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:<math>Y_i = \beta_0 + \beta_1 \phi_1(X_{i1}) + \cdots + \beta_p \phi_p(X_{ip}) + \varepsilon_i \qquad i = 1, \ldots, n </math>
where <math> \phi_1, \ldots, \phi_p </math> may be [[Nonlinear system|nonlinear]] functions. In the above, the quantities ''ε<sub>i</sub>'' are [[Random variable|random variables]] representing errors in the relationship. The "linear" part of the designation relates to the appearance of the [[regression coefficient]]s, ''β<sub>j</sub>'' in a linear way in the above relationship. Alternatively, one may say that the predicted values corresponding to the above model, namely
:<math>\hat{Y}_i = \beta_0 + \beta_1 \phi_1(X_{i1}) + \cdots + \beta_p \phi_p(X_{ip}) \qquad (i = 1, \ldots, n), </math>
are linear functions of the ''β<sub>j</sub>''.
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