Regression Analysis
Statistical method for modeling and quantifying relationships between a target variable and explanatory variables for description, prediction and causal estimation.
Classification
- ComplexityMedium
- Impact areaTechnical
- Decision typeDesign
- Organizational maturityIntermediate
Technical context
Principles & goals
Use cases & scenarios
Compromises
- False causal claims due to uncontrolled confounders
- Overfitting with too many features without regularization
- Misinterpretation of coefficients with multicollinear predictors
- Exploratory data analysis to identify relationships and outliers
- Cross-validation and hold-out sets for objective evaluation
- Use regularized models when many predictors are present
I/O & resources
- Structured datasets with target variable and predictors
- Documented domain variables and data provenance
- Arrangements for data cleaning and feature engineering
- Parameter estimates and model equation
- Predictions for new observations
- Validation reports and goodness-of-fit measures
Description
Regression analysis is a statistical technique for modeling and quantifying relationships between a dependent target variable and one or more independent predictors. It is used for description, prediction and causal estimation. Key aspects include model assumptions, goodness-of-fit metrics, regularization and careful validation to avoid bias.
✔Benefits
- Clearly quantifiable relationships and effect estimates
- Broad methodological basis and established diagnostics
- Easily interpretable model parameters for simple models
✖Limitations
- Sensitive to violations of model assumptions
- Linear models do not automatically capture complex nonlinear patterns
- Requires sufficient sample size and high-quality data
Trade-offs
Metrics
- R-squared
Proportion of explained variance; indicator of model fit.
- MSE / RMSE
Mean squared error and its root to evaluate prediction accuracy.
- MAE
Mean absolute error as a robust metric against outliers.
Examples & implementations
House price prediction
Linear and regularized regression models to estimate property prices based on location, size and features.
Fuel consumption in vehicle development
Regression models to quantify the influence of weight, aerodynamics and engine parameters on consumption.
Econometric analysis of policy interventions
Regression-based estimation of policy effects controlling for relevant covariates.
Implementation steps
Define the problem and determine the target variable
Collect, clean data and create relevant features
Select appropriate regression methods and regularization
Fit model, run diagnostics and validate
Interpret results and prepare them for stakeholders
⚠️ Technical debt & bottlenecks
Technical debt
- Insufficiently documented feature pipelines
- Outdated training data without regular refresh
- Missing automation for validation and monitoring processes
Known bottlenecks
Misuse examples
- Drawing causal conclusions from purely observational correlations
- Applying a model despite violated assumptions (e.g. homoskedasticity)
- Overinterpreting complex models on small samples
Typical traps
- Multicollinearity leads to unstable coefficients
- Confusing predictive performance with causal identification
- Ignoring temporal dependencies in time series data
Required skills
Architectural drivers
Constraints
- • Assumptions (linearity, homoskedasticity, independence) must be checked
- • Regulatory requirements for personal data must be considered
- • Limited compute resources may preclude complex models