A LOESS will always give a better fit than regression, unless the fit is perfect. It is a locally linear approximation that is designed to pass close to the data. These methods are basically exploratory. And while it is dangerous to extrapolate a linear model beyond the limits of the fit, you simple could not do it intelligently with a LOWESS.

If your model gives you negative costs, that's a pretty good sign that a linear regression is not appropriate on the variables you have. You say that you tried transformations. Did you take the log of cost against your predictors?

In the nature of things, it is unlikely that there is a simple relationship between cost and the variables you mention. Sometimes the purpose of a linear regression is simply to demonstrate that some sort of correlation exists, and perhaps to select a sensible set of predictors.

A LOESS will always give a better fit than regression, unless the data truly lie along a straight line. LOESS is a locally linear approximation that is designed to pass close to the data. These methods are basically exploratory. And while it is dangerous to extrapolate a linear model beyond the limits of the fit, extrapolation would be reckless in the case of LOESS.

If your model gives you negative costs, that's a pretty good sign that a linear regression is not appropriate on the variables you have. You say that you tried transformations. Did you take the log of cost against your predictors?

In the nature of things, it is unlikely that there is a simple relationship between cost and the variables you mention. Sometimes the purpose of a linear regression is simply to demonstrate that some sort of correlation exists, and perhaps to select a sensible set of predictors.