Multivariate and Factor Analysis
Multivariate General Linear Model Statistical Calculator
Multivariate General Linear Model Calculator the multivariate general linear model statistical calculator fits multiple continuous outcomes to multiple numeric or categorical predictors in one model. Use the tabbed test workspace below for data, variables, analysis, visualizations, results, interpretation and reporting.
Quick method summary
The multivariate general linear model statistical calculator evaluates multiple dependent outcomes and multiple independent variables in one model.
Multivariate and Factor Analysis
Multivariate General Linear Model Calculator
Fit two or more continuous dependent variables to one or more continuous, ordinal, binary, or categorical independent variables. The calculator retains every selected variable, reference-codes categorical predictors, and reports multivariate omnibus statistics and model coefficients.
Calculated result
When to use
Use this method when the study contains at least two continuous dependent outcomes and one or more explanatory variables. Continuous predictors produce multivariate multiple regression; categorical factors and covariates produce a multivariate GLM or MANCOVA-style model.
Formula or algorithm
B=(X′X)−1X′Y. The omnibus model partitions the outcome cross-product matrix into hypothesis H and error E and reports Wilks’ lambda, Pillai trace, Hotelling–Lawley trace, and Roy’s largest root.
Assumptions and limits
Use continuous outcomes, independent observations, adequate complete cases, a full-rank design matrix, and nonsingular residual covariance. Review multivariate normality, linearity, influential observations, and covariance structure before final reporting.
Variable handling
All dependent and independent variables selected in the analysis studio are retained. Categorical predictors are reference coded; the coefficient table identifies the encoded terms.
Formula review
Formula, matrix algebra, reference coding, input validation, fixture, and statsmodels comparison reviewed 2026-08-03.
Multivariate General Linear Model Calculator method, assumptions and reporting guideComplete selected-test explanation, assumptions, formula and reporting details
Data Import and Variable Requirements
Assign every dependent outcome and every independent predictor or factor explicitly. Categorical predictors are reference coded and all selected variables are used; none are silently dropped.
Uploaded files are processed locally in the browser. The cleaning report appears before variable selection, and the selected cleaned columns are mapped to this exact calculator rather than a generic fallback.
Multivariate General Linear Model Calculator Workspace Features
- Multiple dependent and multiple independent variable assignment
- Reference-coded categorical predictors
- Wilks lambda, Pillai trace, Hotelling-Lawley trace, and Roy root
- Same-page execution, plots, interpretation, and report
About the Multivariate General Linear Model Calculator
The multivariate general linear model statistical calculator fits multiple continuous outcomes to multiple numeric or categorical predictors in one model. This calculator applies the displayed method to the requested inputs and reports the intermediate values used in the result.
When to Use the Multivariate General Linear Model Calculator
Use when a study has multiple continuous outcomes and one or more explanatory variables. With categorical factors it provides a MANCOVA/factorial-MANOVA style omnibus model; with continuous predictors it provides multivariate multiple regression.
How the Multivariate General Linear Model Calculator Works
The multivariate general linear model estimates B=(X'X)^-1X'Y, partitions the outcome cross-product matrix into hypothesis H and error E, and tests the complete predictor set with Wilks' lambda, Pillai trace, Hotelling-Lawley trace, and Roy's largest root.
The calculation runs in the browser. Submitted values are validated for required numeric ranges, data shape, units and method-specific restrictions before results are shown.
Assumptions and Checks
- Independent observations.
- Continuous dependent variables.
- Adequate complete cases relative to the number of outcomes and encoded predictor parameters.
- Nonsingular design and residual cross-product matrices.
- Review multivariate normality, linearity, outliers, and covariance structure before final interpretation.
Required Inputs
- Rows by dependent outcome variables (required)
- Matching rows by encoded independent variables (required)
- Encoded predictor term names (optional)
- Alpha (required)
Results Reported
The result workspace shows the final answer and intermediate quantities needed to audit the calculation. Depending on the method, reported values include:
- Observations
observations - Dependent Variables
dependent_variables - Encoded Predictor Parameters
predictor_parameters - Model DF
model_degrees_of_freedom - Error DF
error_degrees_of_freedom - Wilks Lambda
wilks_lambda - Pillai Trace
pillai_trace - Hotelling-Lawley Trace
hotelling_lawley_trace - Roy Largest Root
roy_largest_root - Approximate F
f_approximation - DF 1
degrees_of_freedom_1 - DF 2
degrees_of_freedom_2 - P Value
p_value - Coefficient Matrix
coefficient_matrix - Predictor Terms
predictor_terms
Multivariate General Linear Model Calculator Worked Example
Upload a dataset, place at least two continuous outcomes in Dependent Variables, place one or more predictors or factors in Independent Variables, choose this method, and run the model.
| Input | Example value |
|---|---|
| Rows by dependent outcome variables | 8,12
10,14
11,15
13,18
15,20
16,22
18,25
20,27 |
| Matching rows by encoded independent variables | 0,18,1
0,20,0
0,22,1
1,19,0
1,21,1
1,23,0
2,24,1
2,26,0 |
| Encoded predictor term names | Treatment B, Age, Gender 1 |
| Alpha | 0.05 |
How to Use This Workspace
- Confirm that the method matches the quantity, hypothesis, model or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date or option format.
- Use Example Data to inspect a valid input layout, or enter your own values and run the calculation.
- Review the result table, formula, substitutions, warnings and interpretation rather than relying only on the headline number.
- Copy, download or print the result when you need a reusable analysis record.
Understanding and Reporting the Result
Interpret the omnibus multivariate p-value together with Wilks lambda, Pillai trace, model degrees of freedom, coefficients, and diagnostics. Follow a significant omnibus result with outcome-specific models when scientifically justified.
Review the formula, units, assumptions, and result interpretation before using the calculation.
Keep the entered values, units, selected options and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size and decision. For an estimate or conversion, report the formula convention and final unit.
How to Report the Result
Report the selected outcomes, original predictors and factors, reference coding, complete-case sample size, Wilks lambda, approximate F and degrees of freedom, p-value, Pillai trace, and relevant follow-up analyses.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the Multivariate General Linear Model Calculator calculate?
The multivariate general linear model statistical calculator fits multiple continuous outcomes to multiple numeric or categorical predictors in one model.
Which formula does the Multivariate General Linear Model Calculator use?
The multivariate general linear model estimates B=(X'X)^-1X'Y, partitions the outcome cross-product matrix into hypothesis H and error E, and tests the complete predictor set with Wilks' lambda, Pillai trace, Hotelling-Lawley trace, and Roy's largest root.
What does the multivariate general linear model statistical calculator analyze?
It analyzes two or more continuous dependent variables using one or more continuous or categorical predictors in the same model.
Does it support multiple variables on both sides?
Yes. Multiple dependent outcomes and multiple independent predictors or factors are retained, encoded, and tested together.
How are categorical independent variables handled?
Categorical predictors are converted to reference-coded indicator variables while continuous predictors remain numeric.
Which multivariate statistics are reported?
The calculator reports Wilks lambda, Pillai trace, Hotelling-Lawley trace, Roy largest root, an approximate F test, coefficients, and model dimensions.