← Back to Modules Directory

Module 10 - GLM vs OLS

This study reference evaluates the core differences and underlying structural frameworks of Ordinary Least Squares (OLS) linear regression versus Generalized Linear Models (GLMs) for estimation and data exploration.

1. Modeling Fundamentals

Data science tasks switch between these regression architectures depending on target features and residual error assumptions:

Ordinary Least Squares (OLS)

A classic parametric statistical method used to estimate parameters in standard linear regression models. The optimization engine solves for weight coefficients by fitting a straight line that minimizes the vertical sum of the squared differences (residuals) between the true observed targets and the model's projections.

Generalized Linear Models (GLMs)

A highly flexible generalization of classical ordinary linear regression that extends estimation capabilities to target variables containing error distribution profiles other than a symmetric normal shape. It uses mathematical link functions to safely connect a linear input space directly to exponential distribution families (such as Binomial, Poisson, or Gamma shapes).

2. Key Fit & Evaluation Statistics

Evaluating parametric boundaries utilizes standard probability and predictive error information criteria:

R-squared: The coefficient of determination. It indicates the proportion of total variance within the continuous dependent target variable explained by the variance of the independent predictor features.
Log-likelihood: The exact mathematical probability of observing your true historical dataset given a specific, fitted set of internal model parameters. Higher metrics confirm an optimized fit.
AIC (Akaike Information Criterion): An informational metric used to approximate out-of-sample prediction errors across statistical models. It balances log-likelihood values against parameter complexity to assist in model selection, where a lower relative score marks the preferred model configuration.
BIC (Bayesian Information Criterion): Similar to AIC for model comparison tasks, but enforces a much stricter mathematical penalty for adding extraneous predictor features to prevent overfitting.

3. Python Programmatic Ecosystem

Building and evaluating these statistical estimators requires specialized open-source modules:

statsmodels: A dedicated Python statistics package providing explicit optimization classes, functions, summary reports, and residual diagnostics tests for OLS, GLMs, and experimental data analysis.
scikit-learn: A production-focused machine learning library containing uniform APIs for data preprocessing, train-test splitting, cross-validation, and predictive model fitting.
matplotlib.pyplot: A core, low-level visualization and plotting architecture used to construct data figures, residual histogram curves, and visual regression line evaluations.