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Nonlinear Models and Linear Regression

In many cases, simple transformation of variables help to recast a non-linear model in a linear form. For instance, suppose we wish to fit certain kinetic data to the exponential model $ \hat{y}$ = $ \alpha$exp($ \beta$x). There are non-linear regression programs which accomplish this task, but we can use a linear regression procedure if we try to fit y* $ \equiv$ ln($ \hat{y}$) vs. x. This is because, we have ln($ \hat{y}$) = ln($ \alpha$) + $ \beta$x and letting y* = ln($ \hat{y}$) and $ \alpha^{*}_{}$ = ln($ \alpha$), we get y* = $ \alpha^{*}_{}$ + $ \beta$x. The linear regression procedure will give $ \alpha^{*}_{}$ and $ \beta$ for the best fit.

Michael Zeltkevic