nav[aria-label="Primary Navigation"] { padding: 0; & ul { list-style: none; width: 100%; display: flex; flex-direction: row; justify-content: start; align-items: start; gap: 30px; padding: 0; & li { margin: 0; } & ul li { list-style: none; } } }

Table-Lookup Methods in JMP?

DaeYun_Kim

Dear All,

One of my customers wanted to know whether JMP can do the "Table-Lookup Methods".

Unfortunately, I have no idea with this method, so I have to ask whether JMP can do this or not.

Here's simple sample data. I made not perfect relation(y=2x), and when I fitted using Fit Y by X, the equation is Y = 0.22 + 1.9636364*X. I have attached sample JMP data table.

If I draw the graph, you can see the actual y-value and predicted value below.

Here is the thing. Even if I fitted simple linear regression, but my customer didn't want to use the predicted value.

For example, he just wanted to know that JMP can predict below y-value, 3.1 when x is 1.5.

If he use the fitted equation, he can simply calculate y-value when x is 1.5, and the predicted value is 3.1654546.

That is, he wanted to keep the original y-value of x's and he wanted to estimate like below.

When you draw lines between x=1 and x=2, then estimate y-value on the drawn line.

Above is a very simple case when the order is 1st. My customer wanted to expand 2nd, 3rd, 4th order.

Is it possible in JMP?

I'm wondering whether I expressed correctly or not.

Thanks in advance

Sample.jmp

Accepted answers

XanGregg

It sounds like they want an equation for the poly-line that connects the points. You can get that with the Interpolate() function. A formula for row number vs. height in Big Class might be:

Interpolate(Row(), Index( 1, 40 )`, :height << Get Values())

I don't think we have higher order interpolations built-in such as quadratic or cubic, but you may be able to get a smooth curve through all the points by using a cubic spline fit with extreme flexibility.

tight spline.png

Then you can Save Formula in the Smoother red triangle menu and get something like:

Spline Eval(
	(Row() - 20.5) / 11.6904519445001,
	[-1.66802789939819 59.0183447680287 67.0542214924897 0 -6114.92267621147,
	-1.58248800712136 60.9268154536107 -67.1757884730832 -1569.20948101439
	18279.9261202017,
	-1.49694811484453 55.1400210864711 65.6308625267318 3121.77925244172
	-28393.7693701355,
	-1.4114082225677 65.8246580886567 -23.5736797641351 -4164.62066732922
	30053.5344109193,
	-1.32586833029087 52.1458907102262 -76.3443553068368 3547.70762082262
	-18576.7023311001,
	-1.24032843801404 59.9470503756883 122.815429439912 -1219.43972796528
	-926.827560568223,
	-1.15478854573721 60.9498363629197 -106.151051728446 -1457.28191703613
	15794.3847995258,
	-1.06924865346038 51.0923799351482 -8.75652033434328 2595.86800595864
	-14998.926916498,
	-0.983708761183547 59.9496511528336 106.099281663174 -1253.15177216108
	1784.02213896353,
	-0.898168868906717 60.9725914678676 -69.128191944071 -795.336587401361
	10920.1995164073,
	-0.812628976629887 56.074808274755 34.517492737342 2007.00148342636
	-14015.8920685629,
	-0.727089084353056 64.940237609938 70.2089506643812 -1589.75220970287
	5904.90461874832,
	-0.641549192076226 63.0094599936372 -72.1456573804648 -74.4374947232843
	2751.57340636646,
	-0.556009299799396 58.0156779748937 -24.4800160933476 631.670383594554
	-2474.41822487614,
	-0.470469407522566 58.9948960001446 29.2695194216624 -3.31402161727232
	-773.084939751894,
	-0.384929515245736 60.9904834598012 11.7324001033135 -201.702829019121
	2399.09512650552,
	-0.299389622968906 62.0197949422314 29.8881873234231 413.952187030946
	-4199.21895063639,
	-0.213849730692075 64.9770476346172 8.52906133096856 -663.650023022914
	3451.56951030417,
	-0.128309838415245 63.0109898982455 -29.2418816444876 222.090629270203
	-211.729904869771,
	-0.0427699461384151 62.0021737803252 4.10560574334321 167.756569507118
	-936.323346594096,
	0.0427699461384151 62.9948076189749 12.2519241965941 -72.5224251049424
	794.470328437968,
	0.128309838415245 64.0094442940094 17.2843959097936 131.354293830426
	-2353.62767470502,
	0.213849730692075 64.9759391904696 -11.9085375389192 -472.632879432277
	5666.64216876905,
	0.299389622968906 64.0457554984761 31.6232374185545 981.539002632721
	-9585.19065658272,
	0.384929515245736 67.9334098676484 -10.8619056489616 -1478.20952602063
	12611.5201272486,
	0.470469407522566 64.0816876317685 13.0845738100385 1758.15469337836
	-14617.6904622184,
	0.556009299799396 68.9162506116075 -7.00683213237878 -1993.03230904802
	13298.7723352415,
	0.641549192076226 62.0574472671871 -56.0500993990532 1419.69434986733
	-5850.31672709992,
	0.727089084353056 63.9892123433098 58.4093174157582 -81.6120379985711
	-2254.43116371026,
	0.812628976629887 66.977325622374 -5.04036581175411 -660.143434667063
	5303.69471162635,
	0.898168868906717 65.035446734542 -1.55499554849997 700.888988239435
	-6511.88346904176,
	0.983708761183547 65.9550899812104 -24.5908419112682 -970.188443145545
	8458.12279413183,
	1.06924865346038 62.0466052047974 -4.9043616258981 1200.33229487934
	-7076.94547163824,
	1.15478854573721 65.9805340170929 45.1006452509867 -615.751165001277
	-588.284502618647,
	1.24032843801404 64.9647337828676 -73.1554936486288 -766.716543947811
	11167.1212081812,
	1.32586833029087 60.086419282381 40.8067341591618 2098.98649162542
	-17639.3062521174,
	1.4114082225677 67.8949897678514 12.6966073442869 -2427.60657831152
	17364.1044640538,
	1.49694811484453 62.0863028779283 -21.4545343309934 2028.3642977093
	-11403.5215120075,
	1.58248800712136 67.9552913662762 75.2363887951914 -898.003707434553
	3499.35639591204,
	1.66802789939819 70.0104980691878 0 0 0],
	0
)

Savitzky-Golay doesn't guarantee the curve will go through all the data points.

All comments

ian_jmp

Please see @XanGregg 's response below . . .

If I understand correctly, this is a version of Savitzky-Golay (SG), in which one fits a local polynomial to the data. Usually, this is applied to smooth the data (generate new Y values at existing X values), but not, in my experience at least, to interpolate (get Y values in between existing X values), which is what's required here I think.

Can JMP do this? I'm sure it can, but the generality of what's needed will determine how much work it would take. It might not be too hard to come up with a formula (at least for simple cases), and such a formula would make interpolation easy just by appending new rows. Alternatively, the code for my very old SG add-in might provide a starting point.

Finally, be aware that in JMP 16 @XanGregg has added SG smoothing to Graph Builder, but I don't think it helps in this case because, even if a formula is calculated internally, it's not available through messaging the line segment that's drawn.

Cheers, and for those to which this applies, 'Happy Easter',

Ian

XanGregg

It sounds like they want an equation for the poly-line that connects the points. You can get that with the Interpolate() function. A formula for row number vs. height in Big Class might be:

Interpolate(Row(), Index( 1, 40 )`, :height << Get Values())

tight spline.png

Then you can Save Formula in the Smoother red triangle menu and get something like:

Spline Eval(
	(Row() - 20.5) / 11.6904519445001,
	[-1.66802789939819 59.0183447680287 67.0542214924897 0 -6114.92267621147,
	-1.58248800712136 60.9268154536107 -67.1757884730832 -1569.20948101439
	18279.9261202017,
	-1.49694811484453 55.1400210864711 65.6308625267318 3121.77925244172
	-28393.7693701355,
	-1.4114082225677 65.8246580886567 -23.5736797641351 -4164.62066732922
	30053.5344109193,
	-1.32586833029087 52.1458907102262 -76.3443553068368 3547.70762082262
	-18576.7023311001,
	-1.24032843801404 59.9470503756883 122.815429439912 -1219.43972796528
	-926.827560568223,
	-1.15478854573721 60.9498363629197 -106.151051728446 -1457.28191703613
	15794.3847995258,
	-1.06924865346038 51.0923799351482 -8.75652033434328 2595.86800595864
	-14998.926916498,
	-0.983708761183547 59.9496511528336 106.099281663174 -1253.15177216108
	1784.02213896353,
	-0.898168868906717 60.9725914678676 -69.128191944071 -795.336587401361
	10920.1995164073,
	-0.812628976629887 56.074808274755 34.517492737342 2007.00148342636
	-14015.8920685629,
	-0.727089084353056 64.940237609938 70.2089506643812 -1589.75220970287
	5904.90461874832,
	-0.641549192076226 63.0094599936372 -72.1456573804648 -74.4374947232843
	2751.57340636646,
	-0.556009299799396 58.0156779748937 -24.4800160933476 631.670383594554
	-2474.41822487614,
	-0.470469407522566 58.9948960001446 29.2695194216624 -3.31402161727232
	-773.084939751894,
	-0.384929515245736 60.9904834598012 11.7324001033135 -201.702829019121
	2399.09512650552,
	-0.299389622968906 62.0197949422314 29.8881873234231 413.952187030946
	-4199.21895063639,
	-0.213849730692075 64.9770476346172 8.52906133096856 -663.650023022914
	3451.56951030417,
	-0.128309838415245 63.0109898982455 -29.2418816444876 222.090629270203
	-211.729904869771,
	-0.0427699461384151 62.0021737803252 4.10560574334321 167.756569507118
	-936.323346594096,
	0.0427699461384151 62.9948076189749 12.2519241965941 -72.5224251049424
	794.470328437968,
	0.128309838415245 64.0094442940094 17.2843959097936 131.354293830426
	-2353.62767470502,
	0.213849730692075 64.9759391904696 -11.9085375389192 -472.632879432277
	5666.64216876905,
	0.299389622968906 64.0457554984761 31.6232374185545 981.539002632721
	-9585.19065658272,
	0.384929515245736 67.9334098676484 -10.8619056489616 -1478.20952602063
	12611.5201272486,
	0.470469407522566 64.0816876317685 13.0845738100385 1758.15469337836
	-14617.6904622184,
	0.556009299799396 68.9162506116075 -7.00683213237878 -1993.03230904802
	13298.7723352415,
	0.641549192076226 62.0574472671871 -56.0500993990532 1419.69434986733
	-5850.31672709992,
	0.727089084353056 63.9892123433098 58.4093174157582 -81.6120379985711
	-2254.43116371026,
	0.812628976629887 66.977325622374 -5.04036581175411 -660.143434667063
	5303.69471162635,
	0.898168868906717 65.035446734542 -1.55499554849997 700.888988239435
	-6511.88346904176,
	0.983708761183547 65.9550899812104 -24.5908419112682 -970.188443145545
	8458.12279413183,
	1.06924865346038 62.0466052047974 -4.9043616258981 1200.33229487934
	-7076.94547163824,
	1.15478854573721 65.9805340170929 45.1006452509867 -615.751165001277
	-588.284502618647,
	1.24032843801404 64.9647337828676 -73.1554936486288 -766.716543947811
	11167.1212081812,
	1.32586833029087 60.086419282381 40.8067341591618 2098.98649162542
	-17639.3062521174,
	1.4114082225677 67.8949897678514 12.6966073442869 -2427.60657831152
	17364.1044640538,
	1.49694811484453 62.0863028779283 -21.4545343309934 2028.3642977093
	-11403.5215120075,
	1.58248800712136 67.9552913662762 75.2363887951914 -898.003707434553
	3499.35639591204,
	1.66802789939819 70.0104980691878 0 0 0],
	0
)

Savitzky-Golay doesn't guarantee the curve will go through all the data points.

ian_jmp

Doh! "Savitzky-Golay doesn't guarantee the curve will go through all the data points": @XanGregg is quite right, of course.

ian_jmp

In so far as the Gaussian Process can be made to interpolate between fixed (X, Y) values, and produces a formula, it might possibly be of interest too.

Sample with GP.jmp

DaeYun_Kim

Dear @ian_jmp and @XanGregg

Thanks for your professional opinions and comments. I will share your comments and answers to my customer.

Thanks again and stay safe.

Best

DaeYun