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.