Predicting extrapolated values and their errors

[#1]

I have a data set where log(y) is a linear function of x when y is grouped by a nominal variable. X varies from 44 to 107. R2 Adj = 0.98. Y is a measured quantity and x is exact. I want to find:

1. The predicted value of y when x = 0, and the associated uncertainty in this prediction (obviously I expect a significant degree of uncertainty as this would be extrapolating beyond my data set)

2. The predicted value of x when y = 50, and the associated uncertainty in this prediction (again this is extrapolating)

I don't particularly want to get the pen and paper out to use the prediction formula and all the algebra needed to calculate how the standard errors of the prediction parameters propagate into standard errors of y and x. This route also wouldn't be able to account for the widening of the confidence intervals due to extrapolation. So what would be the best way of using JMP to do this?

Although it is imprecise, it seems like the crosshair tool should be able to help by reading values from my fitted line and confidence intervals, however my fitted line only runs from around x = 40 to 100. Is there a way to extend the fitted line to other x values? And is there a way of checking whether my crosshair is actually on my fitted line or confidence intervals?

For Q1, maybe I could save the prediction formula and the confidence intervals to new columns, then add a row to my data table with x = 0 and see what the formula predicts for y and the CIs of y. However I don't see how I could address my Q2 this way...

Any thoughts appreciated.

Thanks,

Alex

[#2 · Accepted solution]

For Q2 you can use Estimates -> Inverse Prediction… under the upper left red triangle menu in the Fit Model report.

If you use the Fit Y by X platform you can get extended regression line and confidence lines by expanding the x-axis scale before fitting the line.

I don't think there is any way to be sure that the crosshair is exactly on the line, but you can use the magnifier tool to zoom in and get as close as you wish.