Common Errors in Statistics (and How to Avoid Them), 4th Edition

LINEAR VERSUS NONLINEAR REGRESSION

Linear regression is a much misunderstood and mistaught concept. If a linear model provides a good fit to data, this does not imply that a plot of the dependent variable with respect to the predictor would be a straight line, only that a plot of the dependent variable with respect to some not-necessarily monotonic function of the predictor would be a line.

For example, y = A + B log[x] and y = A cos(x) + B sin(x) are both linear models whose coefficients A and B might be derived by OLS or LAD methods. Y = Ax⁵ is a linear model. Y = x^A is nonlinear.