How do you diagnose a marketing regression before interpreting it?
Diagnosis examines functional form, residuals, heteroskedasticity, collinearity, influence, temporal dependence and out-of-sample stability before reading coefficients.
Scientific editorial team : Marketing Science Center
Direct answer
Determine which interpretations remain compatible with diagnostics.
Diagnosis examines functional form, residuals, heteroskedasticity, collinearity, influence, temporal dependence and out-of-sample stability before reading coefficients.
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Operational summary
Scientific question and scope
How do you diagnose a marketing regression before interpreting it?
Supported
Determine which interpretations remain compatible with diagnostics.
Forbidden
Validate a model from R-squared alone.
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Three reading levels
- 01
Decision-maker — Connect the result to a declared decision, useful threshold and error cost.
- 02
Practitioner — Fix population, unit, horizon, available variables and analysis rule before calculation.
- 03
Analyst — Reproduce the calculation, quantify uncertainty and document diagnostics, failures and sensitivities.
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Concrete marketing situation
Diagnosis examines functional form, residuals, heteroskedasticity, collinearity, influence, temporal dependence and out-of-sample stability before reading coefficients.
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Scientific question and scope
How do you diagnose a marketing regression before interpreting it?
Diagnostic evidence
Required data
observation × residual
Population, unit of analysis, origin date and horizon must be declared in the deliverable. Without them, the estimand silently changes.
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Why a simple analysis can fail
- Validate a model from R-squared alone.
- Residual plots
- Robust variance
- Influence and holdout
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Method intuition
The method does not automatically turn an association into evidence. It links a declared question to an estimand, specification, compatible data and a bounded interpretation rule.
Diagnostic evidence
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Required data
Scientific symbol dictionary
r_i- Standardized residual for observation or cluster i under the declared fitted model. Unit:
standard deviation· Type:number· Role:diagnostic h_i- Leverage of observation or cluster i under the declared design matrix. Unit:
dimensionless· Type:number in [0, 1]· Role:diagnostic D_i- Cook's distance for observation or cluster i under the declared model. Unit:
dimensionless· Type:nonnegative number· Role:diagnostic RMSE_holdout- Root mean squared prediction error on observations excluded from fitting. Unit:
outcome· Type:nonnegative number· Role:diagnostic
Exact sealed engine inputs
residual_mean- Value:
0.02· Unit:outcome· Type:number· Data status:synthetic residual_sd- Value:
1.20· Unit:outcome· Type:number· Data status:synthetic maximum_absolute_standardized_residual- Value:
2.40· Unit:dimensionless· Type:number· Data status:synthetic maximum_leverage- Value:
0.08· Unit:dimensionless· Type:number· Data status:synthetic maximum_cooks_distance- Value:
0.06· Unit:dimensionless· Type:number· Data status:synthetic sample_size- Value:
100· Unit:observation· Type:integer· Data status:synthetic parameter_count- Value:
5· Unit:parameter· Type:integer· Data status:parameter cluster_count- Value:
30· Unit:cluster· Type:integer· Data status:synthetic holdout_rmse- Value:
1.35· Unit:outcome· Type:number· Data status:synthetic
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Formal model
Formal model
Report residual_mean, residual_sd, maximum_absolute_standardized_residual, maximum_leverage, maximum_cooks_distance, cluster_count and holdout_rmse; infer influence only after case-deletion or cluster-deletion refit sensitivityEvidence claims: MSC-P019-C01 · MSC-P019-C02 · MSC-P019-C03 · MSC-P019-C04 · MSC-P019-C05
Scientific question and scope
Diagnostic evidence
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Declared calculation
- 01
Lock the model, residual definition, cluster structure and holdout split before inspecting extrema.
- 02
Report descriptive residual mean/SD, maximum absolute standardized residual, leverage, Cook's distance and holdout RMSE without universal cutoffs.
- 03
Require case-deletion or cluster-deletion refitting and sensitivity of the decision quantity before calling a point influential.
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Numerical example or application case
Synthetic illustration — teaching values, not observed — synthetic data or declared parameters; no real observations
Sealed inputs
residual_mean=0.02 [outcome]residual_sd=1.20 [outcome]maximum_absolute_standardized_residual=2.40 [dimensionless]maximum_leverage=0.08 [dimensionless]maximum_cooks_distance=0.06 [dimensionless]sample_size=100 [observation]parameter_count=5 [parameter]cluster_count=30 [cluster]holdout_rmse=1.35 [outcome]
Reproducible results
descriptive_max_standardized_residual=2.4descriptive_max_leverage=0.08descriptive_max_Cook_D=0.06holdout_RMSE=1.35
Verified dossier: claims are linked to passage-level sources, the Python/R calculation is reproduced, limits are explicit, and independent scientific review is complete.
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Validity assumptions
- Are residuals, leverage and Cook's distance defined for the exact fitted model and dependence structure?
- Was the holdout excluded from all model and specification selection?
- Does deletion/refit sensitivity materially change the decision-relevant quantity?
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Diagnostics and uncertainty
Diagnostics and uncertainty
Residual plots · Robust variance · Influence and holdout
Bounded diagnostic
Descriptive inspection only: there is no universal cutoff here, and influence requires case-deletion/refit sensitivity before any conclusion.
Explicit uncertainty contract · not_estimable_from_sealed_inputs
Method : Explicit non-estimability assessment against the sealed input schema.
Target : Uncertainty and decision sensitivity of regression diagnostics.
Engine evidence : diagnostic=descriptive_inspection_only_no_universal_cutoff_influence_conclusion_requires_case_deletion_refit_sensitivity
Interpretation : Sealed extrema and one holdout RMSE do not provide refit distributions; case- or cluster-deletion refits are required.
Stop when
Validate a model from R-squared alone.
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Result interpretation
- Determine which interpretations remain compatible with diagnostics.
- The result is conditional on the declared population, horizon, specification and diagnostics. It must not be extended to another decision without new justification.
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Supported and forbidden conclusions
Supported
Determine which interpretations remain compatible with diagnostics.
Forbidden
Validate a model from R-squared alone.
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Possible marketing decision
- 01
Determine which interpretations remain compatible with diagnostics.
- 02
The result is conditional on the declared population, horizon, specification and diagnostics. It must not be extended to another decision without new justification.
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When to use — when to stop
Use when
Determine which interpretations remain compatible with diagnostics.
observation × residual
Stop when
Validate a model from R-squared alone.
Methodological alternatives
- Use robust regression and compare decision quantities under alternative specifications.
- Use cluster-deletion or leave-one-group-out refitting when dependence is grouped.
- Use graphical residual checks and domain-specific falsification tests instead of universal numeric cutoffs.
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Reproducibility contract
Python and R are the executable references. SPSS and SAS remain secondary syntaxes until checked on the same data, specification and diagnostics.
The engine selects only this page’s explicit slice and branch. Its hash, outputs, and diagnostics remain sealed in the atomic dossier; no generic fallback branch is allowed.
Slice fingerprint: fe38d763c26218df98d157e806962f0ec5f9b9a4baeca89b39123cc1db00b769
CSV · CC0
msc-validation-inputs-v1.csv ↓Python · MIT
msc-validation-reference-v1.py ↓R · MIT
msc-validation-reference-v1.R ↓SPSS / SAS · MIT · inspection only
SPSS ↓SAS ↓Formal model
Report residual_mean, residual_sd, maximum_absolute_standardized_residual, maximum_leverage, maximum_cooks_distance, cluster_count and holdout_rmse; infer influence only after case-deletion or cluster-deletion refit sensitivityVerified dossier: claims are linked to passage-level sources, the Python/R calculation is reproduced, limits are explicit, and independent scientific review is complete.
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Expected final deliverable
- 01
How do you diagnose a marketing regression before interpreting it? —
observation × residual - 02
r_i · h_i · D_i · RMSE_holdout
- 03
Report residual_mean, residual_sd, maximum_absolute_standardized_residual, maximum_leverage, maximum_cooks_distance, cluster_count and holdout_rmse; infer influence only after case-deletion or cluster-deletion refit sensitivity - 04
Residual plots · Robust variance · Influence and holdout
- 05
Determine which interpretations remain compatible with diagnostics. / Validate a model from R-squared alone.
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Scientific sources and evidence status
Verified dossier: claims are linked to passage-level sources, the Python/R calculation is reproduced, limits are explicit, and independent scientific review is complete.
MSC-P019-C01— Predictive accuracy should be evaluated on observations excluded from model fitting.MSC-P019-C02— Fitting a regression does not itself establish a causal design.MSC-P019-C03— Influence diagnostics target observations or clusters under the declared model.MSC-P019-C04— Deletion diagnostics depend on the observational unit being removed.MSC-P019-C05— Cook's distance is an influence diagnostic, not a model-validity verdict.
Method connections