both types of models are the functional forms
both forms of regression can fit curvature in your data

the functional form is a linear combination of feature functions 𝑓_𝑖(𝒙) whose inputs are regressors 𝒙 and do not contain any regression coefficients 𝜃_𝑖:

• 𝑦̂ = 𝜃₀ + 𝜃₁𝑓₁(𝒙) + … + 𝜃_𝑝𝑓_𝑝(𝒙)

function form are those that do NOT follow the form of linear regression models

as 𝑓_𝑖(𝒙) increases by one unit, the mean of the dependent variable 𝑦̂ always changes by a specific amount 𝜃_𝑖

as 𝑓_𝑖(𝒙) increases by one unit, the mean of the dependent variable 𝑦̂ changes by some ARBITRARY amount

relatively restricted in the shapes of the curves that it can fit

much more flexible in the shapes of the curves that it can fit

easier to use, simpler to interpret, and you obtain more statistics that help you assess the model

can require more effort both to find the best fit and to interpret the role of the independent variables

• R-Squared is valid for linear regression
• p-values can be calculated for the parameter estimates 𝜃_𝑖ˆ

• R-Squared is NOT valid for nonlinear regression
• p-values are impossible to calculate for the parameter estimates 𝜃_𝑖ˆ