You might try one of these two approaches. Both of them are based on the logit transform of the response Y. The logit expects an argument [0, 1] for the constraint you want but produces a response [-infinity, infinity] that regression requires.
I mocked up some data to illustrate this approach.
![table.PNG table.PNG](https://community.jmp.com/t5/image/serverpage/image-id/38094i2EECECF8198A6A27/image-size/large?v=v2&px=999)
Apply the Logit transform to the response Y in the Fit Model dialog. Select Analyze > Fit Model and enter the data columns in the respective analysis roles. Select the column in the Y role, then click the red triangle next to Transform and select Logit.
![logit.PNG logit.PNG](https://community.jmp.com/t5/image/serverpage/image-id/38095i49049F3DB1114F53/image-size/large?v=v2&px=999)
Your result will be familiar, you can use the Profiler for example, but the constraint should apply.
![fit least squ.PNG fit least squ.PNG](https://community.jmp.com/t5/image/serverpage/image-id/38096iAA3A7759E6011EAA/image-size/large?v=v2&px=999)
The other approach is to use a Generalized Linear Model. Start as before but do not apply the transformation. Instead, click Personality and select Generalized Linear Model. Click Distribution and select Normal. Click Link and select Logit.
![glm.PNG glm.PNG](https://community.jmp.com/t5/image/serverpage/image-id/38097i6625D4ECC89CFD5A/image-size/large?v=v2&px=999)
![glm result.PNG glm result.PNG](https://community.jmp.com/t5/image/serverpage/image-id/38098iBD6F6296B2E1C80F/image-size/large?v=v2&px=999)