Technical Visualizations
A technical visualization is a statistical chart produced during the analysis to test a modelling assumption. Its audience is the team building the model. The IIBA guide names eight families, each tied to one assumption. A business analyst rarely builds them; they read them. The output is a verdict on a modelling decision, reached before the model goes into service and its results start circulating as facts.
Goal
A technical visualization is a statistical chart the analysis team produces for itself, during the analysis, to test a modelling assumption. A chart built for a stakeholder who has to decide is a business visualization. The distinction is one of audience and moment: the same scatter plot is a diagnostic while the model is being built, then gets redrawn as a reporting exhibit for the committee.
A predictive model rests on assumptions its performance figure does not show: independent predictors, an error of constant spread, a distribution with no extreme skew, a number of clusters that has some basis in the data. An accuracy of 94% or an R² of 0.87 summarises average performance and leaves those assumptions out of frame. The technical visualization is where they become checkable again, because a defect in the fit has a shape before it has a number.
The deliverable is the verdict reached on a modelling decision: the constant-variance assumption holds, the redundant pair of variables comes down to one, the classification threshold is set at 0.31 rather than at maximum accuracy. The business analyst sits in when these charts are presented, and their contribution is to know what each one tests and so to recognise when the chart does not support the conclusion stated beside it. That is their share of the evaluation phase of a data mining project: saying whether the model answers the question asked and at what cost of error.
Usage
When to use it
- A variable list to settle: the correlation matrix shows the predictors that measure the same thing twice.
- A model announced as "fitting well": the residual plot says where the error concentrates.
- A threshold to set on a classification model: the ROC curve puts a number on the trade-off between the two kinds of error.
- A segmentation to restate in business language: the silhouette plot and the PCA projection say how many clusters exist.
- A movement attributed to a sales campaign: the autocorrelation plot says whether the series already carries a seasonal pattern at that period.
When not to use it
- Reporting to a committee: the diagnostic is redrawn as a business visualization before it goes on screen.
- Field definitions not settled: the diagnostic would run on variables whose sense still shifts; establish the data dictionary first.
Description
What each family tests
The IIBA guide lists eight families, drawn from four disciplines: time-series statistics, regression diagnostics, unsupervised learning and signal detection theory.
| Family | What it tests | The question the analyst asks |
|---|---|---|
| Autocorrelation plot | whether a time series carries a structure, seasonality or trend, or takes its values at random | is the October rise down to the campaign or to the season? |
| Box-Cox plot | the power that brings a skewed distribution closer to the normal | does the model output still read in business units after the transformation? |
| Contour plot | a third continuous dimension brought onto a map as contour lines | past what point does the setting stop gaining performance? |
| Correlation matrix | the pairwise linear association between the candidate variables | are two predictors saying the same thing? |
| PCA projection | the axes that account for the most variance when the variables are many | what would this axis be called in business terms? |
| Residual plot | the shape of the error of a regression model | does the stated error hold for every case? |
| ROC curve | the trade-off between true positive rate and false positive rate as the threshold moves | what does each of the two errors cost? |
| Silhouette plot | how sharp the clusters from a partitioning are and how many there are | do the ten segments announced exist in the data? |
Testing a time series before modelling it
A time series is first tested on its autocorrelation plot, which plots the correlation of the series with itself shifted by one lag, two lags, then n. The NIST handbook gives the reading rule: values staying inside the confidence band signal a random series, a slow decay signals non-stationarity, a spike repeating at a fixed interval signals seasonality. This is the first step in identifying a model by the Box-Jenkins method.
Reading a correlation matrix before settling the variable list
The correlation matrix carries, for each pair of variables, a coefficient between -1 and 1 measuring their linear association. Many models assume independent inputs; two strongly associated predictors count the same effect twice and make the weights the model gives them unstable. This is collinearity. A retailer in French-speaking Switzerland preparing a model to forecast weekly turnover per outlet builds the matrix over its 34 stores.
| Pearson coefficient | Floor area | Headcount | Checkout transactions | SKUs on shelf |
|---|---|---|---|---|
| Headcount (FTE) | 0.94 | |||
| Checkout transactions | 0.71 | 0.68 | ||
| SKUs on shelf | 0.62 | 0.55 | 0.41 | |
| Parking spaces | 0.38 | 0.31 | 0.44 | 0.12 |
The p-value that comes with the coefficient gives the probability of observing an association at least that strong when there is none: a 0.41 over 34 stores and the same 0.41 over 3'400 transactions do not carry the same weight of evidence.
What does a residual plot say?
A residual is the gap between the observed value and the predicted one. The plot puts those gaps on the vertical axis, the predicted value on the horizontal one. The NIST handbook fixes the reading: a cloud centred on zero, with no structure and a constant spread, indicates an acceptable fit. The fan, whose spread opens with the predicted value, signals heteroscedasticity, an error variance that changes across the range of values; the stated average error then does not hold from one end of the range to the other. The curve, in a U or an inverted U, signals a non-linear relationship the model has not captured.
When the fan comes from a strongly skewed distribution of the response variable, the Box-Cox transformation looks for the power that brings it closer to the normal. A model fitted on the logarithm of turnover produces results that have to be brought back into francs before any business discussion.
The threshold of a classifier is a business trade-off
A classification model returns a probability, and a threshold turns it into a decision. The ROC curve plots the true positive rate against the false positive rate for every value of that threshold; the area under the curve, the AUC, summarises the model's power to discriminate and allows two models to be compared. On the same retailer's online shop, a model detecting fraudulent orders reaches an AUC of 0.95. At a threshold of 0.20 it intercepts 82% of the fraud and blocks 6% of legitimate orders; at 0.45 it intercepts 61% and blocks no more than 1.2%. As Fawcett establishes, no point on the curve is better in itself: the choice depends on the respective cost of the two errors. A fraudulent order let through costs CHF 380 on average; a refused honest order, CHF 12 in lost margin and dispute handling. That cost ratio comes from the business, and stating it is the business analyst's work.
A segmentation is checked before it is named
A partitioning algorithm with a fixed number of clusters, k-means for instance, always returns the number it is asked for, including when that number does not exist in the data. The silhouette plot, due to Rousseeuw, carries for each observation a score between -1 and 1 measuring its closeness to its own cluster against the neighbouring one, then stacks those scores by cluster. Wide and long silhouettes mark a sharp partition. The IIBA guide gives the typical reading on a customer segmentation: ten clusters requested, four to five dominant, one narrow cluster that would gain from being split, two clusters with negative scores whose members resemble the neighbouring cluster more than their own. The PCA projection completes the diagnostic by showing on which axes the clusters separate. The analyst then names those axes in business terms, large infrequent baskets against short regular visits, failing which the segmentation stays an algorithm output.
What makes the reading fail
The aggregate figure taken for a diagnostic. Two models with the same R² are wrong in different ways, and only the shape of the cloud shows it.
The correlation coefficient taken for a measure of dependence. Pearson measures linear association. Two variables linked in a U give a coefficient close to zero, which the matrix displays as an absence of association while the dependence is strong.
The variable dropped without asking the business. Between two predictors correlated at 0.94, the statistics are indifferent to the choice. The business is not: a store's headcount is decided, its floor area is fixed and dropping the first deprives the model of the only input a decision can act on.
The diagnostic taken for proof of validity. The IIBA guide states the limit: these charts are built on the data available and can steer the model toward an internal consistency foreign to the business context. An impeccable residual cloud on a dataset missing the decisive variable is still an impeccable residual cloud.
AI considerations
A coding assistant produces the eight charts in a few lines, from an already fitted model and an instruction in plain language. The cost of production becomes negligible, which moves the bottleneck to the reading: it is tempting to stack up diagnostics without questioning any of them. Given a screenshot of a residual plot, a multimodal model names the shape, fan or curve. That name is a first opinion, to be checked against the chart.
Two failure modes belong to these charts in particular. The first is the plausible interpretation of a principal component: shown a PCA projection, a language model will name its first axis "premium customers" with confidence, whereas the name of a component is checked against the variable weights and against domain knowledge. The second concerns the automatic tuning of a classification threshold, which learning pipelines optimise by default on accuracy or the F1 score. Those criteria assume the two errors cost the same, an assumption the business has not validated and that is false as soon as an undetected fraud costs thirty times a wrongful block.
Then there is confidentiality. A diagnostic chart carries the real distribution of the data; on a sparse cloud, one isolated point is sometimes enough to identify the individual behind it. Submitting the chart to a hosted tool requires the same approvals as an extract from the database. The question arises before the screenshot is taken.
Examples
The retailer in French-speaking Switzerland puts its weekly forecasting model into service, fitted on 34 stores and two years of history. The documentation states an average error of CHF 6'200, and the automatic replenishment rule has been set on that figure to size its safety margin. In the residual plot, the gap between actual and predicted turnover, in francs, is plotted against the predicted turnover.
The left-hand panel shows what this diagnostic would look like on a correctly specified model: a cloud centred on zero whose spread does not depend on the size of the store. The model in service gives the right-hand panel. The fan is read at a glance: the gaps stay within ±CHF 3'000 for stores forecast under CHF 100'000 and reach ±CHF 34'000 for the three largest. The average error of CHF 6'200 describes neither the small stores nor the large ones: it doubles the margin the small ones need and cuts to a fifth what the large ones need; those large stores run out of stock every week on the fast-moving items. The analyst reports that the error interval has to be published by size class and that the replenishment rule depends on it.
Visualizations
A residual plot is drawn as a scatter plot over a zero reference line in dashes, both axes graduated in business units. Two clouds are compared in twin panels sharing the same vertical scale, failing which the fan in the defective panel reads as an effect of the scale.
A correlation matrix is drawn as a half-table, the diagonal and the upper half left empty since they repeat the same information. The strength of the association is coded by the tint of the cell, and the coefficient stays written out: a heat map without values is read by eye, which is enough to spot a suspect pair and never enough to decide on a removal.
Cost
| Phase | Level | Rationale |
|---|---|---|
| Preparation | Low | The data and the fitted model are already there: these charts are by-products of the modelling. |
| Execution | Low | A few lines of code per chart. The cost sits in the competence to read them, which the IIBA guide cites as the technique's first limitation. |
| Documentation | Medium | The chart alone does not travel. The assumption tested, the verdict and the decision taken have to be written down, otherwise the diagnostic is lost the first time the model is picked up again. |
Tooling
The Python libraries (matplotlib, seaborn, statsmodels, scikit-learn) cover the eight families and are the de facto tool of data science teams. The charts are written beside the code that produced the model, which makes them reproducible.
R builds the diagnostic into the language: calling plot on a regression object returns the four expected residual charts, and ggplot2 takes over for the formatting.
The notebook (Jupyter, Quarto, R Markdown) is the medium that holds the chart, the code and the written verdict in one versioned document. It is the answer to the documentation cost.
The spreadsheet draws a scatter plot and a trend line, which makes a hand-built residual plot possible. It returns neither a silhouette plot, nor an ROC curve, nor a PCA projection. BI platforms (Power BI, Tableau) are built for business reporting and expose these diagnostics only through embedded R or Python code.
Sources
- IIBA, Guide to Business Data Analytics, §3.18 Technical Visualizations: the purpose of the technique, its distinction from business visualizations, the inventory of the eight families, the typical reading of the silhouette plot on a customer segmentation, together with the strengths and limitations stated there.
- NIST/SEMATECH, e-Handbook of Statistical Methods: the reading rule for the autocorrelation plot and its use in identifying a Box-Jenkins model (§1.3.3.1), the construction of the Box-Cox normality plot (§1.3.3.6) and the criterion of a residual cloud centred with a constant spread (Process Modeling chapter).
- George E. P. Box and David R. Cox, "An Analysis of Transformations", Journal of the Royal Statistical Society, Series B, vol. 26, 1964, pp. 211-252: the original paper on the power transformation.
- Tom Fawcett, "An Introduction to ROC Analysis", Pattern Recognition Letters, vol. 27, 2006, pp. 861-874: the practitioner reference on the ROC curve, the area under the curve and the trade-off between true and false positive rates as the threshold moves.
- Peter J. Rousseeuw, "Silhouettes: A Graphical Aid to the Interpretation and Validation of Cluster Analysis", Journal of Computational and Applied Mathematics, vol. 20, 1987, pp. 53-65: the paper defining the silhouette coefficient and the plot that carries it.