Capability from a bivariate regression

[#1]

Hi

I read this post by Phil Kay, and it helped we some of the way towards my goal:

https://community.jmp.com/t5/Discussions/Tolerance-Interval-for-Regression/m-p/302845

Would it also be possible to calculate an expected capability from a bivariate regression, if I have a lower and upper spec limit?

Example: I have data measured for and Response(Y) at several different temperature levels (X) and I want to predict what the capability of the response is at a higher temperature.

Thanks

[#2]

I was just sitting here, looking at the numbers, and maybe I have an idea. What if:

1. I use the regression line to calculate the Response(Y) at the higher temperature (let's say 60degC):  Y(60)
2. I "transform" my spec limits to a set of spec limits for the residuals: Ymin - Y(60) and Ymax - Y60)
3. Now, I can calculate the capability with the "residual spec limits"

Or, something completely different?

[#3]

Here's what I suggest: Recreate the model in the Fit Model Standard Least Squares platform, then use the simulation capability within the Prediction Profiler to simulate the response for assumed variances of the x values. From there lots of options to export the simulated predictions to the Capability platforms in JMP for additional analysis and visualizations.

[#4]

Hi P_Bartell

Thank you for the suggestion. In my case, I want to fix the x value (at an extrapolated point) and estimate the mean and variance at this point, and thus the capability. So I am not sure you suggestion would serve the purpose, as I want to see the variation in the other dimension than you suggested. Or?

[#5]

The simulator allows you to set any independent variable at any mean and estimated variance. So even if your x set point is extrapolated from your empirical space...the simulator will still work.

[#6]

I still think that it's not what I am looking for. Allow me to elaborate

I can fit a model to my Response as a function of the temperature:

But I would like to calculate: If I fix the temperature to 80 degrees, what will the distribution of the response be?