Regression analysis

Regression analysis involves statistical methods for modeling relationships between dependent and independent variables. It is useful for predictive analysis and causal inference. Key aspects:

Used to estimate continuous numeric outcomes rather than discrete categories.
Involves fitting a function minimizing residuals between predictions and actual data.
Regression coefficients indicate how predictors influence the target variable.
Allows inferring effects, forecasting trends, and performing what-if analysis.

Types of regression include:

Linear regression for modeling linear effects of variables.
Logistic regression for binary outcomes like pass/fail.
Polynomial regression fits nonlinear relationships.
Regularization avoids overfitting like in ridge/lasso regression.

Regressions can include multiple explanatory variables. Assumptions like linearity, normality, homoscedasticity must be validated.

Regression is fundamental to statistical data analysis across sciences, business, and policy research. It is used heavily in predictive analytics and machine learning pipelines.