Can I add an intercept line to a linear regression graph (possibly using crosshair tool?)

[#1]

Hello,

I have made a simple linear regression plot in JMP using Analyze > Fit Y by X. I have several data points plotted, with the x-axis being time and the y-axis being the parameter I'm measuring at each time point. I used Fit Line to add the simple regression line. I have also plotted my 95% confidence interval lines around the data (using Confid Curves Fit on the Linear Fit red triangle menu), and as well as that, I have included my lower and upper spec limits as the LSL and USL lines (plotted using Analyze > Quality and Process > Manage Spec Limits). The data show an increase over time, and the trend is significant. My data points fall within my spec lines, but there is a point where my 95% confidence interval line intersects the USL line.

My aim is to be able to show, on the graph, the x-value for where this intersection occurs, i.e. at what time point (measured on x-axis) the 95% confidence interval breaches the USL (not where the regression line would be predicted to intersect it). I've looked in all the red triangle menus and can't see anything to add this. I can use the Crosshairs tool to physically click where this confid line intersects the USL, but this is just a temporary look that only lasts as long as I hold down the mouse button. If possible, I would like to have a vertical line coming down from the intersection point of the lines to the x-axis (thus displaying the x-value at the intersection), or even if this could be listed on the stats and figures beneath the graph that would be fine too. I have seen plenty of help examples with extrapolation and predictions for the future, but this is not what I'm doing here; I'm just trying to visually pinpoint where this confid line-USL line intersect is from a data time point that's already been measured.

It feels like this should be a really simple thing to add, so I'm hoping someone is able to help. I'm on JMP 16.1.0. At the moment, the closest I can get to doing this is clicking on the upper confidence interval line and USL line interception point with the Crosshairs tool, and taking a screen grab at the same time, but I'm sure there must be a simple way JMP can show this intercept - especially as I know the USL point (i.e. the y-value of the intercept I want) so if I know the y, the x can be calculated, but I just don't have this particular equation of the confid line stated anywhere.

Would really appreciate any help or tips on this, thanks in advance for any help you can offer.

[#2]

This is knowns as a 'calibration' problem or 'inverse prediction.' Are you determining expiry?

Try using Fit Least Squares platform. Select Analyze > Fit Model. Assign the data column with the parameter values and click Y. Select the data column with time and click Add. Standard Least Squares should be automatically selected for you as the fitting personality. Click Run.

The common results should match what you obtained in Bivariate platform. Click the red triangle at the top and select Estimates > Inverse Prediction.

This way is different than what you asked for, but I think that it will give you what you actually want. The result is the lower or upper bound on X given the regression line and the standard error of the predicted response.

[#3]

Hi Mark,

Thanks so much for your help on this and taking the time to answer my question. Yes, it is for determining expiry. Before seeing your post, I had managed to get a slight work around with the way I originally did the bivariate fit Y by X plots - this was by setting the crosshairs tool at my (known) USL value for the intercept with the confid curve, and using this tool to view the x-value at that point, then I clicked on the x-axis menu to input a reference line here and manually entered the x-value I'd viewed (I didn't know I could add lines to graphs in this way, so I learnt something new there as well!). I know this is really not a very sophisticated way of doing it, but for the purposes of producing a very quick and straightforward visual for a report, it seemed to be fine for the time being. 

Your method gives me a whole lot of information and plots which look really useful, but I'll need to read up on these different statistical assessments to understand them better. As you suggested, it's reassuring that I can see the same results from the analysis done through the bivariate platform, e.g. significance as Prob > F/Prob>|t| matches what I got previously, so I can follow some parts of it. I can also see the value I got using the Crosshairs tool in the stats/test box under Inverse Prediction (specifically the Lower 95% value) and I've checked this on 3 separate sets of data so I think I have a basic grip of what's going on. Although both methods seem to lead to the same result, what you have suggested looks like a better approach. It might take a while for me to get a handle on this, but thank you.

Do you know of any learning materials or training videos that specifically discuss this Fit Least squares platform and specifically this Inverse Prediction analysis?

[#4 · Accepted solution]

There is a free on-line JMP training course called "Statistical Thinking for Industrial Problem Solving." It is arranged in seven modules. One of the modules addresses regression and uses Fit Least Squares.

I cannot remember now if that course covers inverse prediction. You will find the JMP Help about inverse prediction here.

Another useful platform is Degradation. It is applied to many situations, including determining expiry. Be aware that the terminology and labels are mainly from reliability, but the methods and the results are the same for stability.

There is also a JMP training course about stability analysis that covers both of these topics in the context of compliance with ICH Q1A and Q1E.