Hi @Chantal,
Yes, you have a singularity in your model, as the intercept is a linear combination of some of the terms, so it can't be estimated independently, creating the error in the prediction profiler you mentioned.
One possible option to create your responses' model is to launch the platform "Fit Model" from the script "Model" in the datatable provided, but switch the model personality from "Standard Least Squares" to "Stepwise Regression". This way, you'll be able for each response to test which terms are significant, and get more reliable models. Click on CTRL+"Go" to launch stepwise regression on all responses, and on CTRL+"Run Model" to open a "Fit Group" platform containing each model for the responses. Once the stepwise regression is done, you can still remove manually terms in each response's model if needed from the generated "Fit Response/Model" platform.
See script "Stepwise analysis" in your datatable to see the results for each of the 4 responses and the prediction profiler.
For more infos about Stepwise regression and how to use it, you can search here : Stepwise Regression Models (jmp.com)
I hope this first answer will help you,
Victor GUILLER
L'Oréal Data & Analytics
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)