Quick Overview

Inputs

  • Dataset: tabular data frame
  • Target: numeric column name
  • Features: list of predictor column names
  • Optional: user context, processing ID

What

  • Fit an OLS regression using the provided target and features
  • Return coefficients with standard errors and 95% confidence intervals
  • Compute performance metrics and ANOVA
  • Provide residual, Q‑Q, histogram, Cook’s D, and VIF data

Why

  • Establish an interpretable baseline for drivers and forecasts
  • Quantify effect sizes and uncertainty
  • Validate assumptions via visual diagnostics

Outputs

  • Metrics: R², Adj R², RMSE, MAE, AIC, BIC, F‑stat, p‑value
  • Tables: coefficients (with CI), ANOVA, VIF (when available)
  • Diagnostic datasets: residuals, Q‑Q points, histogram bins, influential points
  • Predictions: fitted values with 95% prediction intervals

Use OLS to quantify relationships and build an interpretable baseline. Validate assumptions and diagnostics before drawing conclusions or operationalizing results.

What You Get

  • Clear coefficients with confidence intervals and effect direction
  • Performance metrics: RMSE, MAE, R², Adjusted R²
  • Diagnostics: residual analysis via plots (residuals, Q‑Q, histogram), influence and leverage
  • Collinearity assessment via VIF (when available)
  • Predictions with intervals for practical planning

When To Use

  • Target is numeric and approximately continuous
  • Goal is explanation/attribution as much as prediction
  • Relationships are roughly linear or can be linearized with simple transforms
  • Features are not extremely collinear or high‑dimensional vs sample size

When Not To Use

  • Classification problems (use logistic regression or other classifiers)
  • Strong nonlinear interactions that can’t be handled by simple feature engineering (consider tree‑based models)
  • Severe multicollinearity or p ≫ n (prefer regularization like Ridge/Lasso/Elastic Net)

Data Requirements

  • Tabular data with a numeric target and candidate features (numeric or encoded categorical)
  • Sufficient sample size: a practical rule is 10–20 observations per predictor
  • Minimal missingness in key variables or a clear imputation strategy
  • Reasonable handling of outliers to avoid dominance by a few extreme points

Interpreting Coefficients

  • Each coefficient estimates the expected change in the target for a one‑unit change in the feature, holding other features constant
  • Use confidence intervals to judge estimation uncertainty, not just point values
  • Consider practical significance (magnitude and units), not only statistical significance
  • Standardized effects are helpful for comparing relative importance across features with different scales

Core Assumptions

  • Linearity: additive, approximately linear relationships between predictors and target
  • Independence: observations are not systematically dependent over time or grouping
  • Homoscedasticity: residual variability is roughly constant across fitted values
  • Normality (for inference): residuals are approximately normal so intervals/p‑values are reliable

Diagnostics Checklist

  • Residual vs. Fitted: look for randomness; patterns suggest misspecification or nonlinearity
  • Q‑Q Plot: heavy tails or curvature indicate deviations from normality
  • Scale‑Location: funnel shapes suggest heteroscedasticity (non‑constant variance)
  • Influence: large Cook’s D or leverage points can distort estimates; investigate and justify
  • Collinearity: high VIFs or strong pairwise correlations reduce stability and interpretability

Performance Metrics

  • R² / Adjusted R²: variance explained; use adjusted R² when comparing models with different feature counts
  • RMSE / MAE: average error in the target’s units; prefer MAE when robustness is important
  • Prediction Intervals: communicate uncertainty for individual predictions, not just means

Common Pitfalls

  • Data leakage: including post‑outcome or target‑derived features inflates performance
  • Multicollinearity: unstable coefficients and counterintuitive signs when predictors overlap
  • Outliers: a few points can dominate the fit; validate, cap, or robustify
  • Nonlinearity: forcing linear fits where relationships are curved; consider transforms or nonlinear models

Making It Actionable

  • Prioritize drivers by standardized effect sizes and practical impact
  • Translate coefficients into business terms (per $1k spend, per 1% change, etc.)
  • Communicate limitations and diagnostic findings alongside the headline result
  • Use prediction intervals for planning ranges, not point targets

Related Tools

  • Ridge/Lasso/Elastic Net: handle collinearity, improve generalization, enable feature selection
  • Tree‑based methods (Random Forest, XGBoost): capture nonlinearities and interactions
  • Logistic Regression: use when the target is categorical (classification)

Try It

  • Example questions: “What drives monthly revenue?” “How does price affect demand after controlling for promotions?”
  • Upload a dataset with a clear numeric target and candidate features
  • Compare OLS with a regularized model if VIFs are high or signs are unstable
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