python-regression-statistics

Regression models with p-values and confidence intervals are built using statsmodels for OLS, GLM, and time-series approaches. Fit a model, extract coefficients with confidence intervals, and validate assumptions using diagnostic tests and residual plots.

Regression diagnostics use residual analysis, VIF for multicollinearity, Cook's distance for influential points, and Q-Q plots for normality. These checks identify assumption violations before interpreting coefficients or making predictions.

Outlier detection uses PyOD's isolation forest, LOF, COPOD, and ECOD detectors or ensemble methods to flag anomalies. Remove or downweight outliers, then refit the regression model to improve fit and inference quality.

Cross-validation validates model generalization using scikit-learn's CV tools; statsmodels provides prediction intervals that quantify uncertainty around forecasts. Combine both for robust end-to-end validation pipelines.

Statistical regression (OLS, GLM via statsmodels) prioritizes inference, p-values, and interpretability; ML regression (Ridge, Lasso, ElasticNet via scikit-learn) prioritizes prediction accuracy. Choose based on whether you need hypothesis tests or predictive performance.

Yes, statsmodels provides WLS for heteroscedastic data and robust regression methods to reduce outlier influence. Both fit alternative models when standard OLS assumptions are violated.