Multivariate Input-Output Estimator
Use historical data with multiple inputs and multiple outputs to estimate what outputs may be expected for a new operating scenario.
Browser-based calculationLinear, ridge, and polynomial modelsScenario support check
Why use this tool?
Decision Supported
Use this tool when you have historical operating data and need to estimate likely outputs for a new input plan.
What It Tells You
It fits one model per output, compares linear, ridge, and polynomial relationships, and estimates expected outputs for entered input values.
Example Input
Warehouse labour hours, overtime hours, and floor area can be used to estimate orders shipped and lines picked.
Sample Output Interpretation
If the scenario is outside the historical operating region, estimates are flagged as extrapolation and should be treated cautiously.
- 1Set Up DataClassify inputs and outputs
- 2Select ModelFit linear, ridge, or polynomial models
- 3Plan ScenarioEnter new input values
- 4InterpretReview estimates and support
1. Add Data
Enter historical observations manually, import a CSV, or load sample warehouse data to see the workflow.
Sample data is an editable example only. For a real decision, replace it with your own comparable observations and confirm each input and output definition.
CSV data, model fitting, and scenario estimates remain in your browser. Nothing is uploaded to a server.
Prepare your input-output file
Upload a CSV with one row per historical observation. The first column should identify the observation, and numeric columns should represent operating inputs or outputs.
ObservationMonth, branch, shift, route, production line, supplier, or another comparable record.
InputsResources or conditions used to estimate outputs, such as labour, cost, hours, distance, or machine time.
OutputsExpected outcomes, such as orders, lines picked, units produced, on-time deliveries, or completed tickets.
Example row: Apr | 1610 | 170 | 31800 | 74500
Important: This estimator models observed relationships. It does not measure DEA efficiency and does not guarantee future performance.
Column guidance:
- Use inputs for controllable resources or operating conditions, such as labour hours, overtime, cost, distance, machine hours, or available capacity.
- Use outputs for outcomes you want to estimate, such as orders shipped, lines picked, units produced, on-time deliveries, or resolved tickets.
- Avoid duplicate or derived variables that represent the same thing twice, such as total labour cost and labour hours, unless there is a clear reason.
Load sample data, add rows manually, or import a CSV.
Column classification
Name each numeric column and classify it as an input, output, or ignored field. Enter integer or decimal values in the observations table below.
Historical observations
Use at least five complete observations. Decimal values are accepted. More observations are recommended for polynomial models.
Data Quality Check
Review missing values, numeric fields, constant columns, and sample size before fitting.
2. Model Selection
Choose the relationship form. For multiple outputs, the tool fits a separate model for each output using the same inputs.
Model Selection Guidance
Use Linear Regression when the relationship is broadly proportional and easy to explain. Use Ridge or Lasso when a stable linear estimate is useful. Use Robust Regression when a few unusual observations may distort the fit. Use k-Nearest Neighbour for local pattern matching. Use Polynomial Regression only when curvature or interactions are plausible and the dataset has enough observations. Auto Select compares out-of-sample error and keeps the simpler model unless a more complex model performs materially better.
Prepare data to see model guidance.
Linear: Yk = beta0 + beta1X1 + ... + betapXp. It fits the straight-line relationship that minimises squared prediction error.
Ridge: uses the same linear equation, but estimates the coefficients by minimising squared prediction error plus a penalty for large coefficients.
Lasso: uses the same linear equation, but adds an absolute-value penalty that can shrink weak coefficients to zero.
Robust: uses a linear equation with reduced weight for observations that have unusually large residuals.
kNN: estimates outputs from the most similar historical observations in the standardised input space.
Polynomial: adds squared terms and pairwise interaction terms so the fitted relationship can bend or reflect combined input effects.
About this estimator
Method
The tool fits estimation models using selected input columns to estimate each selected output column.
Multiple Outputs
Each output receives its own model, so one output may be predicted more reliably than another.
Historical Support
The scenario is assessed against the multivariate input space, using convex-hull membership where practical and nearest-neighbour support otherwise.
Decision Use
Use the result as a planning estimate and compare it with operational constraints, not as a guaranteed forecast.
Guidance
Use When
You want an expected output baseline from historical input-output relationships, such as output levels for a proposed labour or resource plan.
Do Not Use When
You need a causal proof, an efficiency frontier, or a forecast where future conditions are structurally different from history.
Check First
Make sure observations are comparable, columns are measured consistently, and outputs are not simply restatements of inputs.
Scenario Warning
Extrapolated scenarios are less reliable because they extend beyond operating conditions represented in the historical dataset.
Methodology, Assumptions, and Limitations
Linear Model
Yk = beta0 + beta1X1 + ... + betapXp. Inputs are standardised internally before fitting to improve numerical stability.
Ridge Model
Ridge keeps the linear equation but adds a coefficient penalty, which can make estimates more stable when inputs move together.
Lasso Model
Lasso keeps a linear equation but penalises the absolute size of coefficients, which can reduce weak input effects.
Robust Model
Robust regression reduces the influence of observations with unusually large residuals, while keeping an interpretable linear form.
kNN Model
k-Nearest Neighbour estimates outputs from the closest historical input patterns. It is local and intuitive, but less formula-driven.
Polynomial Model
Degree 2 adds squared terms and pairwise interactions. This can capture curvature but may overfit small datasets.
Auto Select
Linear, ridge, lasso, robust, polynomial, and kNN models are compared using cross-validated RMSE. Lower out-of-sample error is preferred, with a preference for simpler models when performance is similar.
Limitations
Regression describes observed association. It does not prove causality, determine efficiency, or guarantee future performance.
FAQ
How is this different from DEA?
DEA benchmarks relative efficiency against an observed frontier. This estimator predicts expected outputs from historical input-output relationships.
Why fit one model per output?
Multiple outputs often behave differently. Separate models let diagnostics show which outputs are estimated more reliably.
What does extrapolation mean?
The scenario sits outside the historical multivariate input region, so the model is estimating beyond observed operating conditions.
When should I use ridge regression?
Use Ridge when input measures are correlated, such as labour hours and overtime hours. It keeps a linear equation but reduces unstable coefficient swings.
When should I use lasso regression?
Use Lasso when you want a linear model that can shrink weak input effects toward zero. Treat it as a screening aid, not proof that an input has no operational relevance.
When should I use robust regression?
Use Robust Regression when a few unusual historical observations may distort a standard linear fit. It still assumes a broadly linear relationship.
When should I use k-Nearest Neighbour?
Use kNN when local similarity is more useful than a global equation. It estimates from nearby historical observations, so it needs enough comparable history.
Should I choose polynomial regression?
Use it only when cross-validation improves materially and there are enough observations for the number of polynomial terms.