Entry 1: 600 fruit from three seasons, a fourth season held back
We want to predict dry matter in whole fruit from a scan. 600 fruit from three seasons build the model; 100 from a fourth season test it.
Dry matter by laboratory, 10.9 to 22.9 % in calibration, 12.0 to 23.8 % in the unseen season.
The two seasons overlap but the fourth runs higher on average.
Check that your own test set covers a different season, lot or range.
What the laboratory measured
Each bar is the share of fruit in a dry-matter range.
Source: Spectra Lab engine run, 9 Oct 2026, mango teaching subset (CC BY 4.0).
Where the data comes from
Anderson, Walsh, Subedi and Hayes (2020), Postharvest Biology and Technology 168; dataset licensed CC BY 4.0 (Mendeley Data, doi 10.17632/46htwnp833). Teaching subset: 600 calibration and 100 unseen-season spectra, 684 to 990 nm, 103 points.
Entry 2: every fruit gives a curve, and the curves look alike
The instrument records absorbance at 103 wavelengths. The line is the mean; the band is one standard deviation across fruit.
Absorbance at 103 wavelengths for each of 600 fruit.
The mean curve falls steeply at the short end and rises again at the long end; the band shows how much fruit differs at each wavelength.
Plot your own spectra before modelling. Odd curves here are easier to fix than odd predictions later.
What the instrument saw
Source: Spectra Lab engine run, 9 Oct 2026, mango teaching subset (CC BY 4.0).
Entry 3: the same data gave 1.00 with a 1st derivative and 1.20 with SNV
Four pipelines, one model type, one unseen season. SNV was about 20 % worse than the 1st derivative here; on other data the order can change.
Raw spectra and three corrections, each fitted on the calibration fruit only.
Derivatives remove the height and slope differences. The lowest unseen-season error came from the 1st derivative.
Compare on your own data. Do not carry a choice over from someone else's.
Drag from raw to corrected
Raw spectra: the curves differ mostly by height and slope.
Source: Spectra Lab engine run, 9 Oct 2026, mango teaching subset (CC BY 4.0). Twelve of the 600 calibration fruit, coloured from low to high dry matter.
Error by preprocessing
Source: Spectra Lab engine run, 9 Oct 2026, mango teaching subset (CC BY 4.0).
All the numbers
Bias is predicted minus reference; SEP is the error after removing the bias.
| Pipeline | Components | RMSECV | RMSEP | Bias | SEP | RPD |
|---|---|---|---|---|---|---|
| Raw spectra | 11 | 0.867 | 1.059 | -0.206 | 1.044 | 2.78 |
| 1st derivative | 10 | 0.853 | 0.999 | -0.187 | 0.987 | 2.94 |
| 2nd derivative | 9 | 0.892 | 1.028 | -0.028 | 1.033 | 2.81 |
| SNV | 10 | 1.005 | 1.197 | +0.038 | 1.202 | 2.42 |
Entry 4: the error stops falling around 10 components, and the smoothing window barely matters
The Lab fits 1 to 15 PLS components and picks the lowest cross-validated error. The slider shows what each number does to the error on the unseen season.
PLS with 1 to 15 components on each pipeline, and seven smoothing windows from 5 to 31 points.
Both errors are flat from about 9 components. The window changes the error by about 0.04.
Stop where the curve goes flat. A simpler model transfers better.
Drag the number of components
10 components with 1st derivative.
Source: Spectra Lab engine run, 9 Oct 2026, mango teaching subset (CC BY 4.0).
Drag the smoothing window
Window 11 points: the Lab default.
Source: Spectra Lab engine run, 9 Oct 2026, mango teaching subset (CC BY 4.0). 1st derivative, engine Savitzky-Golay with a 2nd-order polynomial.
Entry 5: on a season the model never saw, the typical error is 1.00 % and the model under-predicts by 0.19
100 fruit from a season the model never saw: predicted dry matter against the laboratory value.
Predictions from the model for 100 fruit in the fourth season, against the laboratory values.
Most points sit near the dashed line. High values run low, which is why the slope is below 1.
Report the number from data the model never saw, with its bias.
Predicted against reference
1st derivative: typical error 1.00 % dry matter, bias -0.19, error after removing bias 0.99, RPD 2.94, which the Lab bands as rough quantitative.
Source: Spectra Lab engine run, 9 Oct 2026, mango teaching subset (CC BY 4.0). 100 fruit from a season the model never saw. RPD here is the spread of the reference values divided by the error after removing bias.
What the numbers say
| Statistic | Value | What it tells you |
|---|---|---|
| RMSEP | 0.999 % | typical error on new samples |
| Bias | -0.187 % | average predicted minus reference |
| SEP | 0.987 % | error after removing the bias |
| RPD | 2.94 | spread of reference divided by SEP |
| Slope | 0.855 | 1.000 would mean predictions scale perfectly with reference |
| R² | 0.886 | squared correlation, reference and predicted |
Entry 6: rough quantitative, RPD 2.94
The Lab sorts models by RPD into four bands. Whether the band is enough depends on what you need it for.
RPD on the unseen season, with the Lab's bands: below 1 no predictive value, 1 to 2 screening only, 2 to 3 rough quantitative, 3 or more quantitative.
The model is 2.94, just under the quantitative line.
Put your own limit in and read the verdict.
Where the model sits
Source: Spectra Lab engine run, 9 Oct 2026, mango teaching subset (CC BY 4.0).
Is that good enough for you?
Your limit is 1.00; 1st derivative gives a typical error of 1.00 on a season it never saw, and an RPD of 2.94 (rough quantitative).
Source: Spectra Lab engine run, 9 Oct 2026, mango teaching subset (CC BY 4.0). Your limit is your own requirement; the Lab does not set it.
Entry 7: 33 of 100 fruit exceed the T² limit; 4 exceed the Q limit
T² says a sample sits far from the calibration centre; Q says the model cannot rebuild its spectrum. A new season shifts spectra, so flags are information about the season.
T² and Q for each unseen-season fruit against the limits set on the calibration fruit.
A third of the fruit are flagged on T². That tells us the season differs, not that the scans are bad.
Inspect the flagged samples before dropping any. We are still refining how the Lab explains this.
Each point is one unseen-season fruit
Dashed lines are the limits; red points are beyond at least one.
Source: Spectra Lab engine run, 9 Oct 2026, mango teaching subset (CC BY 4.0).
Entry 8: what this report does not cover, and where the data came from
One dataset, one split, one model family.
Six limits
- One dataset, one split. Mango fruit, seasons 1 to 3 against season 4. Grain, dairy or feed would behave differently.
- One model family. Partial least squares, 5-fold cross-validation, 1 to 15 components.
- Not an accredited method. The report supports decisions; validate against your own requirements and standards before relying on a calibration.
- Teaching subset. 600 + 100 spectra from the larger archive of 11,691.
- Reproducible. The same files through the same engine give the same numbers; we re-ran it to check.
- RPD here is the spread of the unseen-season reference values divided by the error after removing bias; the Lab's model overview computes RPD from cross-validation instead.
Attribution
Anderson, Walsh, Subedi and Hayes (2020), Postharvest Biology and Technology 168; dataset licensed CC BY 4.0 (Mendeley Data, doi 10.17632/46htwnp833). Teaching subset: 600 calibration and 100 unseen-season spectra, 684 to 990 nm, 103 points.
Engine: the Spectra Lab modelling engine (scikit-learn PLS). The published 1.01 comparison is the figure from the dataset paper for PLS on the full data.