( bxb in this section we discuss some strategies for handling general prediction functions ( )where the functional form is known up to an unknown parameter vector so the regression model becomes yi (xi bei ( where en are independent with expectation and unknown variance the model can be further specified by assuming that the error terms have normal distribution table gives some common examples of nonlinear prediction functions for data taking values in table common nonlinear prediction functions for one-dimensional data name ( bb bx exponential ab power law ax ab logistic ( ea+bx )- ab weibull exp(- /aab - - polynomial {bk } = = bk the logistic and polynomial prediction functions in table can be readily generalized to higher dimensions for examplefor general second-order polynomial prediction function is of the form ( bb (