Home / DOE / Charts / Observed vs Predicted / Observed vs Predicted How-To
Observed vs Predicted How-To¶
This walkthrough draws all sixteen runs against their fitted values, and finds the one run the model struggles with.
Every chart in this family is drawn from a fitted model, so the walkthrough starts by building one. The same experiment is used on all ten chart walkthroughs, so once you have the regression sheet you can work through any of the others without setting the data up again.
The data is on this page rather than in a file to download. Press Copy for Excel, then paste it into a blank worksheet.
The data¶
A three factor experiment on a bonding process, run twice through. Temp is in degrees C, Press in psi and Time in seconds, and the response Strength is the peel strength of the finished bond. Each of the eight factor combinations was run twice, giving 16 runs.
| Temp | Press | Time | Strength |
|---|---|---|---|
| 180 | 40 | 10 | 49.5 |
| 220 | 40 | 10 | 65.4 |
| 180 | 60 | 10 | 61.8 |
| 220 | 60 | 10 | 66.8 |
| 180 | 40 | 20 | 52.3 |
| 220 | 40 | 20 | 70.7 |
| 180 | 60 | 20 | 60.7 |
| 220 | 60 | 20 | 70.0 |
| 180 | 40 | 10 | 50.6 |
| 220 | 40 | 10 | 66.4 |
| 180 | 60 | 10 | 61.2 |
| 220 | 60 | 10 | 67.2 |
| 180 | 40 | 20 | 51.4 |
| 220 | 40 | 20 | 67.1 |
| 180 | 60 | 20 | 61.9 |
| 220 | 60 | 20 | 71.6 |
Each factor takes exactly two values, so this is a full factorial of the three at two levels each, replicated once. That matters for more than one chart: a factor with exactly two observed values is the only kind that can carry a Cube Plot axis, and a design with centre points would have failed that test.
Steps¶
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Put the data in Excel
Press Copy for Excel above the table. In Excel, open a blank worksheet, click cell A1, and press Ctrl+V. You should have headers in row 1 and the 16 runs in rows 2 through 17.
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Make a design sheet to hold it
From the Excel ribbon: QXL DOE New > Create Design > Special > Create Custom Design.
On the first page set the number of factors to 3 and the number of runs to 16. On the second page set the number of outputs to 1. That gives you an empty design sheet of the right shape, which is how data collected outside Quantum XL gets analysed.
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Fill in the design sheet
Copy the four columns of data into the three factor columns and the one output column. Name the factors Temp, Press and Time, and the output Strength, so the names on your charts match the ones quoted below.
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Check the model holds the three two-factor interactions
The charts below assume a model of the three main effects plus AB, AC and BC. Add any that are missing with QXL DOE New > Modify Design > Inputs > Add/Remove Interactions.
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Run the regression
QXL DOE New > Analyze Design > Run Regression. A worksheet called Regression is added after the design sheet. Every chart in this family reads that sheet.
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Draw the plot
QXL DOE New > Charts > Regression > Observed vs Predicted.
In the Outputs tree tick Strength Y-Hat. The panel on the right holds only a description; there is nothing to set. Press Create.
Check the fit first¶
Before drawing anything, check the coefficient table on the Regression sheet against this. If these numbers match, every chart number quoted further down will match too; if they do not, the design was not entered the way this walkthrough assumes and nothing below will line up.
| Term | Coefficient | Standard error | t | p |
|---|---|---|---|---|
| Constant | 62.1625 | 0.2912 | 213.477 | 0.000000 |
| Temp (A) | 5.9875 | 0.2912 | 20.562 | 0.000000 |
| Press (B) | 2.9875 | 0.2912 | 10.260 | 0.000003 |
| Time (C) | 1.0500 | 0.2912 | 3.606 | 0.005696 |
| AB | -2.2375 | 0.2912 | -7.684 | 0.000030 |
| AC | 0.6500 | 0.2912 | 2.232 | 0.052506 |
| BC | -0.1500 | 0.2912 | -0.515 | 0.618877 |
The fitted equation is
Strength = 62.1625 + 5.9875 A + 2.9875 B + 1.0500 C - 2.2375 AB + 0.6500 AC - 0.1500 BC
in coded units, where each factor runs from -1 at its low value to +1 at its high value.
Every standard error is the same 0.2912. That is not a coincidence and it is a useful sign that the design was entered correctly: on a balanced full factorial every coded column is orthogonal to every other and carries the same amount of information, so every coefficient is estimated equally precisely.
What you should see¶
A worksheet called Observed vs Predicted holding one scatter of sixteen points, one per run, with a 45 degree reference line through them.
Observed is on the horizontal axis. This is the reverse of the arrangement most people expect, and it matters for reading the chart: a run the model under-predicts sits below the line, not above it. Check the axis titles before drawing any conclusion.
| Value | |
|---|---|
| Points | 16 |
| Smallest value on either axis | 49.5000 |
| Largest value on either axis | 71.6000 |
| Axis range, both axes | 45 to 75 |
| Tick spacing, both axes | 5 |
Both axes carry the same scale, and that is deliberate. It is what keeps the reference line at a true 45 degrees on the page, so the distance of a point from the line reads as the size of the error. The range is computed once from the observed and the predicted values pooled together.
The points hug the line. The model explains almost all of the variation here, so the scatter is tight.
The one run to look at¶
Run 14 sits furthest below the line. It was measured at 67.1 and the model predicts 69.25, so it falls 2.15 short, the largest miss on the chart in either direction.
Run 14 is worth understanding rather than just noting, and its neighbour explains it:
| Run | Temp | Press | Time | Observed | Predicted |
|---|---|---|---|---|---|
| 6 | 220 | 40 | 20 | 70.7 | 69.2500 |
| 14 | 220 | 40 | 20 | 67.1 | 69.2500 |
Those two runs are the same design point measured twice, and they disagree by 3.6. The model has one prediction for that combination, 69.25, so it lands between them and both runs get a large residual of opposite sign. Run 6 is 1.45 above the line and run 14 is 2.15 below it.
That is a measurement disagreement, not a model failure. No fitted surface can pass through two different responses at identical settings, and this design has eight such pairs. The chart is showing you the repeatability of the experiment.
Things to try next¶
- Look at the same runs as residuals. Residual Plots How-To plots the gap from the line directly, and reports the scaled forms that say how unusual run 14 really is.
- Draw the standard deviation model. If the design has a usable S-Hat model, ticking Strength S-Hat plots the per-group standard deviations against their fitted values. It will not have sixteen points, because an S-Hat model is fitted to one value per replicate group rather than one per run.
- Nothing to configure. There are no set points on this dialog. Every point sits at the settings its own run used, which is why the extrapolation prompt can never appear here.