How to extract (predict) value in JMP?

[#1]

How can I extract the estimated value of of y @x=4.5? This is a simplified example of the problem i am facing. 

[#2]

There are a number of ways, but I would: Run the fit Y by X platform.  Then fit the appropriate curve (I did a cubic).  The from the red triangle next to the "Polynomial fit Degree=3", Save Predicted. This will save the model to the data table.  Then just enter 4.5 in an open row for X.  I attached the data table with the script and prediction formula saved.  You can also re-run with a different model.

[#3]

Another approach, but similar. It looks like you just did a piece-wise fit. In other words, straight lines between each data point. So if you truly want the mid-point of 4 and 5, exclude all rows in the table EXCEPT 4 and 5. Use Fit Y by X and fit that straight line and follow @statman 's suggestion of saving the prediction formula.

Or you could use Fit Model to fit between 4 and 5 and use the prediction profiler to drag the X-value to get the most flexibility.

So many choices depending on what you are really trying to accomplish.

[#4]

One way is to use the Crosshairs tool

Another way is to use the Interpolate() function in JSL to find the value

names default to here(1);
dt=current data table();

xMat = :x << get values;
yMat = :y << get values;

yi= interpolate( 4.5, xMat, yMat);
show(yi);

/*:

//:*/
names default to here(1);
dt=current data table();

xMat = :x << get values;
yMat = :y << get values;

yi= interpolate( 4.5, xMat, yMat);
show(yi);
/*:

yi = 2.65;

[#5]

Please have a look at
https://community.jmp.com/t5/Discussions/How-to-get-exact-cumulative-Prob-at-specified-value-in-CDF-... 

In this post, @jthi  shows some JSL/Graph Builder magic : )

[#6]

Do you need the exact value at 4.5 - or is this an example and you want to get a dynamic reading depending on the current position of the mouse?

Here is a wish to give a Crosshair the ability to snap on a smoother-ed curve 

You could vote there and add the comment to provide a similar functionality also for line graphs.

a related post (no interpolation - but with appealing dynamic effect):
https://community.jmp.com/t5/Discussions/Can-JMP-graphics-have-this-effect/m-p/813471/highlight/true...