I think that setting up Nonlinear, as previously described, is straight-forward but the results may disappoint you.
- You have collinear predictor variables, so all model fitting procedures will have difficulty except PLS.
- The non-linear model that you specified will require careful attention to the starting values, as stated previously. Is there a theoretical basis for such a model?
- The non-linear model parameters will be highly correlated, as stated previously, which will further hamper fitting procedures.
I tried fitting a linear model using ordinarly least squares regression based on a second-order polynomial function with second-order cross terms. I achieved a reasonably good fit after removing non-significant terms. This result shows no particular problem in the residual analysis except that there is a large component of random errors in the pricing.
![Capture.PNG Capture.PNG](https://community.jmp.com/t5/image/serverpage/image-id/6126i06EA3F05E83025E4/image-size/large?v=v2&px=999)
There is also apparently a noticeable right skew in the distribution of the residuals, so a GLM with non-Gaussian distribution might improve the fit. This fit has R square of 0.95, which is quite good. The effects of the predictors through this model seem reasonable, too, and quite interpretable:
![Capture.PNG Capture.PNG](https://community.jmp.com/t5/image/serverpage/image-id/6128iB0011262808DA7E0/image-size/large?v=v2&px=999)
Interestingly, the Neural model using 4-6 hidden nodes gives similar results, which is encouraging:
![Capture.PNG Capture.PNG](https://community.jmp.com/t5/image/serverpage/image-id/6130i379152D49687E6B5/image-size/large?v=v2&px=999)
The residuals show do particular problem.
![Capture.PNG Capture.PNG](https://community.jmp.com/t5/image/serverpage/image-id/6129i17FB7D7246CA171E/image-size/large?v=v2&px=999)
The prediction profiles are quite similar except for Lot Size, but I did not spend a lot of time on my model selection using Fit Least Squares.
It seems to come down to which is more important, fitting a particular non-linear model or predicting. The former will be very difficult with results that are likely no better in performance than alternative models. The latter does not provide theoretical rigor but is likely to perform as well as can be expected.